Statistics 222, Education 351A Autumn 2015
Statistical Methods for Longitudinal Research
David Rogosa
Sequoia 224, rag{AT}stat{DOT}stanford{DOT}edu
Upcoming Office Hours (additional to after class): Tues Nov 17 3:15 - 4 PM
Course web page: http://rogosateaching.com/stat222//
To see full course materials from Autumn 2014 go here
Registrar's information
STATS 222 (Same as EDUC 351A): Statistical Methods for Longitudinal Research Units: 2-3
Lecture Th 3:00PM - 5:15PM Sequoia 200
Rogosa Office Hour: 5:15 - 5:50PM, Sequoia 200
Grading Basis: Letter or Credit/No Credit
Course Description:
STATS 222: Statistical Methods for Longitudinal Research (EDUC 351A)
Research designs and statistical procedures for time-ordered (repeated-measures) data.
The analysis of longitudinal panel data is central to empirical research on learning, development, aging, and the effects of interventions.
Topics include: measurement of change, growth curve models, analysis of durations including survival analysis,
experimental and non-experimental group comparisons, reciprocal effects, stability.
See http://rogosateaching.com/stat222/. Prerequisite: intermediate statistical methods
Terms: Aut | Units: 2-3 | Grading: Letter or Credit/No Credit
Instructors: Rogosa, D. (PI)
STATS 222: Statistical Methods for Longitudinal Research (EDUC 351A)
2015-2016 Autumn
STATS 222 | 2-3 units | Class # 15464 | Section 01 | Grading: Letter or Credit/No Credit | LEC
09/21/2015 - 12/04/2015 Thu 3:00 PM - 5:50 PM at Sequoia Hall 200 with Rogosa, D. (PI)
Axess Enrollment will open for students on August 1st.
Instructors: Rogosa, D. (PI)
Preliminary Course Outline
Week 1. Course Overview, Longitudinal Research; Individual Histories and Growth Trajectories
Week 2. Introduction to Data Analysis Methods for Individual Change and Collections of Growth Curves (mixed-effects models)
Week 3. Collections of growth curves: linear and non-linear mixed-effects models
Week 4. Special case of time-1, time-2 data; Traditional measurement of change
Week 5. Assessing Group Growth and Comparing Treatments: Traditional Repeated Measures Analysis of Variance and Linear Mixed-effects Models
Week 6. Comparing group growth: Power calculations, Cohort Designs, Cross-over Designs, Methods for missing data. Observational studies.
Week 7. Analysis of Durations: Introduction to Survival Analysis and Event History Analysis
Weeks 8-9. Further topics in analysis of durations: Recurrent Events, Frailty Models, Behavioral Observations, Series of Events (renewal processes)
Dead Week. Assorted Special Topics (enrichment): Assessments of Stability (including Tracking), Reciprocal Effects, (mis)Applications of Structural Equation Models, Longitudinal Network Analysis
Texts and Resources for Course Content (reserves in Math/Stat library)
1. Garrett M. Fitzmaurice Nan M. Laird James H. Ware Applied Longitudinal Analysis (Wiley Series in Probability and Statistics; 2nd ed 2011)
Text Website second edition website Text lecture slides
2. Peter Diggle , Patrick Heagerty, Kung-Yee Liang , Scott Zeger. Analysis of Longitudinal Data 2nd Ed, 2002
Amazon page Peter Diggle home page
Book data sets
A Short Course in Longitudinal Data Analysis Peter J Diggle, Nicola Reeve, Michelle Stanton (School of Health and Medicine, Lancaster University), June 2011
3. Judith D. Singer and John B. Willett . Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence New York: Oxford University Press, March, 2003.
Text web page Text data examples Powerpoint presentations good gentle intro to modelling collections of growth curves (and survival analysis) is Willett and Singer (1998)
4. Douglas M. Bates. lme4: Mixed-effects modeling with R February 17, 2010 Springer (chapters). An merged version of Bates book: lme4: Mixed-effects modeling with R January 11, 2010
Manual for R-package lme4 and mlmRev, Bates-Pinheiro book datasets.
Additional Doug Bates materials. Collection of all Doug Bates lme4 talks Mixed models in R using the lme4 package Part 2: Longitudinal data, modeling interactions Douglas Bates 8th International Amsterdam Conference on Multilevel Analysis 2011-03-16 another version
Fitting linear mixed-effects models using lme4, Journal of Statistical Software Douglas Bates Martin Machler Ben Bolker.
Technical topics: Mixed models in R using the lme4 package Part 4: Theory of linear mixed models
5. A handbook of statistical analyses using R (second edition). Brian Everitt, Torsten Hothorn CRC Press, Index of book chapters Stanford access Longitudinal chapters: Chap11 Chap12 Chap13. Data sets etc Package 'HSAUR2' August 2014, Title A Handbook of Statistical Analyses Using R (2nd Edition)
There is now a third edition of HSAUR, but full text not yet available in crcnetbase.com. CRAN HSAUR3 page with Vignettes (chapter pieces) and data in reference manual
6. Longitudinal and Panel Data: Analysis and Applications for the Social Sciences by Edward W. Frees (2004). Full book available and
book data and programs (mostly SAS).
7. Growth Curve Analysis and Visualization Using R. Daniel Mirman Chapman and Hall/CRC 2014 Print ISBN: 978-1-4665-8432-7 Stanford Access Mirman web page (including data links).
8. Longitudinal Data Analysis Edited by Geert Verbeke , Marie Davidian , Garrett Fitzmaurice , and Geert Molenberghs Chapman and Hall/CRC 2008. online supplement for LDA book .
9. Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer Series in Statistics. New-York: Springer. Extended presentation: Introduction to Longitudinal Data Analysis A shorter exposition: Methods for Analyzing Continuous, Discrete, and Incomplete Longitudinal Data
10. Survival analysis Rupert G. Miller. Available as Stanford Tech Report
11. Event History Analysis with R (Stanford access). Goran Brostrom CRC Press 2012. R-package eha
12. John D. Kalbfleisch , Ross L. Prentice The Statistical Analysis of Failure Time Data 2nd Ed
Amazon page online from Wiley
Additional Specialized Resources
Harvey Goldstein. The Design and Analysis of Longitudinal Studies: Their Role in the Measurment of Change (1979). Elsevier
Amazon page Goldstein Chap 6 Repeated measures data Multilevel Statistical Models by Harvey Goldstein with data sets
Cook, R. J. and Lawless, J. F. (2007). The Statistical Analysis of Recurrent Events. (Stanford access) Springer, New. York.
David Roxbee Cox, Peter A. W. Lewis The statistical analysis of series of events. Chapman and Hall, 1966
Google books Poisson process computing program
Joint Models for Longitudinal and Time-to-Event Data. With Applications in R. (Stanford access) Dimitris Rizopoulos. Chapman and Hall/CRC 2012. Book Table of Contents Book website
David J Bartholomew. Stochastic Models for Social Processes, Chichester 3rd edition: John Wiley and Sons.
David J Bartholomew web page
Grading, Exams, and Credit Units
Stat222/Ed351A is listed as Letter or Credit/No Credit grading (Stat MS students should check whether S/NC is a viable option for their degree program.)
Grading (for the 2-unit base) will be based on two components:
Each week I will post a few exercises for that week's content--towards the end of the qtr I'll identify a subset of those exercises to be turned in.
During the Autumn qtr exam period we will have an in-class (all materials available, "open" everything) exam.
My reading of the Registrar's chart indicates Tuesday, December 8, 2015 3:30-6:30 p.m.
see Class Calendar for details
The Registrar requires clear identification of the requirements for incremental units. The additional requirement for a 3-unit registration (the one unit above 2-units) is satisfied by a student presentation:
a mini-lecture, approximately 15 minutes with handout. These are done with Rogosa in Sequoia 224, which has worked out well. Good topics would include empirical longitudinal research, such as a data set or set of studies you are involved with,
or an extension of class lecture topics such as preparing an additional data analysis example or a report on some technical readings. Discussion with Rogosa is encouraged.
Note to auditors. The Registrar does have a form (no-fee) for faculty, staff, post-docs: Application for Auditor or Permit to Attend (PTA) Status
Statistical computing
Class presentation will be in, and students are encouraged to use, R (occasionally, some references to SAS and Mathematica).
1/7/09. NY Times endorses R: Data Analysts Captivated by R's Power
Current version of R is version 3.2.2 (Fire Safety) 2015-08-14.
For references and software: The R Project for Statistical Computing Closest download mirror is Berkeley
The CRAN Task View: Statistics for the Social Sciences provides an overview of some relevant R packages. Also the new CRAN Task View: Psychometric Models and Methods and CRAN Task View: Survival Analysis and CRAN Task View: Computational Econometrics.
A good R-primer on various applications (repeated measures and lots else). Notes on the use of R for psychology experiments and questionnaires
Jonathan Baron, Yuelin Li. Another version
A Stat209 text, Data analysis and graphics using R (2007) J. Maindonald and J. Braun, Cambridge 2nd edition 2007. 3rd edition 2010 has available a short version in CRAN .
According to Peter Diggle: "The best resource for R that I have found is Karl Broman's Introduction to R page."
Course Content: Files, Readings, Examples
9/24. First class: Course Overview, Individual Trajectories.
A. Initial meet-and-greet. Class logistics and longitudinal research overview
B. Examples, illustrations for longitudinal research overview, taken from course resources above:
Laird,Ware (#1) slides 1-16; Diggle (#2) slides 4-14, 22-28 Verbeke (#7) slides from Ch 2 and Sec3.3
C. Data Analysis Examples of Model Fitting for Individual Trajectories and Histories.
Motto: Individual trajectories are the proper starting point for longitudinal data analysis
ascii version of class handout annotated version pdf version with plots datasets
Starting up R-addendum: installing packages and obtaining data (sleepstudy in lme4)
Additional materials for the trajectory examples
For Count Data (glm) example. Link functions for generalized linear mixed models (GLMMs), Bates slides (pdf pages 11-18)
AIDS in Belgium example, (from Simon Wood) single trajectory, count data using glm. Rogosa R session for aids data
A very comprehensive introduction to analysis of count data Regression Models for Count Data in R
Achim Zeileis Christian Kleiber Simon Jackman (Stanford University)
Non-linear models, esp logistic. From week 1, also week 3 Self-Starting Logistic model SSlogis help page, do ?SSlogis post of annotated logistic curve with SSlogis arguments
Trend in Proportions: College fund raising example prop.trend.test help page ?prop.trend.test in R-session.
Trend in proportions, group growth, Cochran-Armitage test. Expository paper: G. Salanti and K. Ulm (2003): Tests for Trend in Binary Response
WEEK 1 Review Questions
1. For the straight-line (constant rate of change) fit example to subj 372 in the sleepstudy data. Obtain a confidence interval for the rate of change from the OLS fit. Now compare the OLS fit with day-to-day differences. Under the constant rate of change model these 9 day to day differences also estimate the rate of change. Obtain a estimate of the mean and a confidence interval for rate of change from these first differences. Compare with OLS results.
2. Revisit the Belgium Aids data example (counts of new cases by year). Use the parameter estimates for am2 (quadratic in time glm fit) to compute by hand (or calculator) the values of the glm fit at year = 5 and year = 9. Compare those values with results from the model am2 using predict
3. Paul Rosenbaum has a little data set on growth in vocabulary that I grabbed from his Wharton coursesite. Following the chicks class example, plot these data and try to fit a logistic growth curve to these data. What is the
estimate of the final vocab level (asymptote)? Compare the data and the fits from the logistic growth curve.
