Stat209/Ed260/HRP239 D Rogosa 2/24/19
Assignment 7.
Compliance and experimental protocols; intent to treat
Problem 1
Non-compliance. Class example week 7.
Adapted from (linked on class page):
An introduction to instrumental variables for epidemiologists,
Sander Greenland, International Journal of Epidemiology 2000;29:722-729
Additional Reference:
Sommer and Zeger (1991). On Estimating Efficacy from Clinical
Trials. Statistics in Medicine
Greenland discusses randomized trials with non-compliance where
Z indicates treatment assignment, which is randomized; X indicates
treatment received, which is affected but not fully determined by
assignment Z.
To illustrate Greenland presents in his Table 1 individual one-
year mortality data from a cluster-randomized trial of vitamin A
supplementation in childhood. Of 450 villages, 229 were assigned
to a treatment in which village children received two oral doses
of vitamin A; children in the 221 control villages were assigned
none. This protocol resulted in 12,094 children assigned to the
treatment (Z = 1) and 11,588 assigned to the control (Z = 0).
Only children assigned to treatment received the treatment; that
is, no one had Z = 0 and X = 1. Unfortunately, 2419 (20%) of
those assigned to the treatment did not receive the treatment
(had Z = 1 and X = 0), resulting in only 9675 receiving treatment
(X = 1). Class handout has depiction and Greenland's
table of results. Use as the outcome measure Y, the Deaths per 100,000
within one year (labeled Risk in Greenland's Table 1).
Part 1,
using data summary from class handout
a. Give the ITT (intent-to-treat) estimate of the effect of vitamin A on Risk
b. What is the compliance rate in the treatment group (Z=1)? In the control
group (Z=0)?
c. What is the instrumental variables estimate (following Angrist Imbens Rubin)
of the effect of vitamin A on Risk? What interpretation is given to this
estimate (c.f. Booil Jo presentation)? Compare with part (a) result and comment.
Part 2
Don Rubin has a great overview talk
For Objective Causal Inference, Design Trumps Analysis Don Rubin, posted at
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/trumps.pdf
Starting pdf page 21 Rubin takes up noncompliance using the Viamin A data (slightly different
tabulated values than in the Greenland paper handout)
d. Recreate the calculations (ITT As-treated, Per Protocol) shown on pdf p.23;
refer to Booil Jo handout
e. also CACE estimate pdf p.24
The Bayesian estimates (Imbens and Rubin 1997) pdf page 25 onward are implimented in
part in the experiment package (Imai) mentioned in class and class materials.
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Problem 2
From the Booil Jo presentation slides in lecture, consider the
JHU PIRC Intervention Study: N=284
Estimate Intervention Effects With Noncompliance
The Johns Hopkins Public School Preventive Intervention Study was
conducted by the Johns Hopkins University Preventive Intervention
Research Center (JHU PIRC) in 1993-1994 (lalongo et al., 1999~
The study was designed to improve academic achievement and to
reduce early behavioral problems of school children. Teachers and
first-grade children were randomly assigned to intervention
conditions. The control condition and the Family-School
Partnership Intervention condition are compared in this example.
In the intervention condition, parents were asked to implement 66
take-home activities related to literacy and mathematics over a
six-month period. One of the major outcome measures in the JHU
PIRC preventive trial was the TOCA-R (Teacher Observation of
Classroom Adaptation)
• Completed at least 45 activities = compliers.
• Outcome: change score (baseline - followup) of anti-social behavior .
From the means and compliance data given in the class materials
(also linked Booil talk)
compute treatment effect estimate of change in anti-social
behavior: give ITT estimate and CACE estimate
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Problem 3
Artificial data in the image of Efron-Feldman
data frame containing Compliance, Group, and Outcome in
file http://web.stanford.edu/~rag/stat209/hw7efdata
Obtain ITT estimate of group (treatment) effect with a
confidence interval.
Try using G as an instrument for the Y ~ comp regression.
What does that produce?
Alternatively use the Rubin formulation with a dichotomous
compliance indicator defined as TRUE for compliance > .8
in these data. What is your CACE estimate. What assumptions
did you make? Compare with ITT estimate.
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end HW7 2019