Statistics 222,   Education 351A  Autumn 2017
    Statistical Methods for Longitudinal Research

David Rogosa Sequoia 224,   rag{AT}stat{DOT}stanford{DOT}edu   
       Office Hours after class (plus additional TBA)
Course web page: http://rogosateaching.com/stat222//



                To see full course materials from Autumn 2015 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  160-321 Wallenberg Hall, Main Quad
Rogosa Office Hour: 5:15 - 5:50PM,  Sequoia 224 
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) 


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
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   [note: Harvard links broken in August, now (9/21) fine]
2. 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)
3. 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
Original Bates-Pinheiro text (2000).  Mixed-Effects Models in S and S-PLUS (Stanford access). Appendix C has non-linear regression models.
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
4. 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
5. 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     earlier version    associated exercises:  Lab 1  Lab2  Lab3
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
13. Advanced survival analysis topics.
   Interval-Censored Time-to-Event Data Methods and Applications Chapman and Hall/CRC 2012 (esp Chap 14--glrt).
   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.
    Joint Models for Longitudinal and Time-to-Event Data. With Applications in R. Dimitris Rizopoulos. Chapman and Hall/CRC 2012(Stanford access)    Book website

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   
David Roxbee Cox, Peter A. W. Lewis The statistical analysis of series of events. Chapman and Hall, 1966
  Google books    Poisson process computing program
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 12, 2017   3:30-6:30 p.m.  Location: Sequoia 200 (Statistics).
           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   

Course Problem Set 2017    posted xxxxxxx
  
Cumulative Collection of Course Handounts 2017

Statistical computing
Class presentation will be in, and students are encouraged to use, R (occasionally, some references to SAS and Mathematica).
Current version of R is R version 3.4.1 (Single Candle) released 2017-06-30.
    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

9/28. First class: Course Overview, Individual Trajectories.
In the news
1.   Sedentary behavior can cause death (Daily Mail).  Publication: Patterns of Sedentary Behavior and Mortality in U.S. Middle-Aged and Older Adults: A National Cohort Study. Ann Intern Med. 2017.
2. Four cups of coffee a day could slash chance of early death  (Telegraph)     Higher coffee consumption associated with lower risk of early death
3. Can drinking a little bit help you live longer?   Publication: Relationship of Alcohol Consumption to All-Cause, Cardiovascular, and Cancer-Related Mortality in U.S.  Journal of the American College of Cardiology Volume 70, Issue 8, August 2017 DOI: 10.1016/j.jacc.2017.06.054
Also People who drink alcohol every day are less likely to get dementia, according to a new study

Lecture Topics
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
        aditional expositions of AIDS data, Poisson regression:  Duke   Kentucky
    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 (SU access)


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.
Solution for question 1
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
Solution for question 2
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
Solution for question 3
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 remediation. 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
Solution for question 4
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'.


10/5. Analysis of collections of growth curves (Mixed-effects Models, lmer)   Constant rate of change models

In the news
Breakfast.   Skipping breakfast may double risk of hard arteries    Publication: The Importance of Breakfast in Atherosclerosis Disease Insights From the PESA Study Journal of the American College of Cardiology Volume 70, Issue 15, October 2017 DOI: 10.1016/j.jacc.2017.08.027

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)

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

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 likelihood 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.       
 Solution for Review Question 1       2017 redo/update using 3.3.3 (barebones)
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   and   2017 redo/check of widetolong.     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)       
 Solution for Review Question 2
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).       
 Solution for Review Question 3
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.

WEEK 2 Exercises
1. Tolerance data [note: 10/12/17 data location updated]
A subsample of data from the National Youth Survey is obtained in long-form by
read.table("https://stats.idre.ucla.edu/wp-content/uploads/2016/02/tolerance1_pp.txt", sep=",", header=T)
and in wide form by
read.table("https://stats.idre.ucla.edu/wp-content/uploads/2016/02/tolerance1.txt", sep=",", header=T)
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.