For reference, Self-Starting Logistic model SSlogis help page, do ?SSlogis post of annotated logistic curve with SSlogis arguments additional tools in the grofit package
4. More on autocorrelation[extension/enrichment]. In standard regression courses you may have seen in addition to Durbin-Watson test for AR(1) (dwtest()), versions of the Cochrane-Orcutt procedure for remdiation. Uses a first difference transformation of the data with an estimate of the autocorrelation (therefore hopeless when you have 3,4 5 observations per unit). To illustrate the statements in class and the similarities to OLS result, the solution to this problem does the straight-line and polynomial examples from the Week 1 class handout using the R-package orcutt
WEEK 1 Exercises
1. Straight-line fits for NC Fem data: North Carolina Achievement Data (see Williamson, Applebaum, Epanchin, 1991). These education data are eight yearly observations
on achievement test scores in math (Y), for 277 females each followed from grade 1 to grade 8, with a verbal ability background measure (W).
North Carolina, female math performance (also in Rogosa-Saner) North Carolina data (wide format); NC data (long)
a. Here we will use the 8 yearly observations on female ID 705810, which you can obtain from either the long form or wide form of these data.
For that female, what is the rate of improvement over grades 1 through 8? Compare the observed improvement for grades 1 through 8 (the difference score) with the amount of improvement indicated by the model fit. Obtain a 95% confidence interval for each (if possible).
b. More on OLS and the difference score. Refer to an old publication: A growth curve approach to the measurement of change. Rogosa, David; Brandt, David; Zimowski, Michele Psychological Bulletin. 1982 Nov Vol 92(3) 726-748 APA record direct link; Equation 4, page 728, shows a useful form for the OLS slope. (actually reading the first three pages of that pub is a decent intro to the growth curve topic.) For equally spaced data, that Eq (4) gives a useful equivalence between difference scores (amounts of change) and OLS slopes (multiply rates of change by time interval). For the part a NC data show that the OLS slope can be expressed as a
weighted sum of the four differences: { 8-1,7-2,6-3,5-4}. [to say that better {score at time 8 minus score at time 1; score at time 7 minus score at time 2; ...} and so forth]
Seperately, consider three observations at taken at equally spaced time intervals: What is a simple expression for the OLS slope (rate of change)?
2. Revisit the Berkeley Growth Data example from week 1 lecture. Consider the quadratic (polynomial degree 2) fit to these data, and also a (innapropriate?) constant-rate-of-change (straight-line) fit to these data. Then refer to Seigel, D. G. Several approaches for measuring average
rates of change for a second degree polynomial. The American Statistician, 1975, 29, 36-37. JStor Link for equivalences for the slope of the straight-line fit to an average rate of change for the quadratic fit. Compare Seigel 'Approach 3" to 'Approach 1'.
10/1. Analysis of collections of growth curves (Mixed-effects Models, lmer) Constant rate of change models
Growth modelling handout
Class Examples
1. Data frame sleepstudy available in lme4 package.
a. Published Treatments, Sleepstudy example
Source Publication: Belenky, G., Wesensten, N. J., Thorne, D. R., Thomas, M. L., Sing, H. C., Redmond, D. P.,
Russo, M., & Balkin, T. (2003). Patterns of performance degradation and restoration during
sleep restriction and subsequent recovery: A sleep dose-response study. Journal of Sleep Research, 12(1), 1-12.
Sleepstudy data analysis from Doug Bates lme4 book lme4: Mixed-effects modeling with R February 17, 2010 (draft chapters) Chapter 4: Sleepstudy example or Chap 3 in merged version of Bates book: lme4: Mixed-effects modeling with R January 11, 2010. Or a set of Bates slides for the sleepstudy example
Why lmer (lme4) does not provide p-values for fixed effects : Doug Bates lmer, p-values and all that There are a number of add-on packages.(see Review Question 1)
Music to accompany long-distance truck driver data: 1971 The Flying Burrito Brothers "Six Days on the Road"
b. Class Materials, Sleepstudy example
Individual plots (frame-by-frame) Plot of straight-line fits Sleepstudy, Bates Ch 4, lme4 analyses handout, ascii Sleepstudy class handout, pdf scan more Doug Bates Slides (pdf pages 8-28)
2. North Carolina, female math performance (also in Rogosa-Saner) North Carolina data (wide format); NC data (long)
plots for NC data North Carolina example. Smart First Year Student Analysis for NC Initial SFYS and lmer analyses of NC data, ascii
Model Comparisons for North Carolina, female math performance ascii version NC class handout, pdf scan model ncCon2 without redundent model term NC bootstrap results (SAS)
Background:
North Carolina Data also in (with full development of the modelling) Longitudinal Data Analysis Examples with Random Coefficient Models. David Rogosa; Hilary Saner . Journal of Educational and Behavioral Statistics, Vol. 20, No. 2, Special Issue: Hierarchical Linear Models: Problems and Prospects. (Summer, 1995), pp. 149-170. Jstor
Data formatting: wide to long North Carolina data (wide format); making the "Long" version
Background Readings
Fitting linear mixed-effects models using lme4, Journal of Statistical Software Douglas Bates Martin Machler Ben Bolker also Rnews_2005 pp.27-30
Douglas Bates item #4, Texts and Resources. Other Doug Bates materials: Three packages, "SASmixed", "mlmRev" and "MEMSS" with examples and data sets for mixed effect models
North Carolina Data also in (with full development of the modelling) Longitudinal Data Analysis Examples with Random Coefficient Models. David Rogosa; Hilary Saner . Journal of Educational and Behavioral Statistics, Vol. 20, No. 2, Special Issue: Hierarchical Linear Models: Problems and Prospects. (Summer, 1995), pp. 149-170. Jstor Data sets for Rogosa-Saner
Additional talk materials: An Assortment of Longitudinal Data Analysis Examples and Problems 1/97, Stanford biostat. Overview and Implementation for Basic Longitudinal Data Analysis CRESST Sept '97.
Another version (short) of the expository material is from the Timepath '97 (old SAS progranms) site: Growth Curve models ;
Data Analysis and Parameter Estimation ; Derived quantities for properties of collections of growth curves and bootstrap inference procedures
WEEK 2 Review Questions
1. More sleepstudy. Confidence interval and p-values. Add on, extension to class example.
I start by fitting the lmer model for the collection of growth curves: sleeplmer = lmer(Reaction ~ Days + (1 + Days|Subject), sleepstudy).
Then try out confint from lme4 (link to manual using likleihood profile or bootstrap methods.
Then look at the pvalues entry in the manual and try out add-on packages, esp for p-values for the fixed effects.
2. Ramus Data example. Example consists of 4 longitudinal observations on each of 20 cases. The measurement is the height of the mandibular ramus bone (in mm) for boys each measured at 8, 8.5, 9, 9.5 years of age. These data, which have been used by a number of authors (e.g., Elston
and Grizzle 1962), can be found in Table 4.1 of Goldstein (1979). Ramus data example long form for Ramus data tutorial on creating long form data manipulation . Use lmList to obtain the 20 OLS fits, with the initial time set to 8 years of age, i.e. intercepts are fits for the time of initial measurement (not t=0). Fit the lmer model for the collection of growth curves (using initial time = 8); verify that fixed effects are the sample means (over persons) of the lmList intercepts and slopes. Verify that the random effects variance for "age" (i.e. slopes) is the method-of-moments estimate for Var(theta). Compare the random effect estimates (ranef) which borrow strength for each subject with the OLS estimates from lmList (c.f. Bates Chap 4 discussion of sleepstudy data)
3. Artificial data example (used in Myths chapter to illustrate time-1,time-2 data analysis) Two part artificial data example. The bottom frame (the X's) is 40 subjects each with three equally spaced time observations (here in wide form).For these the fallible "X" measurements (constructed by adding noise to the Xi measurements).
Follow the class examples 'wide-to-long' and obtain the plot showing each subject's data and straight-line fit. Use lmList to obtain the 40 slopes for the straight-line fits. Solution uses current version of reshape package
WEEK 2 Exercises
1. Tolerance data
A subsample of data from the National Youth Survey is obtained in long-form by
read.csv("http://www.ats.ucla.edu/stat/r/examples/alda/data/tolerance1_pp.txt")
and in wide form by
read.csv("http://www.ats.ucla.edu/stat/r/examples/alda/data/tolerance1.txt")
Yearly observations from ages 11 to 15 on the tolerance measure (tolerance to deviant behavior e.g. cheat, drug, steal, beat; larger values indicates more tolerance on a 1to4 scale). Also in this data set are gender (is_male) and an exposure measure obtained at age 11 (self report of close friends involvement in deviant behaviors). note: the time measure is age - 11.
i. obtain individual OLS fits (tolerance over time) and plot the collection of those straight-lines. Provide descriptive statistic summaries for the rate of change in tolerance and initial level.
ii. fit a mixed effects model for tolerance over time (unconditional) for this collection of individuals. Obtain interval estimates for the fixed and random effects. Show that the fixed effects estimates correspond to quantities obtained in part i. Explain.
iii. Investigate whether the exposure measure is a useful predictor of level or rate of change in tolerance. What appears to be the best fitting mixed model for these data using these measures? Show specifics.
2. lmer/lme vs lm
Consider the sleepstudy and Ramus examples, collections of growth trajectories with no exogenous variable. Ramus Data example. Example consists of 4 longitudinal observations on each of 20 cases. The measurement is the height of the mandibular ramus bone (in mm) for boys each measured at 8, 8.5, 9, 9.5 years of age. These data, which have been used by a number of authors (e.g., Elston and Grizzle 1962), can be found in Table 4.1 of Goldstein (1979). Ramus data example long form for Ramus data tutorial on creating long form data manipulation .
Fitting the lmer models with Formula: Reaction ~ 1 + Days + (1 + Days | Subject) or Formula: ramus ~ I(age - 8) + (age | subj) has motivated the student question, what is going on here beyond what lm would do? So let's look at what lm would do in these examples.
Verify (or disprove) the assertion that the fixed effects from lmer, which we have seen are the averages of the individual fit parameter estimates (i.e. lmList), and therefore the coefficients of the average growth curve are identical to the fit from lm (which ignores the existence of individual trajectories). Compare the results of the lm and lmer analyses for these two data sets.
3. Early Education data (From Bates and Willett-Singer).
Data on early childhood cognitive development described in Doug Bates talk materials (pdf pages 49-52). Obtain these data from the R-package "mlmRev" or the Willett-Singer book site (in our week 1 intro links). Data are in long form and consist of 3 observations 58 treatment and 45 control children; see the Early entry in the mlmRev package docs.
Produce the plot of individual trajectories shown pdf p.49, Bates talk. (note:Bates does connect-the-dots, we have done straight-line fit, your choice). Show five-number summaries of rates of impovement in cognitive scores for
treatment and control groups. Develop and fit the fm12 lmer model shown in Bates pdf p.50 (note fm12 allows trt to effect rates of improvement but not level;). Interpret results. Note: this moves us into the comparing groups topics, where the individual attribute is group membership.
4. Standardizing is always a bad idea is a good motto for life, especially with longitudinal data.
Artificial data example from Review Question 3 (used in Myths chapter to illustrate time-1,time-2 data analysis) Start out with the "X" data, and standardize (i.e. transform to mean 0, var 1) at each of the 3 time points. Note "scale" will do this for you (in wide form). For the standardized data obtain the plot showing each subject's data and straight-line fit. What do you have here? Compare the results the mixed-effects models fitting the collection of straight-line growth curves for the measured and standardized data.
