Covariate Adjustment in Randomized Trials
1
Covariate Adjustment: Opportunities and Challenges
1.1
Using this Book
1.2
Case Studies
1.2.1
Buprenorphine tapering schedule and illicit opioid use: CTN-03
1.2.2
Functional Outcome in Hemorrhagic Stroke: MISTIE III
2
Introduction
2.1
Notation and Assumptions
2.2
The Analysis of Covariance (ANCOVA)
2.3
Generalizing the ANCOVA: G-computation
2.4
Combining Covariate Adjustment and Stratified Randomization
3
Targets of Inference: Estimands
3.1
Estimands for Continuous and Binary Outcomes
3.1.1
Difference in Means
3.1.2
Ratio of Means
3.2
Estimands for Ordinal Outcomes
3.2.1
Difference in Mean Utility
3.2.2
Mann-Whitney (M-W) Estimand
3.2.3
Log Odds Ratio (LOR)
3.3
Survival/Time-To-Event Outcomes
3.3.1
Survival Function
3.3.2
Hazard Ratio
3.3.3
Restricted Mean Survival Time
4
Using R
4.1
Installing Packages
4.1.1
Packages from CRAN
4.1.2
Packages from Github
4.1.3
Loading Packages into Workspace
4.2
Loading the Data: MISTIE-III
4.3
Assessing Baseline Balance
4.4
Visualizing Data
4.5
Fitting Regression Models
4.5.1
Generalized Linear Model
4.5.2
Logrank Test and Cox Proportional Hazards Model
4.6
Variance Estimation
4.6.1
Robust Standard Errors
4.6.2
Bootstrap Estimator
4.7
Addressing Multiplicity
5
Applying Covariate Adjustment: ANCOVA & G-Computation
5.1
Computing the Estimate
5.2
Standard Error & Inference
5.3
Calculating Precision Gain
5.4
Covariate Adjustment with Binary Outcomes
5.5
Stratified Randomization & Covariate Adjustment
5.6
Missing Outcome Data: Inverse Weighting
6
Doubly Robust Estimators
6.1
Augmented Inverse Probability Weighted Estimation
6.2
Targeted Maximum Likelihood Estimation
7
Time-To-Event Outcomes
7.1
Unadjusted Estimators
7.1.1
Kaplan-Meier Estimator
7.1.2
Logrank Test
7.1.3
Cox Proportional Hazards Model
7.1.4
Survival Probability
7.1.5
Restricted Mean Survival Time (RMST)
7.2
Covariate-Adjusted Estimators
7.2.1
Covariate Adjusted Estimates of Survival Function
7.2.2
Conditional Hazard Ratio
7.2.3
Marginal Hazard Ratio
7.2.4
Survival Probability
7.2.5
Restricted Mean Survival Time (RMST)
8
Group Sequential Designs
8.1
Group Sequential Designs
8.2
Power & Sample Size Calculations
8.3
Analyses: Unadjusted and Adjusted
9
Information Adaptive Designs
9.1
Information Adaptive Designs
9.2
Power & Sample Size Calculations
9.3
Analyses: Unadjusted and Adjusted
10
Protocol and Statistical Analysis Plan Considerations
10.1
Study Protocol
10.1.1
Sample Size Justification (9.4.1)
10.1.2
General Approach (9.4.1)
10.1.3
Analysis of the Primary/Secondary Endpoints (9.4.2-3)
11
Guidance on Applying Covariate Adjustment
11.1
Relevant Regulatory Guidance
11.2
Missing Covariates
11.3
Statistical Analysis Plans
11.4
Sample size for adjusted vs. unadjusted
11.5
Number of parameters vs. sample size
11.6
Data-Adaptive Covariate Adjustment
12
Appendices
12.1
Appendix A: Glossary of Terms
12.2
Appendix B: Resources for Using R
12.3
Appendix C:
References
Published with bookdown
Covariate Adjustment in Randomized Trials
Chapter 6
Doubly Robust Estimators
6.1
Augmented Inverse Probability Weighted Estimation
6.2
Targeted Maximum Likelihood Estimation