10/12.  Collections of growth curves continued: linear and non-linear mixed-effects models

In the news
Marriage troubles linked to health problems for men (NY Post).   Publication: Changes in marital quality over 6 years and its association with cardiovascular disease risk factors in men: findings from the ALSPAC prospective cohort study BMJ's Journal of Epidemiology & Community Health, Oct 2017.

Lecture Topics
0. Review model formulation, North Carolina example (week 2 handouts),
a. plotting residuals ,   ascii session.
b. lm and gee alternatives (ignore individual growth). ascii session
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?.       
 Solution for Review Question 1
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).       
 Solution for Review Question 2
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.       
 Solution for Review Question 3
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.       
 Solution for Review Question 4

WEEK 3 Exercises
1. Teen age drinking. [note: data location updated 10/12/17]
The UCLA data archive has a comma delimited file (access by read.table("https://stats.idre.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.



10/19. Special case of time-1, time-2 data; Traditional measurement of change and more
Longitudinal in the news
Skipping breakfast may double risk of hard arteries     Publication: The Importance of Breakfast in Atherosclerosis Disease Insights From the PESA Study  Journal of the American College of Cardiology Volume 70, Issue 15, October 2017 DOI: 10.1016/j.jacc.2017.08.027

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
        Technical results: Section 3.2.2 esp Equation 27 in Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203-228.      Talk slides
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 overview
    2017 Analysis handout     Extended BK lmer analysis
Additional stuff
     BK repeated measures analysis      pdf version
    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.
Myths Talk. Rogosa, D. R. (1983)
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).       
 Solution for Review Question 1
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.        
 Solution for Review Question 2
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
      
 Solution for Review Question 3
4. 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?       
 Solution for Review Question 4
                   part c. Solution Notes on the ALA (Laird-Ware) assertion

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 Review Question 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.


10/26.  Experimental Protocols and Comparing Group Growth

Longitudinal in the news
One thing at a time. Why listening to a podcast while running could harm performance    Publication: A trade-off between cognitive and physical performance, with relative preservation of brain function  Scientific Reports 7, Article number: 13709 (2017) nature.com.

More crossover designs.
1.This time with 3 conditions   For Exercise, Nothing Like the Great Outdoors   Publication: Niedermeier M, Einwanger J, Hartl A, Kopp M (2017) Affective responses in mountain hiking-- randomized crossover trial focusing on differences between indoor and outdoor activity. PLoS ONE 12(5): e0177719. https://doi.org/10.1371/journal.pone.0177719
2. Does nutrition science know anything?     Is white or whole wheat bread 'healthier?' Depends on the person    Publication: Bread Affects Clinical Parameters and Induces Gut Microbiome-Associated Personal Glycemic Responses Cell Metabolism, Korem et al DOI: 10.1016/j.cmet.2017.05.002

Lecture Topics
1. 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
2. Multi-wave growth example: Bock Vocabulary data, Repeated Measures anova (with linear, quadratic, cubic contrasts): class example. (note Mirman text uses orthogonal polynomials)
3.  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 (Stanford access)
     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     class handout
   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     class handout
        Rogosa note on formulating (g)lmer models.
4. 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
        basic R analogues, power.t.test   power.anova.test
5. 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 pdf pages 89-93
Technical review: Missing data methods in longitudinal studies: a review   Joseph G. Ibrahimcorresponding author and Geert Molenberghs
More on 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. 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)       
 Solution for Review Question 1
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.       
 Solution for Review Question 2
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?       
 Solution for Review Question 3
4. Repeat Brogan-Kutner lmer analyses from lecture. Just another repitition of BK class handout.
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.       
 Solution for Review Question 4
5. Revisit cross-over design, class example, Lecture item 1. The class example used repeated measures analysis of variance for estimation the effect of the drug in the dialysis example, (I messed up the medical context in class). Repeat that analysis using lmer and show identical results to class example analysis. Also examine the effectiveness, increase in precision, resulting from each subject functioning as their own comparison, rather than having two separate (randomly assigned) treatment and control groups.       
 Solution for Review Question 5

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?
6. 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.
7. Beat the Blues from Chap 12 of HSAUR 2nd ed (resource # 4).
Data in wide form: data("BtheB", package = "HSAUR2"). Chap. 12 describes the cognitive behavioural program and conducts various analyses. 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.