10/8. Collections of growth curves continued: linear and non-linear mixed-effects models
Lecture Topics
0. Review model formulation, North Carolina example (week 2 handouts).
1. Individual effects: fixed and random (and BLUPs). sleepstudy Rsession session plots
2. lmList does logistic (respiration data week5); introducing glmer lmList, glmer for respiration data
3. Brain Volume Data, in-class modeling exercise: analyses from "Variation in longitudinal trajectories of regional brain volumes of healthy men and women (ages 10 to 85 years) measured with atlas-based parcellation of MRI" cartoon plot of Lateral Ventricles data; actual data plot of Lateral Ventricles data; development of lmer (random effect) growth models
4. General formulation of mixed effects model in terms of growth trajectories pdf pages 7-8, handout in An Assortment of Longitudinal Data Analysis Examples and Problems , Stanford biostat (pp.7-8). Also Ware-Laird ALA slides 234-240. Douglas M. Bates lme4: Mixed-effects modeling with R section 3.5
5. Beyond Straight-line Growth: Polynomial and Non-linear Models.
Example: Orange Tree growth. Data from MEMSS package Data sets and sample analyses from Pinheiro and Bates, Mixedeffects
Models in S and S-PLUS (Springer, 2000).
Doug Bates Slides Orange trees analysis (pdf pages 8-16), Logistic SS (pdf p.6), pharmacokinetics ex (pdf pages 7, 17-24) Plots and nlmer analysis, Orange tree data Bates NLMM.Rnw From week 1 SSlogis (Self-Starting Logistic model) links and materials. another analysis of Orange Trees in the ASReml package manual section 8.9
Also LDA book Chapter 5. Chapter 5. Non-linear mixed-effects models Marie Davidian
additional tools in the grofit package and nlmeODE package Title Non-linear mixed-effects modelling in nlme using differential equations
WEEK 3 Review Questions
1. More with North Carolina data
a. identify the fastest and slowest growth among the 277 females. Compare medians of growth rates for females with verbal ability (Z) at or above 106 with that for females with verbal ability below 106. Show side-by-side boxplots.
b. In the class handout version of the NC analyses (and other postings, but not all) the first thing to do was make the 'time' variable have intitial value = 0 (making the intercept of a straight line fit correspond to level at initial time): i.e. 1 to 8 becomes 0 to 7. Obtain lmList results and
fit the ncUnc lmer model (straight-line growth, no Z) using time 1 to 8. Comment on differences of these analyses with those using timeInt in the class handout. In particular, look at the correlation of change and initial status. The correlation between observed change and observed initial status
using timeInt was .279 from lmer (Correlation of Fixed Effects) and also from lmList (you should confirm that). What is the result you obtain using time rather than timeInt? The mle of of the correlation of 'true' change and 'true' initial status is .651 using timeInt. What do you obtain using time?.
2. Orange tree extras. Take the fixed effects from the orange tree nlmer model, "m1" in the class materials, as the parameters of the "average" growth curve for this group of trees. Plot that logistic growth curve (either use a formula for logistic or the growfit package has a simple function).
Compare the fixed effects from nlmer to the results from nls for these data. More challenging Try to superimpose the group logistic curve (above) onto the plots of the individual tree trajectories (you may want to refer to the plots week1 Aids data).
3. Asymptotic regression, SSasymp slide (pdf p.5 of Bates slides, Nonlinear mixed models talk linked in Week 3, Topic 4). Data are from Neter-Wasserman text in file CH13TA04.txt. The outcome variable
is manufacturing relative efficiency (RelEff) over 90 weeks duration for two different locations. Plot the RelEff outcome against week for the two locations. Use the SSasymp function for a nlmer fit (or nls if needed)
to see whether the asymptote differs for the two locations.
4. Quadratic (polynomial) Trends. The book by Mirman resource item 7 Growth Curve Analysis and Visualization Using R not surprisingly has some good data examples (primarily psychological learning experiments). Here we use the Chapter 3 data set (sec 3.4) Word Learning. Data at http://www.danmirman.org/gca/WordLearnEx.txt. Use the subset TP == Low. How many subjects in that subset? How many observations on each? Accuracy is the outcome measure, the time ordered measure is Block (see Fig 3.7). Investigate a linear trend versus a quadratic trend using mixed effect models.
WEEK 3 Exercises
1. Teen age drinking. The UCLA data archive has a comma delimited file (access by read.table("http://www.ats.ucla.edu/stat/r/examples/alda/data/alcohol1_pp.txt", header=T, sep=",") .
Measurements on 82 adolescents (initial age 14) included 3 time-ordered observations on alcohol use and two background (exogenous) variables: dichotomous coa (child of an alcoholic) and measured variable peer (alcohol use by target's peers). Describe the collection of time trajectories in alcohol use. Fit an unconditional mixed model to this collection of time-trajectories and obtain interval estimates for the random and fixed effects. Show a plot for the random effects (subjects) and interpret the fixed effects. Now consider the two exogenous variables. Using conditional models, identify the best fitting model. Interpret the fixed effects for the best fitting model.
2. Vocabulary learning data from test results on file in the Records Office of the Laboratory School of the University of Chicago. Source D R Bock, MSMBR. The data consist of
scores, obtained from a cohort of pupils at the eigth through eleventh gade level on alternative forms of the vocabulary section of the Cooperative Reading Tests." There are 64 students in all, 36
male, 28 female (ordered) each with four equally spaced observations (test scores). Wide form of these data are in BOCKwide.dat and I kindly also made a long-form version BOCKlong.dat . Construct the usual collection of individual trajectory displays (either connect-the-dots or compare to a straight-line). Obtain the means (over persons) and plot the group growth curve. Does there appear to be curvature (i.e. deceleration in vocabulary skill growth)?
a. Construct an lmer model with the individual growth curve a quadratic function of grade (year), most convenient to use uncorrelated predictors grade - mean(grade) and (grade - mean(grade))^2. Fit the lmer model and interpret the fixed and random effects you obtain. Compare the results with a lmer model in which the individual trajectories are straight-line. Use the anova model comparison functionality in R (e.g. anova(modLin, modQuad) to test whether the quadratic function for individual growth produces a better model fit.
b. Investigate (via lmer model) gender differences (isMale) in vocabulary growth. Fit appropriate lmer models and interpret results,
3. Data on the growth of chicks on different diets. Hand and Crowder (1996), Table A.2, p. 172 Hand, D. and Crowder, M. (1996), Practical Longitudinal Data Analysis, Chapman and Hall, London. The dataset is available as a .R file; easiest to bring this page down to your machine and then load into your R-session (or try to load remotely). Here we consider the 20 chicks on Diet 1. (select these). Construct the plots analogous to those for the class example Orange trees: individual chicks frame-by-frame and all chicks on one plot. Fit a nlmer model that allows final weight (asymptote) to differ over chicks (other params fixed). Use ranef (individual estimates) to identify the largest asymptote value and smallest value. Plot the "average" growth curve under diet 1. Compare that nlmer maodel with a model that does not allow asymptotes to differ. What is your conclusion. Also compare with a nls model that ignores repeated measurements structure (i.e. ignores individual chicks). Compare the average growth curves.
10/15. Special case of time-1, time-2 data; Traditional measurement of change and more
Longitudinal in the news
Sitting for long periods not bad for health Publication: Associations of sitting behaviours with all-cause
mortality over a 16-year follow-up: the Whitehall II study. International Journal of Epidemiology, 2015, 1-8.
Lecture Topics
1. Properties of Collections of Growth Curves. class handout
2. Time-1, time-2 data. (paired data)
The R-package PairedData has some interesting plots and statistical summaries for "before and after" data;
here is a McNeil plot for Xi.1, Xi.5 in data example
Paired dichotomous data, McNemar's test (in R, mcnemar.test {stats}), Agresti (2nd ed) sec 10.1
Also see R-package PropCIs Prime Minister example
3. Issues in the Measurement of Change. Class lecture covers Myths 1-6+.
Slides from Myths talk .
Class Handout, Companion for Myths talk
4. Examples for Exogenous Variables and Correlates of Change (use of lagged dependent variables)
Time-1,time-2 data analysis examples Measurement of change: time-1,time-2 data
data example for handout scan of regression handout ascii version of data analysis handout
Extra material for Correlates and predictors of change: time-1,time-2 data
Rogosa R-session to replicate handout, demonstrate wide-to-long data set conversion, and descriptive fitting of individual growth curves. Some useful plots from Rogosa R-session
5. Comparing groups on time-1, time-2 measurements: repeated measures anova vs lmer OR the t-test
Comparative Analyses of Pretest-Posttest Research Designs,
Donna R. Brogan; Michael H. Kutner, The American Statistician, Vol. 34, No. 4. (Nov., 1980), pp. 229-232. JSTOR link
urea synthesis, BK data data, long-form
BK plots (by group)
BK repeated measures analysis pdf version
BK lmer analysis
Stat141 analysis
archival example analyses. SAS and minitab
Background Readings and Resources
Myths Chapter. Rogosa, D. R. (1995). Myths and methods: "Myths about longitudinal
research," plus supplemental questions. In The analysis of change, J. M.
Gottman, Ed. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 3-65.
More stuff (if you don't like the ways I said it)
I noticed John Gottman did a pub rewriting the myths: Journal of Consulting and Clinical Psychology 1993, Vol. 61, No. 6,907-910 The Analysis of Change: Issues, Fallacies, and New Ideas
Also John Willett did a rewrite of the Myths 'cuz I didn't want to reprint it again (or write a new version): Questions and Answers in the Measurement of Change REVIEW OF RESEARCH IN EDUCATION 1988 15: 345
Reliability Coefficients: Background info. Short primer on test reliability Informal exposition in Shoe Shopping and the Reliability Coefficient extensive technical material in Chap 7 Revelle text
A growth curve approach to the measurement of change.
Rogosa, David; Brandt, David; Zimowski, Michele
Psychological Bulletin. 1982 Nov Vol 92(3) 726-748 APA record direct link
Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203-228.
available from John Willet's pub page
Demonstrating the Reliability of the Difference Score in the Measurement of Change. David R. Rogosa; John B. Willett Journal of Educational Measurement, Vol. 20, No. 4. (Winter, 1983), pp. 335-343. Jstor
Maris, Eric. (1998). Covariance Adjustment Versus Gain Scores--Revisited. Psychological Methods, 3(3) 309-327. apa link
A good R-primer on repeated measures (a lots else). Notes on the use of R for psychology experiments and questionnaires Jonathan Baron, Yuelin Li. Another version
Multilevel package has behavioral scienes applications including estimates of within-group
agreement, and routines using random group resampling (RGR) to detect group effects.
More repeated measures resources: Background primer on analysis of variance (with R); see sections 6.8, 6.9 of Notes on the use of R for psychology experiments and questionnaires Jonathan Baron, Yuelin Li. Pdf version
The ez package provides extended anova capabities.
Examples (blog notes) : Repeated measures ANOVA with R (functions and tutorials) Repeated Measures ANOVA using R Obtaining the same ANOVA results in R as in SPSS - the difficulties with Type II and Type III sums of squares
Application publications, time-1, time-2 Experimental Group Comparisons:
a. Mere Visual Perception of Other People's Disease Symptoms Facilitates a More Aggressive Immune Response
Psychological Science, April 2010 Pre-post data and difference scores (see Table 1)
b. Guns and testosterone. Guns Up Testosterone, Male Aggression
Guns, Testosterone, and Aggression: An Experimental Test of a Mediational Hypothesis Klinesmith, Jennifer; Kasser, Tim; McAndrew, Francis T, Psychological Science. Vol 17(7), Jul 2006, pp. 568-571.
