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Using regression models to analyze randomized trials: asymptotically valid hypothesis tests despite incorrectly
Michael Rosenblum1, Mark J van der Laan
1Center for AIDS Prevention Studies, University of California, San Francisco, California 94105, USA. mrosenblum@csail.mit.edu
Biometrics
|February 13, 2009
Summary
Standard regression tests in randomized trials maintain correct error rates for large samples, even with misspecified models. This finding enhances the reliability of hypothesis testing in clinical trial analysis.
Area of Science:
- Statistics
- Biostatistics
- Clinical Trial Analysis
Background:
- Regression models are frequently used to infer cause-effect relationships from randomized trial data.
- Commonly used models like linear and logistic regression may fail to capture true variable relationships, leading to erroneous conclusions.
- Model misspecification is a significant concern in hypothesis testing for randomized trials.
Purpose of the Study:
- To evaluate the accuracy of hypothesis tests for treatment effects on primary outcomes in randomized trials.
- To determine if standard regression-based tests maintain correct Type I error rates for large samples, even with model misspecification.
- To investigate the robustness of hypothesis tests across various regression models.
Main Methods:
- Focus on hypothesis tests examining treatment effects on the mean outcome within subgroups defined by baseline variables (e.g., age, sex).
- Utilize robust variance estimators in standard regression-based hypothesis tests.
- Analyze a broad class of commonly used regression models, including Poisson regression.
Main Results:
- Standard regression-based hypothesis tests, when employing robust variance estimators, are guaranteed to have correct Type I error rates for large samples.
- This robustness holds true even when the underlying regression models are incorrectly specified.
- The study identifies this robustness as previously unrecognized for Poisson and other common regression models.
Conclusions:
- Model-based hypothesis tests in randomized trials demonstrate significant robustness to model misspecification when using robust variance estimators.
- These findings bolster confidence in the reliability of widely used statistical tests for analyzing clinical trial data.
- The results have practical implications for interpreting the validity of conclusions drawn from randomized trial analyses.
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