11/2. Comparing Group Growth, continued. Observational Studies, Cohort Designs.

Longitudinal in the news
Another crossover design (from Stat266). RCT (cross-over design). Damn right! The secret of success is swearing: How shouting four letter words can help make you stronger    Swearing can help you boost your physical performance    The full power of swearing is starting to be discovered

Lecture Topics
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 notes   Publication: 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.  class slide
      Austin Nichols slides. Causal inference with observational data A brief review of quasi-experimental methods July 2009
         Angrist Ch 5, MHE. Card and Krueger (1994) data, minumimum wage ex
        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.
Intros: Interrupted Time Series Quasi-Experiments Gene V Glass Arizona State University.
  Time Series Analysis with R section 4.6     Class example: Closing time (glm kludge)
    Rogosa R-session
Original publication (ozone data):
Box, G. E. P. and G. C. Tiao. 1975. Intervention Analysis with Applications to Economic and Environmental Problems." Journal of the American Statistical Association. 70:70-79. SAS example for ozone data     
Applications:
Did fertility go up after the Oklahoma City bombing? An analysis of births in metropolitan counties in Oklahoma, 1990-1999. Demography, 2005.
Box-tiao time series models for impact assessment Evaluation Quarterly 1979
Interrupted time-series analysis and its application to behavioral data Donald P. Hartmann, John M. Gottman, Richard R. Jones, William Gardner, Alan E. Kazdin, and Russell S. Vaught J Appl Behav Anal. 1980 Winter; 13(4): 543-559.
Segmented regression analysis of interrupted time series studies in medication use research. By: Wagner, A. K.; Soumerai, S. B.; Zhang, F.; Ross-Degnan, D.. Journal of Clinical Pharmacy & Therapeutics, Aug2002, Vol. 27 Issue 4, p299-309,
R-packages:
tscountvignette       BayesSingleSub: Computation of Bayes factors for interrupted time-series designs
New resource,   Package Wats        Oklahoma City Fertility analyses
  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   Class handout     Maybe more in Week 10.


WEEK 6 Review Questions
1. Interrupted Time Series example, redux
Create a version of the its 'closing time' example presented in class (example linked above) with the 50 months before intervention having mean fatality = 1 and after intervention mean fatality = 2.
Carry out the glm approximation to the time series analysis.       
 Solution for Review Question 1
2. Observational Studies: Lord's Paradox.   
    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).
Solution to Problem 2 RQ2 solution
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.

4. Time 1 Time 2 observational data, Differences in Differences analysis.
We reuse some time-1, time-2 observational data generated to illustrate Lord's paradox (RQ2) -- gender differences in weight gain. (The 'paradox' is solved by Holland, Wainer, Rubin using potential outcomes.) The set up for these artificial data is females gain, males no change
  corr .7 within gender, equal vars time1 time 2 within gender
means
                M               F
X (t1)         170            120
Y (t2)         170            130 
comparison of "gains" 170 - 170 - (130 - 120) = -10    negative effect males (females gain more).
ancova: 170 - 130 - .7*(170 - 120) = 5 positive male effect
So: does being male cause a student to gain weight or lose weight?   Illustrate forms of diffs-in-diffs analyses.
wide form for these data      long form for these data       
 Solution for Review Question 4

WEEK 6 Exercises
1. Smoking and Lung Function. Data and description available   here  Datasets/ Vlagtwedde-Vlaardingen Study . From these (rather meager) data, what do you make of the effect of being a (self-selected) smoker vs non-smoker throughout the 19 years of this study.
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://stats.idre.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.


11/9. Analysis of Durations: Introduction to Survival Analysis (aka event history) Methods

Longitudinal in the news
Time 1, Time 2 Experiment.  Stents?   A Controversial Experiment Upends The Conventional Wisdom On Heart Stents    Publication: Percutaneous coronary intervention in stable angina (ORBITA): a double-blind, randomised controlled trial The Lancet.