WEEK 4 Review Questions
1. Time1-time2 regressions; Class example
Repeat the handout demonstration regressions using the fallible measures
(the X's) from the bottom half of the linked data page. The X's are simply
error-in-variable versions of the Xi's: X = Xi + error, with error having
mean 0 and variance 10. Compare 5-number summaries for the amount of change from the earliest time "1" to the final observation "5" using the "Xi" measurements (upper frame) and the fallible "X" observations (lower frame).
2. (more challenging). Use mvrnorm to construct a second artificial data
example (n=100) mirroring the week 4 myths data class handout BUT with the correlation
between true individual rate of change and W set to .7 instead of 0. Carry out
the corresponding regression demonstration.
3. Reliability versus precision demonstration
Consider a population with true change between time1 and time2 distributed Uniform [99,101] and measurement error Uniform [-1, 1]. If you used discrete Uniform in this construction then you could say measurement of change is accurate to 1 part in a hundred.
Calculate the reliability of the difference score.
Also try error Uniform [-2,2], accuracy one part in 50.
A similar demonstration can be found in my Shoe Shopping and the Reliability Coefficient
WEEK 4 Exercises
1. Captopril and Blood pressure
The file captopril.dat contains the data shown in Section 2.2 of
Verbeke, Introduction to Longitudinal Data Analysis, slides. Captopril is
an angiotensin-converting enzyme inhibitor (ACE inhibitor) used for
the treatment of hypertension.
a. Smart First Year Student analyses. Use the before and after Spb measurements
to examine the improvement (i.e. decrease) in blood pressure. Obtain a
five-number summary for observed improvement. What is the correlation between change and
initial blood pressure measurement? Obtain a confidence interval for the
correlation and show the corresponding scatterplot. What special challenges are present in this analysis?
b. lmer analyses. Try to obtain a good confidence interval for the amount of decline. Obtain a point and interval estimate for the correlation beween initial status and change in Spb.
2. Regression toward the mean? Galton's data on the heights of parents and their children
In the "HistData" or "psych" packages reside the "galton" dataset, the primordial regression toward mean example.
Description: Galton (1886) presented these data in a table, showing a cross-tabulation of 928 adult children born
to 205 fathers and mothers, by their height and their mid-parent's height. A data frame with 928 observations on the following 2 variables.
parent Mid Parent heights (in inches) child Child Height. Details: Female heights were adjusted by 1.08 to compensate for sex differences. (This was done in the
original data set)
Consider "parent" as time1 data and "child" as time2 data and investigate whether these data indicate regression toward the mean according to either definition (metric or standardized)? Refer to Section 4 of the Myths chapter supplement (pagination 61-63) for an assessment of regression toward the mean (i.e. counting up number of subjects satisfying regression-toward-mean).
Aside: if you like odd plots, look at the sunflowerplot code in the docs for the galton data.
3. Paired and unpaired samples, continuous vs categorical measurements.
Let's use again the 40 subjects in the problem 1 "X" data.
a. Measured data. Take the time1 and time5 observations and obtain a 95% Confidence Interval for the amount of change. Compare the width of that interval with a confidence interval for the difference beween the time5 and time1 means if we were told a different group of 40 subjects was measured at each of the time points (data no longer paired).
b. Dichotomous data. Instead look at these data with the criterion that a score of 50 or above is a "PASS" and below that is "FAIL". Carry out McNemar's test for the paired dichotomous data, and obtain a 95% CI for the difference between dependent proportions. Compare that confidence interval with the "unpaired" version (different group of 40 subjects was measured at each of the time points) for independent proportions.
10/22. Experimental Protocols and Comparing Group Growth
Longitudinal in the news
Washington Post: The latest study about antioxidants is terrifying. Scientists think they may boost cancer cells to spread faster.
Nature publication. Study finds that antioxidants can encourage cancer growth Oxidative stress inhibits distant metastasis by human melanoma cells Nature (2015) Figure 3
Lecture Topics
1. Comparing groups on time-1, time-2 measurements: repeated measures anova vs lmer OR the t-test
Comparative Analyses of Pretest-Posttest Research Designs,
Donna R. Brogan; Michael H. Kutner, The American Statistician, Vol. 34, No. 4. (Nov., 1980), pp. 229-232. JSTOR link
urea synthesis, BK data data, long-form
BK plots (by group)
modern analysis BK lmer analysis
legacy analyses and equivalences BK repeated measures analysis pdf version, repeated measures and equivalences
Stat141 analysis
archival example analyses. SAS and minitab
2. Cross-over designs (usually time-1, time-2). Laird-Ware text slides (pdf pages 135-150). Crossover design data from slide 137, anova for crossover design ex ascii version, anova for crossover design ex
R-resources for crossover designs. package Crossover Crossover vignette package crossdes see Rnews Vol. 5/2, November 2005
also see slides 5-14 Repeated Measures Design Mark Conaway
3. Multi-wave growth example: Bock Vocabulary data, Repeated Measures anova (with linear, quadratic, cubic contrasts): class example. (note Mirman text uses orthogonal polynomials)
4. Group Comparisons for Longitudinal Experimental Designs. Group growth and Experimental comparisons for count and dichotomous outcomes(examples From HSAUR 2ndEd, Ch.13).
Link functions for generalized linear mixed models (GLMMs), Bates slides (pdf pages 11-18)
A Handbook of Statistical Analyses Using R, Second Edition Torsten Hothorn and Brian S . Everitt Chapman and Hall/CRC 2009. Analysing Longitudinal Data II -- Generalised Estimation Equations and Linear Mixed Effect Models: Treating Respiratory Illness and Epileptic Seizures Data sets etc Package 'HSAUR2' August 2014, Title A Handbook of Statistical Analyses Using R (2nd Edition)
A. Analysis of Count data. Epilepsy example, group comparisons, collection of individual trajectories. HSAUR chap 13 Rogosa R-session using gee and lmer Recap Group Comparisons, Epilepsy example. Comparison of lmer models
For SAS (and GEE) fans another analysis
B. Binary Response, dichotomous outcomes. Respiratory Illness Data from HSAUR package. Data and description also at the ALA (Laird-Ware) site Rogosa R-session using lmer Rogosa note on formulating (g)lmer models.
5. Study Design: Power Calculations for Longitudinal Group Comparsions.
R-package longpower Vignettes found by "browseVignettes(package = "longpower")" . Functions in MBESS package--ss.power.pcm.
Background pubs:Sample Size Planning for Longitudinal Models:
Accuracy in Parameter Estimation for Polynomial Change Parameters Ken Kelley Notre Dame Joseph R. Rausch Psychological Methods 2011 Power for linear models of longitudinal data
with applications to Alzheimer's Disease Phase II study design Michael C. Donohue, Steven D. Edland, Anthony C. Gamst
6. Missing Data Concerns. Nontechnical overviews: Phil Lavori et al. Psychiatric Annals, Volume 38, Issue 12, December 2008 Missing Data in Longitudinal Clinical Trials, Part A Part B Robin Henderson, Missing Data in Longitudinal Studies
Missing data and imputation, including mice week 10 topic. Flexible Imputation of Missing Data. Stef van Buuren Chapman and Hall/CRC 2012. Chapter 9, Longitudinal Data Sec 3.8 Multilevel data. He is the originator of mice
WEEK 5 Review Questions
1. Revisit Brogan-Kutner data analysis.
a. Demonstrate the Brogan-Kutner Section 5 equivalences (from paper, shown in class) for repeated measures anova and/or BK lmer analyses.
b. Is amount of gain/decline related to initial status? For the 8 new procedure patients and for the 13 old procedure patients, seperately, estimate the correlation between change and initial status and obtain a confidence interval if possible.
c. Analysis of Covariance. For the Brogan-Kutner data carry out an analysis of covariance (using premeasure as covariate) for the relative effectiveness of the surgery methods. Compare with class analyses.
Slides 203-204 in the Laird-Ware text materials purport to demonstrate that analysis of covariance produces a more precise treatment effect estimate than difference scores (repeated measures anova). What very limiting assumption is slipped into their analysis? Can you create a counter-example to their assertion/proof?
part c. Solution Notes on the ALA (Laird-Ware) assertion
2. Revisit Respiration example.
a. try to do lmList on these data to get odds(good) for each of the each 111 subjects. Investigate effectiveness of treatment.
b Use lmer analyses to compare treament and placebo. Obtain a confidence interval for effectiveness of treament. Investigate gender differences in response to the intervention (i.e. the treatment)
c. Extend the lmer model in part b by adding the age and baseline measurements to the level 2 model. Compare with part b results.
3. Revisit Epilepsy example.
To supplement the longitudinal texts (HSAUR, ALA etc) full model for the epilepsy data, lets try to build up the analysis from basic description comparing placebo vs drug up through some basic some basic glmer models.
A somewhat similar effort was made in the second class posting "Recap group comparisons (epcomp)" linked above. In this exercise treat period as a time measurement (1,2,3,4) rather than an ordered factor.
How many subjects in placebo and drug groups? Use lmList to obtain slopes and intercepts for fits of time trends to seizures for each subject and compare drug and placebo groups.
Fit and compare glmer models with treatment as the only level 2 predictor (for intercept) without and with a time trend. Compare.
Add the baseline to the glmer models above (in level 2 model for intercept; is effect of the drug significant (use confint)? Does adding age help this model?
4. Repeat Brogan-Kutner lmer analyses from lecture.
Use lmer (or lme) to determine the comparative efficacy of the surgical methods on liver function. Investigate whether a model allowing for pretest differences is helpful.
5. Beat the Blues from Chap 12 of HSAUR 2nd ed (resource # 5).
Data in wide form: data("BtheB", package = "HSAUR2"). Chap. 12 describes cognitive behavioural program. We will use the pretest and the two-month followup (additional followups have lots of missing data).
Investigate the effectiveness of Beat the Blues from these 2-wave data.
WEEK 5 Exercises
1. We use a subset of the Baumann data from the car package, which I was nice enought to put in longform at http://rogosateaching.com/stat222/readlongdat .
These data are from a study of reading from Purdue. We use the data to compare two methods: Basal, traditional method of teaching; DRTA, an innovative method; coded 1 and 2 respectively in the data. Random assignment placed twenty-two students in each group; reading test measures were obtained pre and post instruction.
The Directed Reading Thinking Activity (DRTA) is a strategy that guides students in asking questions about a text, making predictions, and then reading to confirm or refute their predictions. The DRTA process encourages students to be active and thoughtful readers, enhancing their comprehension.
Use descriptive and inferential statistical methods to assess the relative efficacy DRTA method.
2.Treatment of Lead Exposed Children (TLC) Trial. Data (wide form) and description: data here
Start out by just using the subset of the longitudinal data Lead Level Week 0 and Week 6. Carry out the repeated measures anova for the relative effectiveness of chelation treatment
with succimer or placebo (A,P). Show the three equivalences in the Brogan-Kutner paper between the repeated measures anova results and simple t-tests for these data. Next compare
with a lmer fit following the B-K class example (posted). Finally use all 4 longitudinal measures (weeks 0,1,4,6) for a Active vs Placebo comparison using lmer. Compare with the results that use only 2 observations.
3. Crossover Design. The dataset consists of safety data from a crossover trial on the
disease cerebrovascular deficiency. The response variable is not a trial endpoint but rather a potential side effect. In this two-period crossover trial, comparing the effects of active drug to placebo, 67 patients were randomly allocated to the two treatment sequences, with 34 patients receiving placebo followed by active treatment, and 33 patients receiving active treatment followed by placebo. The response variable is binary, indicating whether an electrocardiogram (ECG) was abnormal (Y=1) or normal (Y=0). Each patient has a bivariate binary response vector.
Data set is available at http://www.hsph.harvard.edu/fitzmaur/ala/ecg.txt (needs to be cut-and-paste into editor). Carry out the basic analysis of variance for this crossover design following week 5 Lecture topic 2. You may want to use glm to take into account the binary outcome. Does the treatment increase the probability of abnormal ECG? Give a point estimate and significance test for the treatment effect.
4. Data on Amenorrhea from Clinical Trial of Contracepting Women. Source: Table 1 (page 168) of Machin et al. (1988). Reference: Machin D, Farley T, Busca B, Campbell M and d'Arcangues C. (1988). Assessing changes in vaginal bleeding patterns in contracepting women. Contraception, 38, 165-179.
Data in long form and a wide-form version
Description:
The data are from a longitudinal clinical trial of contracepting women.In this trial women received an injection of either 100 mg or 150 mg of depot-medroxyprogesterone acetate (DMPA) on the day of randomization and three additional injections at 90-day intervals. There was a final follow-up visit 90 days after the fourth injection, i.e., one year after the first injection.
Throughout the study each woman completed a menstrual diary that recorded any vaginal bleeding pattern disturbances. The diary data were used to determine whether a women experienced amenorrhea, the absence of menstrual bleeding
for a specified number of days. A total of 1151 women completed the menstrual diaries and the diary data were used to generate a binary sequence for each woman according to whether or not she had experienced amenorrhea in the
four successive three month intervals.
In clinical trials of modern hormonal contraceptives, pregnancy is exceedingly rare (and would be regarded as a failure of the contraceptive method), and is not the main outcome of interest in this study. Instead, the outcome of interest is a binary response indicating whether a woman experienced amenorrhea in the four successive three month intervals.
A feature of this clinical trial is that there was substantial dropout. More than one third of the women dropped out before the completion of the trial. In the linked data, missing data are designated by "." [note: in the week 6 terminology consider the dropouts to be missing at random, not necessarily a correct assumption.]
The purpose of this analysis is to assess the influence of dosage on the risk of amenorrhea and any individual differences in the risk of amenorrhea.
Show your model for these data and the results. Provide significance tests and/or interval estimates for the odds of amenorrhea as a function of dose. Display and interpret individual differences in response by showing the random effects within each experimental group.
5. Chick Data, finale. One more use of the chick data (week 3, problem 2; week 1 class lecture). Use the data for all 4 Diets to construct a nlmer model that allows asymptotes to differ across the four diets. Do the diets produce significantly different results? Which diet produces the heaviest 'mature' chick weight?
10/29. Comparing Group Growth, continued. Power Calculations, Missing Data, Observational Studies, Cohort Designs.
Longitudinal in the news
Shoulder dislocation could be better with no surgery AC Joint Dislocation treatment could get lot easier
Publication: Journal of Orthopaedic Trauma Issue: Volume 29(11), November 2015, p 479-487. Multicenter Randomized Clinical Trial of Nonoperative Versus Operative Treatment of Acute Acromio-Clavicular Joint Dislocation
Lecture Topics
From Week 5 listings
i. topic 4A. Group Comparisons for Longitudinal Experimental Designs. Analysis of Count data. Epilepsy example
ii. topic 5. Study Design: Power Calculations for Longitudinal Group Comparsions.
iii. topic 6. Missing Data Concerns.
New in Week 6
1. Observational Studies: Group Comparisons in Longitudinal Observational (non-experimental, "quasi"-experimental) Designs
A. Regression adjustments in quasi-experiments. Technical resource: Weisberg, H. I. Statistical adjustments and uncontrolled studies. Psychological Bulletin, 1979, 86, 1149-1164. class handout
B. Lord's paradox; pre-post group comparisons. Lord, F. M. (1967). A paradox in the interpretation of group comparisons. Psychological Bulletin, 68, 304-305.
Wainer, H. (1991). Adjusting for differential base rates: Lord's Paradox again. Psychological Bulletin, 109, 147-151.
C. Economist's differences in differences (or diffs in diffs with matching) for observational studies. R-package wfe (my failures). paper On the Use of Linear Fixed Effects Regression Models for Causal Inference(sec 3.2)
D. Interrupted time-series. Interrupted Time Series Quasi-Experiments Gene V Glass Arizona State University. Time Series Analysis with R section 4.6
Did fertility go up after the Oklahoma City bombing? An analysis of births in metropolitan counties in Oklahoma, 1990-1999. Demography, 2005. R package BayesSingleSub: Computation of Bayes factors for interrupted time-series designs
E. Value-added analysis. Value-added does New York City. New York schools release 'value added' teacher rankings
from the unions: THIS IS NO WAY TO RATE A TEACHER
Value-Added Models to Evaluate Teachers: A Cry For Help H Wainer, Chance, 2011. American Statistical Association Statement on Using Value-Added Models for Educational Assessment
2. Cohort effects. Cohort-sequential, Accelerated longitudinal designs. Robinson, K., Schmidt, T. and Teti, D. M. (2008) Issues in the Use of Longitudinal and Cross-Sectional Designs, in Handbook of Research Methods in Developmental Science (ed D. M. Teti), Blackwell Publishing Ltd, Oxford, UK
3. Econometric Approaches to Longitudinal Panel Data. Panel Data Econometrics in R: The plm Package Yves Croissant Giovanni Millo (esp. section 7. "plm versus nlme/lme4" ). R-package plm More in Week 10.
WEEK 6 Review Questions
1. Power (sample size) calculations for experimental group comparisons.
a. Longpower package (vignette). Reconstruct the sample size calculation for the Alzheimer's disease trial (7 waves) on p.4 of the vignette.
b. MBESS package. Recreate the sample size calculation for width of confidence interval for differential growth using ss.aipe.pcm function in the example used in Kelley and Rausch appendix (and MBESS manual)
2. Observational Studies: Lord's Paradox. more in week 10
Part 1. Lord's paradox example
a. construct a two-group pre-post example with 20 observations in
each group that mimics the description in Lord (1967):
statistician 1 (difference scores) obtains 0 group effect
statistician 2 (analysis of covariance) obtains large group effect
for the group higher on the pre-existing differences in pretest
b. construct second example for which
statistician 1 (difference scores) obtains large group effect
statistician 2 (analysis of covariance) obtains 0 group effect
c. construct a third example (if possible) for which
statistician 1 (difference scores) obtains large postive group effect
statistician 2 (analysis of covariance) obtains large negative group effect
Part 2. Group Comparisons by repeated measures analysis of variance or lmer
For the examples in part 1, (a and c), carry out the group
comparison (i.e. is there differential change?) for the artificial
data using a repeated measures anova (one within, one between factor) or
lmer equivalent.
Demonstrate the equivalence from Brogan-Kutner paper that testing
the groupXtime interaction term is equivalent to a
t-test between groups on individual improvement (i.e. a
statistician 1 analysis).
3. Observational Studies: Regression Adjustments. more in week 10
The display from lecture of the regression adjustments also has a numerical example (page 2 of pdf). Recreate the results shown for the Anderson et al Head Start example. Also for lecture materials, Regression Adjustments with Non-equivalent groups
Week 6, show the Belson adjustment procedure (using control group slope) is equivalent to evaluating the vertical distance between the within-group regression fits at the mean of the treatment group. written out proof.
WEEK 6 Exercises
1. Missing Data. Wide-form longitudinal data
Artificial data example from week 2 RQ3 and Week 4 Lecture item 4 (used in Myths examples to illustrate time-1,time-2 data analysis) Two part artificial data example. The top frame (the Xi's) is 40 subjects each with three equally spaced time observations (here in wide form). For these these perfectly measured "Xi" measurements each subject's observation fall on a straight-line.
a. Use data set W6prob1a , for which about 15% of the observations have been made missing. Use these data (with lm) to recreate the multiple regression demonstration in Week 4 lecture, part 4: "Correlates and predictors of change: time-1,time-2 data" .
Compare with the results for the full data on 40 subjects. What does lm do with missing data?
b. Repeat part a with data set W6prob1b. Can you find any reason to doubt a "missing at random" assumption for this data set?
Note: in Week 10 we will demonstrate multiple imputation procedures (mice) for wide-form data, at least.
2. Longitudinal Observational Study: Wages for High School Drop-outs. Data obtained from the National Longitudinal Survey on Youth can be used to look-at the labor-market experiences of high school drop-outs. The subset of these
data we will use is available at UCLA-- it's a csv file here's the appropriate read.table statement.
read.table("http://www.ats.ucla.edu/stat/r/examples/alda/data/wages_pp.txt", header=T, sep=",")
'data.frame': 6402 obs. of 15 variables:
$ id : int 31 31 31 31 31 31 31 31 36 36 ...
$ lnw : num 1.49 1.43 1.47 1.75 1.93 ...
$ exper : num 0.015 0.715 1.734 2.773 3.927 ...
$ ged : int 1 1 1 1 1 1 1 1 1 1 ...
$ postexp : num 0.015 0.715 1.734 2.773 3.927 ...
$ black : int 0 0 0 0 0 0 0 0 0 0 ...
$ hispanic : int 1 1 1 1 1 1 1 1 0 0 ...
$ hgc : int 8 8 8 8 8 8 8 8 9 9 ...
$ hgc.9 : int -1 -1 -1 -1 -1 -1 -1 -1 0 0 ...
$ uerate : num 3.21 3.21 3.21 3.29 2.9 ...
$ ue.7 : num -3.79 -3.79 -3.79 -3.71 -4.11 ...
$ ue.centert1 : num 0 0 0 0.08 -0.32 ...
$ ue.mean : num 3.21 3.21 3.21 3.21 3.21 ...
$ ue.person.cen: num 0 0 0 0.08 -0.32 ...
$ ue1 : num 3.21 3.21 3.21 3.21 3.21 ...
Variables we will use are id, log-wage (hourly) lnw for each observation, exper time in labor force to the nearest day (in years), black (isblack = 1), hcg (highest grade completed; note hgc.9 is hgc - 9)
a. How many individuals in this data set? Give a five-number summary of the number of observations per person. How many of the individuals in these data have black = 1?
b. SFYS descriptive analyses. We are interested in wages (measured by lnw) as a function of experience (lnw ~ exper). Show a five-number summary of the gradient (slope; i.e. change in log-wage for unit change in exper)) and level (here fit for exper = 0, initial status) for the set of individuals. Then stratify on black = 1 vs black = 0 (combining the white and hispanic drop-outs). Also show side-by-side boxplots for gradient and initial level stratifying on black. What do these displays indicate. Also show a plot of the lnw ~ exper fits seperately for black = 1 and black = 0. What do these analyses and displays indicate?
c. Use a formal mixed-effects model analysis to obtain random and fixed effects for the lnw~ exper individual level model. Obtain a point estimate and confidence interval for the variance of gradients. Does the bootstrap CI differ from the profile CI?
d. Are there differences in the lnw ~ exper relation for students black = 1 vs black = 0? Show by estimates and confidence intervals from mixed-effects models.
e. Does inclusion of hgc information confirm or alter your indications in part d?
3. Observational study: Gender differences in Vocabulary learning data-- see Week 3 problem 2-- from test results on file in the Records Office of the Laboratory School of the University of Chicago. Source D R Bock, MSMBR. The data consist of
scores, obtained from a cohort of pupils at the eigth through eleventh gade level on alternative forms of the vocabulary section of the Cooperative Reading Tests." There are 64 students in all, 36
male, 28 female (ordered) each with four equally spaced observations (test scores). Wide form of these data are in BOCKwide.dat and I kindly also made a long-form version BOCKlong.dat .