        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 (9) 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)   
An Introduction to Survival Analysis  Mark Stevenson EpiCentre, IVABS, Massey University.   Author R-package   epiR  
An R overview from openintro.org
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. (Stanford access) Sophia Rabe-Hesketh Chapman and Hall/CRC 2000.
Event History Analysis with R. (Stanford access) 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)   2017 update of exact tests
    Cox fits, zph plot
   Using eha package for aml
          Legacy versions SAS    Minitab
2. Heroin (addict) data. Source: D.J. Hand, (et al.) Handbook of Small Data Sets. Properly formatted version   Analyses in Stevenson and Stata expositions above.   Lou Reed, heroin
  ascii version Rogosa R-session class handout
       Additional analyses for heroin: 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.   Another data location (UCLA)
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   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   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.       
 Solution for Review Question 1
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.       
 Solution for Review Question 2
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).       
 Solution for Review Question 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.       
 Solution for Review Question 4

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://stats.idre.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'".


11/16. More survival analysis and analysis of durations

Longitudinal in the news
Sugar bad.    Sugar can fuel cancerous cells    Publication: Fructose-1,6-bisphosphate couples glycolytic flux to activation of Ras.  Nature Communications 8, Article number: 922 (2017)

Class Topics
1. Continue Cox Regression examples. handout from Ch.6 st745
a. Heroin (addict) data. Source: D.J. Hand, (et al.) Handbook of Small Data Sets. Properly formatted version   Analyses in Stevenson and Stata expositions linked week 7. See also week 8, review question 2
  ascii version Rogosa R-session class handout
       Additional analyses for heroin: Bootstrapping, Math 159 Pomona    analysis in SAS (phreg)
Publication Source: Caplehorn, J., Bell, J. 1991. Methadone dosage and the retention of patients inm aintenance treatment. The Medical Journal of Australia,154,195-199.
Additional survival data.
b.   Fox recidivism example     Rogosa R-session(ascii)   (c.f. week 7, review question 3 and week 8, review question 1a for full output).
Recidivism data from John Fox tutorial.   A very nice survival analysis intro plus analyses of Rossi Data
  Source: Rossi PH, Berk RA, Lenihan KJ (1980). Money, Work, and Crime: Some Experimental Results. Academic Press, New York.

2. Interval Censoring; breast cancer data. interval package. Class analysis handout.
Note: to run the interval package you have to fetch package Icens from bioconductor. After installing interval
source("http://bioconductor.org/biocLite.R")
biocLite("Icens")
library(Icens) 
library(interval)
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
3. Discrete-time survival analysis. Teacher and first-sex examples (ascii) from Willet and Singer (Chap 10,11). Note data locations at UCLA repository have moved from www.ats.ucla.edu to stats.idre.ucla.edu
      [links in text resource number 2, text data examples]     Presentation version Slides for Ch.11

4. Background: renewal processes and hazard functions. Slides on renewal processes and hazard functions
       Multistate models: Package 'etm' Empirical Transition Matrix     etm presentation
       tutorial Computing Cumulative Incidence Functions with the etmCIF Function, with a view Towards Pregnancy Applications .

5. Design: sample size and power calculations for survival analysis. See Power Analysis section of Survival Analysis Task View.
    Function lrSS in package survMisc. Package powerSurvEpi
6. Parametric Survival Models,  survreg in survival package. Application to Rossi data in link for 1b.
   Also package flexsurv    vignette for flexsurv


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 Week 7 RQ 3 and Week 8 Class Topics.
a. From the lecture materials 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.       
 Solution for Review Question 1
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.       
 Solution for Review Question 2
3. firstsex example from Willet-Singer. Discrete-time analyses. Part 3 week 8 lecture materials.   Note data locations at UCLA repository have moved from www.ats.ucla.edu to stats.idre.ucla.edu
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.       
 Solution for Review Question 3


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://stats.idre.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.

11/30. 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