For this problem consider gender differences in Vocabulary growth. Obtain the means (over persons) and plot the group growth curves, separately by gender. Does there appear to be curvature (i.e. deceleration in vocabulary skill growth) for both males and females? Construct an lmer model with the individual growth curve a quadratic function of grade (year), most convenient to use uncorrelated predictors grade - mean(grade) and (grade - mean(grade))^2. In the level II model allow each of the three parameters of the individual quadratic curves to differ by gender. Fit the lmer model and interpret the fixed and random effects you obtain. Compare the results with a lmer model in which the individual trajectories are straight-line. Use
the anova model comparison functionality in R (e.g. anova(modLin, modQuad) to test whether the quadratic function for individual growth produces a better model fit.
4. Observational Studies: Regression Adjustments.
The class handout on regression adjustments shown in class and linked in RQ3 above contained summary statistics for the Head Start data considered in Anderson et al (1980) Statistical Methods for Comparative Studies. I constructed a corresponding data set located at
W6prob3dat
Try out the various regression adjustments described on the handout for these pretest-posttest data. (Handout shows some approximate estimates). Also show the result for the basic diffs-in-diffs estimator from Week 6.
11/5. Analysis of Durations: Introduction to Survival Analysis (aka event history) Methods
Longitudinal in the news
Life-span psychology. Your early 20s really ARE your happiest years People Are Happiest In Their 20s
Useful introductions to Survival Analysis (mostly with R)
John Fox tutorial: Cox Proportional-Hazards Regression for Survival Data
Survival analysis text by Rupert G. Miller (Ch 2,3,4,6). Available as Stanford Tech Report
CHAPTER 11 Survival Analysis: Glioma Treatment and Breast Cancer Survival A handbook of statistical analyses using R (second edition). Brian Everitt, Torsten Hothorn CRC Press, Complete version (through Stanford access) R-code for chapter11
An Introduction to Survival Analysis Mark Stevenson EpiCentre, IVABS, Massey University. Author R-package epiR
Quick overview Survival analysis in clinical trials: Basics and must know areas Perspect Clin Res. 2011 Oct-Dec; 2(4): 145–148. Ritesh Singh and Keshab Mukhopadhyay
CHAPTER 11 Survival Analysis: Retention of Heroin Addicts in Methadone Maintenance Treatment. Handbook of Statistical Analyses Using Stata, Second Edition. Sophia Rabe-Hesketh Chapman and Hall/CRC 2000.
Event History Analysis with R. Goran Brostrom CRC Press 2012. R-package eha
Slides on renewal processes and hazard functions
Set of Slides An introduction to survival analysis, Geert Verbeke
Main R-package: survival; Terry Therneau, Stanford Stat Ph.D
CRAN Task View: Survival Analysis . Survival analysis, also called event history analysis in social science, or reliability analysis in engineering, deals with time until occurrence of an event of interest. However, this failure time may not be observed within the relevant time period, producing so-called censored observations. This task view aims at presenting the useful R packages for the analysis of time to event data.
KM bootstrap in Hmisc package, bootkm. Exact tests, coin package, surv_test.
Class handouts (scanned) week 7
Class Data examples:
1. Miller leukemia data (Kaplan-Meier); pdf p.42 in online version class example in R, data in package survival extensions of leukemia example (week 7) Using eha package for aml Cox fits, zph plot
Legacy versions SAS Minitab
2. Herion (addict) data. Source: D.J. Hand, (et al.) Handbook of Small Data Sets. Properly formatted version Analyses in Stevenson and Stata expositions above. ascii version Rogosa R-session class handout
Additional analyses for herion: Bootstrapping, Math 159 Pomona analysis in SAS (phreg)
Publication Source: Caplehorn, J., Bell, J. 1991. Methadone dosage and the retention of patients inmaintenance treatment. The Medical Journal of Australia,154,195-199.
Additional survival data.
3. Recidivism data from John Fox tutorial. Source: Rossi PH, Berk RA, Lenihan KJ (1980). Money, Work, and Crime: Some Experimental
Results. Academic Press, New York.
4. Kalbfleisch and Prentice (1980) rat survival Data and description plus SAS analysis (Cox regression). Also best subsets Cox regression example, myeloma
5. R Textbook Examples. Applied Survival Analysis Chapter 3: Regression Models for Survival Data
WEEK 7 Review Questions
1.
Part a. In file teacha.dat in the class directory http://web.stanford.edu/~rag/stat222/teacha.dat are 75 "survival times" (variable name 'career') indicating actual length of teachers
careers (in years) in a rather rough school district. What is the median survival time? what proportion of
teachers are still in the district after 2 years? 4 years? 6 years? Plot a survival curve from this complete set of times.
Part b. In file teachb.dat in the class directory are the more realistic data: censored versions of the 75 "survival times" in part a.
Column 1 has the times (career) and Column 2 has the censoring indicator (Note these data have status = 1 if censored). Compute naive answers (ignoring censoring) to the questions in
part a: what is the median survival time? what proportion of teachers are still in the district after 2 years? 4 years? 6 years?
Use the Kaplan-Meier product-limit estimate to answer the questions in part a for these censored data: what is the median survival time?
what proportion of teachers are still in the district after 2 years? 4 years? 6 years? Plot a survival curve with 95% confidence intervals.
Obtain bootstrap (percentile) confidence intervals for the median survival time, and for the lower quartile (25th) of the survival time distribution.
2. Days to vaginal Cancer Mortality in Rats. The link for data example 4 above has these data and description and an assortment of (gratuitous) SAS analyses. From that file
make yourself an R data set. Plot the Kaplan-Meier survival curves for the two groups (with the point-wise condidence intervals for each curve).
Carry out the (asymptotic) log-rank test of identical survival curves. Compare those results with the exact (permutation) test. What are the median survival times in the two groups? Obtain a bootstrap estimate of the confidence interval for the difference of median survival times in the two groups (95% is a good default or 90%). How does this confidence interval compare with the tests for differences between the survival done above? One more thing...Redo the group comparsion of survival using Cox regression with predictor (covariate) Group membership (pretreatment regimes). Do the results agree with the previous analyses. Obtain a confidence interval for the hazard ratio (ratio of the hazard functions) between the two groups.
3. Replicate (some of) the analyses in the John Fox survival analysis tutorial for the Recidivism data (sec 3.2), links above. The experimental variable is fin indicating financial aid (or not). Start with a Kaplan Meier 2-group comparison, with plot and significance test. Then fit the 'full' model (mod.allison) and assess the significance of the experimental manipulation (fin). Plot the survival function from the cox regression (Fox Fig 1). Carry out the comparison (Fig 2) of estimated survival functions for those receiving (fin = 1) and not receiving (fin = 0) financial aid, with other covariates are fixed at their average values. For the model diagnostics in Section 5: use the cox.zph function to assess the proportional hazards assumptions, and plot the scaled Schoenfeld residuals (Fox figure 3).
4. (multiple groups, no censoring). Among the contributions of Carnegie-Mellon Univ is the Data and Story Library (DASL). The Cancer Survival dataset shown in lecture ( presentation slides here) is located
at DASL . Compare survival times for the 5 types of cancer (Organ in the dataset) with relevant plots and inference procedures.
WEEK 7 Exercises
1. Fun with hazards.
Part a. Social Security Life Tables. Use the 2007 Actuarial Life Table, useful discussion on benefits. Plot the hazard functions for males and females. Do these hazard functions appear to be exponential? Also plot the corresponding survival curves. Can you verify (approximately numerically) the relation between surival curve and integrated hazard from the week 7 handout-- S(t) = exp(-H(t)) ?
Part b. Refer to the hazard function shown in class for Alcohol and Incidence of Total Stroke ( Publication: Alcohol Consumption and Risk of Stroke in Women, Stroke, March 2012. Nurses' Health Study). (figure underneath Table 2).
What is the increase in hazard between 2 drinks/day and 3 drinks/day?
2. Melanoma data. In package ISwR data melanom
{ISwR} Survival after malignant melanoma
Description: The melanom data frame has 205 rows and 7 columns. It contains data relating to the survival of patients after an operation for malignant melanoma, collected at Odense University Hospital by K.T. Drzewiecki.
> str(melanom)
'data.frame': 205 obs. of 6 variables:
$ no : int 789 13 97 16 21 469 685 7 932 944 ...
$ status: int 3 3 2 3 1 1 1 1 3 1 ...
$ days : int 10 30 35 99 185 204 210 232 232 279 ...
$ ulc : int 1 2 2 2 1 1 1 1 1 1 ...
$ thick : int 676 65 134 290 1208 484 516 1288 322 741 ...
$ sex : int 2 2 2 1 2 2 2 2 1 1 ... ,
We are interested in
days: time on study after operation for malignant melanoma
status: the patient's status at the end of study
Documentation shows the possible values of status are: 1: dead from malignant melanoma 2: alive at end of study 3: dead from other causes. Consider 'dead from other causes' as censored (along with alive).
Thus, status vector should be status == 1 and the survival object is Surv(days, status == 1) (to do some of the problem for you).
a. How many survival times are censored? Obtain an estimate of the survival curve at each event time (along with CI) using the Kaplan-Meier estimate and plot the survival curve and confidence interval.
b. Does survival differ in men and women? Compare asymptotic (log-rank) and exact tests for gender differences? Compare the exact test with a bootstrap approximation. Plot the male and female survival curves.
c. Use Cox regression to carry out the gender comparison of the survival curves in part b. Obtain a confidence interval for the effect of gender on the hazard.
3. Survival with HIV. The data set obtained from read.table("http://www.ats.ucla.edu/stat/r/examples/asa/hmohiv.csv", sep=",", header = TRUE)
contains 100 members of a Health Maintenance Organization (HMO). All of the members are HIV positive. The HMO wants to examine their survival times. Subjects were enrolled in the study from 1/1/89 to 12/31/91. Study ended 12/31/95. After HIV diagnosis members were followed until death due to AIDS, until end of the study, or until lost to followup. In the dataset the survival time is the variable time is in months elapsed between entrydata and enddata. Each member's age in years at the start of followup is recorded in a variable called age. The ages range from 20 to 54 with a median of 35. The censor indicator has value 1 for death due to AIDS and value 0 for lost to followup or alive. In the data set intravenous drug use is recorded as a binary variable called drug, where 1 is
a history of IV drug use and 0 otherwise.
For example subject 1 died from AIDS 5 months after being seen in the HMO clinic while subject 2 was not known to have died from AIDS at the conclusion of the study and had been followed for 6 months.
a. Give a point and interval estimate of the survival times of these AIDS patients. Compare survival times for IV drug users and non-IV drug users.
b. Use Cox regression to investigate age and drug use as predictors of survival time. Check the proportional hazards assumptions and interpret the coefficients from the fit.
c. Repeat part b using the age information recoded into four categories age, "20:29='A'; 30:34='B'; 35:39='C';40:54='D'".
11/12. More survival analysis and analysis of durations
Longitudinal in the news
Processed, sugary and fried foods all contribute to childhood obesity Publication: Consumption Of Specific Foods And Beverages And Excess Weight Gain Among Children And Adolescents
but Soda and junk foods are not making you fat Publication: Fast Food, Soft Drink, and Candy Intake is Unrelated to Body Mass Index for 95% of American Adults
Class Topics
1. Background: renewal processes and hazard functions. Slides on renewal processes and hazard functions
Package 'etm' Empirical Transition Matrix etm presentation
tutorial Computing Cumulative Incidence Functions with
the etmCIF Function, with a view Towards Pregnancy Applications .
2. Revisit Cox Regression. handout from Ch.6 st745 Fox recidivism example (c.f. week 7, review question 3).
3. Design: sample size and power calculations for survival analysis. Function lrSS in package survMisc. Package powerSurvEpi
4. Parametric Survival Models, survreg package flexsurv vignette for flexsurv
5. Interval Censoring; breast cancer data. interval package. Class analysis handout.
New R Package for Analyzing Interval-Censored Survival Data. Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R Package Interval Censoring: Tutorial on methods for interval-censored data and their implementation in R Statistical Modelling 2009; 9(4): 259-297. Interval-Censored Time-to-Event Data
Methods and Applications Chapman and Hall/CRC 2012 (esp Chap 14--glrt). Also intcox {intcox}Cox proportional hazards model for interval censored data
6. Discrete-time survival analysis. Teacher and first-sex examples (ascii) from Willet and Singer (Chap 10,11)
[links in text resource number 3, text data examples] Presentation version Slides for Ch.11
WEEK 8 Review Questions
1. Fox Recidivism data and Additional Diagnostics for Cox Regression.
Use dx function in package survMisc for another look at the Fox Recidivism data from item #2 in Week 8 Class Topics.
a. From the materials in item 2, for the Cox Regression try out the reduced model that omits the wexp variable (which showed some PH problems). Compare models and results.
b. try out the diagnostic plots from dx on this reduced model.
2. More on Week 7 class example, heroin data.
a. In the class example, after seeing a problem with proportional hazards assumption for the clinic variable, we used strata(clinic) which allows different baseline hazards in each clinic with predictors prison and dose. Look at this further by fitting the coxhernSt model seperately within each clinic (i.e. dropping the strata(clinic) term). Are the effects of clinic and dose similar within each clinic?
b. In class question asked whether some model-modification (e.g. interaction terms) in the coxhern model might mitigate the proportional hazards violation in the coxhern model. (Note the Fox tutorial section 4 does a time-dependent modification.) Try out some augmented models using interactions between the predictors in coxhern.
c. The eha package which goes along with the Event History Analysis book linked in week 7 has an alternative to coxph, coxreg which allows bootstrap replications for the Cox regression. Try out coxreg with B=1000 (bootstrap reps) for the coxhern model. Compare standard errors for coefficients from the coxreg or coxph fits with bootstrap standard errors.
3. firstsex example from Willet-Singer. Discrete-time analyses. Part 4 week 8 lecture materials.
Data Example: Grade at First Intercourse. Research Question: Whether, and when, adolescent males experience heterosexual intercourse for the first time? Citation: Capaldi, et al. (1996). Sample: 180 high-school boys. Research Design:
Event of interest is the first experience of heterosexual intercourse. Boys tracked over time, from 7th thru 12th grade. 54 (30% of sample) were virgins (censored) at end of data collection.
The Willet-Singer displays show lifetables and logistic regression estimates for survival analyses.
a. investigate time-to-event as a function of parental transitions (pt = 1, 1 or more transitions) using Kaplan-Meier and cox regression methods shown in class (not really correct for these interval censored data). Compare with the logistic regression results in the Willet-Singer materials.
b. clearly the firstsex data are really interval censored, rather than inately discrete-time. Sex was had sometime during the reported grade. Indicate how you would set up these data for the proper interval censored analysis. See class examples, week 8 section 6.
WEEK 8 Exercises
1. Data frame pbc in the survival package: Mayo Clinic Primary Biliary Cirrhosis Data, a randomized placebo controlled trial of the drug Dpenicillamine. Refer to the documentation. As the helpfile tells you: "The first 312 cases in the data set participated in the randomized trial and contain largely complete data. The additional 112 cases did not participate in the clinical trial...". So pick out the 312 cases that are the D-penicillmain and placebo groups.
For these data 'status': 0=censored, 1=liver transplant, 2=death; so status = 2 represents observed values of time; otherwise censored.
a. Use Kaplan-Meier methods to carry out a simple two-group comparison of the effectiveness of the drug, along with any useful plots.
b. Extend the two-group comparison with a Cox regression using additional predictors (chosen as you wish) age edema log(bili) log(protime) log(albumin). Identify a useful model and Interpret results. Make sure you check the proportional hazards assumptions for your model.
2. melanom data from week 7, exercise 2. Define the censoring as was done in that problem. I found it useful to make a 0,1 variable isMale from the integer sex designation and make a 0,1 variable isUlcer from the ulceration variable (careful there).
a. Repeat the gender comparison in parts b or c in Ex 2, week 7, stratifying on ulceration of the tumor (or not). Compare with the result in Ex 2 week 7 and interpret.
b. Carry out a Cox regression using predictors log(thick) and the gender indicator, stratifying on ulceration. Interpret the results. Check the viability of the proportional hazards assumption for this cox model.
3. Interval Censored Data. Consider the breast cancer data shown in Week 8 lecture; interval-censored breast cosmesis data set of Finkelstein and Wolfe (1985). The data are
from a study of two groups of breast cancer patients, those treated with radiation therapy
with chemotherapy (treatment = "RadChem") and those treated with radiation therapy alone
(treatment = "Rad"). The response is time (in months) until the appearance of breast
retraction, and the data are interval-censored between the last clinic visit before the event
was observed (left) and the first visit when the event was observed (right) (or Inf if the event
was not observed). One location of these data is:
R> library("interval")
R> data("bcos", package = "interval")
Class examples show parametric and non-parametric survival analyses for these interval censored data. Before these methods were available, various Kludges (imputations) existed. One is to take the midpoint of the interval for any observed event in [left, right] or if right is NA (censored) treat as left+ and carry out a survival analysis for right censored data. Repeat the breast cancer example Cox regression using this strategy and compare with the results from week 8 using the interval censoring.
4. More firstsex data. Follow on part b of Review Question 3 and carry out an (appropriate) interval censoring analysis for these data using the procedures from Class Topic 5 of week 8. Again, investigate time-to-event as a function of parental transitions (pt = 1, 1 or more transitions).
5. The uis data are from a set of trials for residential treatment for drug abuse. Obtain the data from the UCLA archive uis = read.table("http://www.ats.ucla.edu/stat/r/examples/asa/uis.csv", sep=",", header = TRUE). There are 628 subjects with a small amount of missing data. The time variable in the dataset is the outcome of interest: time (in days) to return to drug use (self report) measured from admission. The censor variable is in a convenient form with value 1 indicating return to drug use and 0 otherwise (censored observation). The dichotomous race variable is coded 0 for White and 1 for non-White (other). The variable age is age at enrollment (years). The ivhx variable is an indicator of IV drug use history and is coded in the datset (1=never, 2=previous, 3=recent). For use here make a dichotomous variable drug that combines previous and recent versus never as in uis$drug = as.numeric(uis$ivhx==1) (be careful about the direction here as the code makes drugNever = 1). [note function recode in the car package makes this operation easy].
Use these variables in the uis dataset to investigate influences on time to relapse. Formulate a useful Cox regression model, check the proportional hazards assumption, and provide interpretations of the parameter estimates.
11/19. Advanced topics for Time-to-event data. Time-dependent Covariates, Mixed-model Survival Analysis (Recurrent Events, Frailty Models), Joint Modelling of Longitudinal and Time-to-Event Data
Longitudinal in the news
CDC: Syphilis, gonorrhea, chlamydia rates on the rise 2014 Sexually Transmitted Diseases Surveillance
Lecture Topics
0. Class Logistics Problem Set Posting; Schedule +1-unit presentations (Dec 2, 11? 1-3:30).
1. Time-dependent covariates in survival analysis.
a. Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Model Terry Therneau Cindy Crowson Mayo Clinic July 1, 2015. function tmerge in survival package
b. Recidivism data, weekly employment measure (Section 4, Fox tutorial).
week 9 class handout (ascii), recidivism data longer version shown in class (ascii)
John Fox script from Soc761 fold/unfold functions (wide-to-long): Package RcmdrPlugin.survival web posting of function older version Fox tutorial script
2. Mixed effects (Frailty) survival models.
a. Package coxme Terry Therneau July 2014: Cox proportional hazards models containing Gaussian random
effects, also known as frailty models coxme manual. Maintainer Terry Therneau. Mixed Effects Cox Models Terry Therneau Mayo Clinic June 15, 2015
coxme Class handout plain text version
Additional materials. frailtyHL: A Package for Fitting Frailty Models with H-likelihood by Il Do Ha, Maengseok Noh and Youngjo Lee
b. Recurrent events, Frailty models.
Comparing Survivival curves TestSurvRec package: Statistical tests to compare survival curves of two groups with recurrent events.
Class example (ascii) R-session, tumor recurrence in patients with bladder cancer. plots for bladder recurrence
additional R-packages, coxme frailtypack, parfm, survrec, gmrec,, bivrec package etm empirical transition matrix
Recurrent Events: Chapter 9 of Kalbfleisch and Prentice (2nd edition), "Modeling and Analysis of Recurrent Event Data"
Cook, R. J. and Lawless, J. F. (2007). The Statistical Analysis of Recurrent Events. (Stanford access) Springer, New. York.
Additional examples: Frailty models (individual differences, random effects) and Recurrent events (observe multiple on/off transitions and timing). Asthma data example from Duchateau et al (2003). Evolution of Recurrent Asthma Event Rate over Time in Frailty Models Journal of the Royal Statistical Society. Series C (Applied Statistics) 355-363. see also Ch 3 in Frailty Models in Survival Analysis Andreas Wienke Chapman and Hall/CRC 2010
3. Joint Modelling of Longitudinal and Time-to-Event Data
Class handout. JM for aids example (ascii).
R-package JM, Dimitris Rizopoulos Maintainer: Shared parameter models for the joint modeling of longitudinal and time-to-event data. Expository paper JSS 2010, JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data.
Book (Stanford access) Joint Models for Longitudinal and Time-to-Event Data. With Applications in R. Dimitris Rizopoulos. Chapman and Hall/CRC 2012. Book Table of Contents Book website
Survival summary, a remarkable overview of advanced survival analysis topics. Multiple and Correlated Events Terry M. Therneau Mayo Clinic Spring 2009
WEEK 9 Review Questions
1. Fox Recidivism data, once more.
a. The Week 8 class example and RQ1 did crude stratification on age (to adress violations of proportional hazards). As an exercise, carry out the cox regression, stratifying on age in thirds
(more carefully than I did in the class examples) and also stratifying on age split in fifths. Check the proportional hazards assumptions and compare results.
b. Use the fox.long dataset created and shown in Week 9 lecture and run the original coxph in the Fox tutorial and class example. Show that the same results are obtained in the original wide form and long form.
2. Mixed effects Cox regression models, hierarchical (nested) survival data
a. Class example; eortc breast cancer data
Compare results ignoring center, stratifying on centers, and using coxme (in class example) for patients nested within centers.
b. Rat data (see R Journal December 2012).
The data set presented by Mantel et al. (1977) is based
on a tumorigenesis study of 50 (q = 50) litters of female
rats. For each litter, one rat was selected to receive
the drug and the other two rats were placebo treated
controls (ni = 3). Here each litter is treated
as a cluster. The survival time (time) is the time to
development of tumor, measured in weeks. Death
before occurrence of tumor yields a right-censored
observation; forty rats developed a tumor, leading to
censoring of about 73%. The survival times for rats
in a given litter may be correlated due to a random
effect representing shared genetic or environmental
effects.
Compare Cox regression models that investigate effect of the drug (rx)
(i) ignoring litters and (ii) mixed effects models incorporating the nested structure of these data (rats within litters)
3. More on eortc class example, coxme analysis from Terry Therneau vignette.
Class questions motivated extending the anlaysis allowing treatment effects to vary over the 37 centers (random effects in the survival analsysis). In the class example model efit2 included a random effect for centers but set the treatment effect constant (fixed effect) over centers. Therneau's model efit3 allows treatment effects to vary over centers by nesting treatment within centers with the (1 | center/trt) term. Class question asks why not instead use (1 + trt | center) analogous to a two sample t-test within each center, i.e. a survdiff within each center. A further question asked for more detail on random effect for the efit3 model (where the class handout left off.
WEEK 9 Exercises
1. Dialysis Hemodialysis Data from Brazil.
Data on 6805 hemodialysis patients in all federally funded clinics (67 centers) in Rio de Janeiro State, Brazil.
data(Dialysis) package RcmdrPlugin.survival
Format
A data frame with 6805 observations on the following 7 variables.
center a numeric code indicating in which of 67 centers the patient was treated.
age of the patient.
begin The month in which treatment began, with 1 representing January 1998.
end The month in which observation terminated, either because of death or censoring. The study ended in month 44 (August, 2000).
event 1, death, or 0, censoring.
time the difference between end and begin.
disease a factor with levels congen, (congenital); diabetes; hypert (hypertension); other; and renal.
Use Cox regression with age and disease as predictors to study survival time of patients. Follow the in-class analysis of the eortc data to compare results ignoring centers and using a mixed-effects models with random factor center.
12/3. Special Topics for Longitudinal Data and Overflow
Longitudinal in the news
1. Crossover design in real-life. Daily Dose of Walnuts Linked to Health Improvements Can a handful of walnuts a day keep the doctor away?
2. Breast-feeding may cut moms' risk of type 2 diabetes
Lecture topics:
1. Observational Studies (topics from week 6)
A. Cohort effects. Cohort-sequential, Accelerated longitudinal designs. Robinson, K., Schmidt, T. and Teti, D. M. (2008) Issues in the Use of Longitudinal and Cross-Sectional Designs, in Handbook of Research Methods in Developmental Science (ed D. M. Teti), Blackwell Publishing Ltd, Oxford, UK
B. Econometric Approaches to Longitudinal Panel Data. Panel Data Econometrics in R: The plm Package Yves Croissant Giovanni Millo (esp. section 7. "plm versus nlme/lme4" ). R-package plm. See Week 6, item 5. Class handout
C. Interrupted time-series. Interrupted Time Series Quasi-Experiments Gene V Glass Arizona State University. Time Series Analysis with R section 4.6
Did fertility go up after the Oklahoma City bombing? An analysis of births in metropolitan counties in Oklahoma, 1990-1999. Demography, 2005. R package BayesSingleSub: Computation of Bayes factors for interrupted time-series designs
week 10 topics
2. Structural equation models for longitudinal data (don't do it; Myth 7) (handout in week 10 handout collection)
3. Stability over time (Myth 8). Change and Sameness
4. Reciprocal effects ( Myth 9) Rogosa, Encyclopedia of Social Science
5. Missing data (week 6), mice example nhanes data in package mice R-session using mice package
6. Longitudinal Network Data
7. from week 9 Joint Modelling of Longitudinal and Time-to-Event Data
8. In class exam 12/8, discussion and sample questions
Resources
Applications of Structural Equation Models (LISREL, path analysis, Myth 7)
David Rogosa. Casual Models Do Not Support Scientific Conclusions: A Comment in Support of Freedman. Journal of Educational Statistics, Vol. 12, No. 2. (Summer, 1987), pp. 185-195. Jstor link
Theme Song Ballad of the casual modeler http://www.stanford.edu/class/ed260/ballad.mp3
Rogosa, D. R. (March 1994). Longitudinal reasons to avoid structural equation models, UC Berkeley.
Rogosa, D. R. (1993). Individual unit models versus structural equations: Growth curve examples. In Statistical modeling and latent variables, K. Haagen, D. Bartholomew, and M. Diestler, Eds. Amsterdam: Elsevier North Holland, 259-281.
original publication on the longitudinal path analysis: Some Models for Analysing Longitudinal Data on Educational Attainment. Harvey Goldstein Journal of the Royal Statistical Society. Series A (General), Vol. 142, No. 4. (1979), pp. 407-442. Jstor link
Rogosa, D. R., & Willett, J. B. (1985). Satisfying a simplex structure is simpler than it should be. Journal of Educational Statistics, 10, 99-107. Jstor link
Follow-up paper: Two Aspects of the Simplex Model: Goodness of Fit to Linear Growth Curve Structures and the Analysis of Mean Trends. Frantisek Mandys; Conor V. Dolan; Peter C. M. Molenaar. Journal of Educational and Behavioral Statistics, Vol. 19, No. 3. (Autumn, 1994), pp. 201-215.
Jstor link
Stability: Consistency, Change and Sameness (Myth 8)
J.H. Ware Tracking in S. Kotz, N.L. Johnson (Eds.), The Encyclopedia of Statistical Sciences (13th Edn.), Vol. 9 John Wiley, New York (1988)
Rogosa, D. R., Floden, R. E., & Willett, J. B. (1984). Assessing the stability of teacher behavior. Journal of Educational Psychology, 76, 1000-1027. APA link also available from
John Willet's pub page
Rogosa, D. R., & Willett, J. B. (1983). Comparing two indices of tracking. Biometrics, 39, 795-6. JStor link
Rogosa, D. R. Stability section of Individual unit models versus structural equations (link above)
Rogosa, D. R. Stability of school scores from educational assessments:
Confusions about Consistency in Improvement David Rogosa, June 2003 ; Education Writers Association April 2004
Personality research. Stability versus change, dependability versus error: Issues in the assessment of personality over time David Watson Journal of Research in Personality 38 (2004) 319-350.
Some applications: A Stochastic Model for Analysis of Longitudinal AIDS Data J.M.G. Taylor, W.G. Cumberland, Sy J.P.; Journal of the American Statistical Association, Vol. 89, 1994
Tracking of objectively measured physical activity from childhood to adolescence: The European youth heart study. Scandinavian Journal of Medicine & Science in SportsVolume 18, Issue 2, 2007.
Factors Associated With Tracking of BMI: A Meta-Regression Analysis on BMI Tracking. Obesity (2011) 19 5, 1069-1076. doi:10.1038/oby.2010.250
Long-term tracking of cardiovascular risk factors among men and women in a large population-based health system The Vorarlberg Health Monitoring and Promotion Programme. European Heart Journal (2003) 24, 1004-1013.
Journal of Traumatic Stress. Reliability of Reports of Violent Victimization and Posttraumatic Stress Disorder Among Men and Women With Serious Mental Illness Volume 12 Issue4 587 - 599 1999-10-01 Lisa A. Goodman Kim M. Thompson Kevin Weinfurt Susan Corl Pat Acker Kim T. Mueser Stanley D. Rosenberg
Computing: Foulkes-Davis gamma (not in R). A GAUSS program for computing the Foulkes-Davis tracking index for polynomial growth curves TRACK: A FORTRAN program for calculating the Foulkes-Davis tracking index Gerard E. Dallal Computers in Biology and Medicine Volume 19, Issue 5, 1989, Pages 367-371
Reciprocal effects (Myth 9).
Rogosa, D. R. (1980). A critique of cross-lagged correlation. Psychological Bulletin, 88, 245-258. APA site version
Granger Causality. Nobel 2003. Complete Granger
Relationships--and the Lack Thereof--Between Economic Time Series, with Special Reference to Money and Interest Rates. David A. Pierce Journal of the American Statistical Association, Vol. 72, No. 357. (Mar., 1977), pp. 11-26. Jstor
Longitudinal Networks
R-package RSiena manual, RSiena Resource page
Huisman, M. E. and Snijders, T. A. B. (2003). Statistical analysis of longitudinal network data with changing composition. Sociological Methods and Research, 32:253-287.
Application: Kids' friends influence physical activity levels Publication: The Distribution of Physical Activity in an After-school Friendship Network Sabina B. Gesell, Eric Tesdahl, Eileen Ruchman, Pediatrics; originally published online May 28, 2012.
Missing Data. See also Week 6
Multiple Imputation. van Buuren S and Groothuis-Oudshoorn K (2011). mice: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software, 45(3), 1-67. see also multiple imputation online Flexible Imputation of Missing Data. Stef van Buuren Chapman and Hall/CRC 2012. Chapter 9, Longitudinal Data Sec 3.8 Multilevel data. He is the originator of mice
CHAPTER 17 Incomplete data: Introduction and overview. Longitudinal Data Analysis Edited by Geert Verbeke , Marie Davidian , Garrett Fitzmaurice , and Geert Molenberghs Chapman and Hall/CRC 2008. Also CHAPTER 21 Multiple imputation Michael G. Kenward and James R. Carpenter and CHAPTER 22 Sensitivity analysis for incomplete data. online supplement for LDA book . van Buuren S (2010). Multiple Imputation of Multilevel Data. In JJ Hox, K Roberts (eds.), The Handbook of Advanced Multilevel Analysis, chapter 10, pp. 173{196. Routledge, Milton Park, UK
Handling drop-out in longitudinal studies (pages 1455-1497) Joseph W. Hogan, Jason Roy and Christina Korkontzelou, Statistics in Medicine 15 May 2004 Volume 23, Issue 9. (SAS implementations)
Bayesian approach. Missing Data in Longitudinal Studies. Strategies for Bayesian Modeling and Sensitivity Analysis Joseph W . Hogan and Michael J . Daniels Chapman and Hall/CRC 2008 Ch 5 Missing Data Mechanisms and
Longitudinal Data Corresponding talk, A Brief Tour of Missing Data in Longitudinal Studies Mike Daniels
Overview and applications paper: Assessing missing data assumptions in longitudinal studies: an example using a smoking cessation trial Xiaowei Yanga, Steven Shoptawb. Drug and Alcohol Dependence Volume 77, Issue 3, 7 March 2005, Pages 213-225
R resources. Multivariate Analysis Task View, Missing data section, esp packages mice and mi R-package pan Multiple imputation for multivariate panel or clustered data. Schafer tech report Schafer talk: Missing Data in Longitudinal Studies: A Review
Efficient ways to impute incomplete panel data. Kristian Kleinke · Mark Stemmler · Jost Reinecke ·Friedrich Losel AStA Adv Stat Anal (2011) 95:351-373 DOI 10.1007/s10182-011-0179-9
WEEK 10 Review Questions
1. Stability of Individual Differences
For the Ramus data (week 2 exercise, 20 individuals, 4 time points), the Foulkes-Davis (gamma) index of tracking has point estimate .83 and (bootstrap) standard error .06 for the 18-month time interval 8yrs to 9.5 years. Compare
that estimate of consistency of individual differences with time1-time2 correlations for the time intervals [8, 9.5] and [9, 9.5].
2. Path Analysis. Replicate the 3-wave path analysis example based on the Goldstein model for UK reading scores. Use the perfectly measured data Xi(t) in Week 1 Myths chapter data examples and description. Repeat with the fallible X(t) and compare results.
3. Try a path analysis on the 4-waves of the Ramus data. Compare with the growth curve analyses in week 2 exercises. (Solution: see pages 52-54 of 1994 Myths chap on class memory stick)