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Testing treatment effects in unconfounded studies under model misspecification: logistic regression, discretization,
M Z Cangul1, Y R Chretien, R Gutman
1Department of Statistics, Harvard University, Science Center, Cambridge, MA 02138-2901, USA.
Statistics in Medicine
|July 3, 2009
Summary
Logistic regression for treatment effects is invalid if covariate distributions differ. Discretizing covariates and using regression adjustment within intervals corrects this flaw for valid hypothesis testing.
Area of Science:
- Biostatistics
- Epidemiology
- Observational Studies
Background:
- Logistic regression is a standard method for analyzing treatment effects in observational research.
- Differences in continuous covariate distributions between treatment and control groups can invalidate standard logistic regression tests.
- This issue persists even in unbiased studies if the assumed link function is not logistic.
Purpose of the Study:
- To identify the conditions under which logistic regression yields invalid hypothesis tests for treatment effects.
- To propose and validate a method for obtaining accurate hypothesis tests when covariate distributions differ.
Main Methods:
- The study analyzes the impact of differing covariate distributions on logistic regression validity.
- It evaluates the effectiveness of covariate discretization as a standalone method.
- A valid approach combining discretization and regression adjustment within intervals is proposed.
Main Results:
- Standard logistic regression provides invalid hypothesis tests when continuous covariate distributions differ between groups.
- Discretizing the covariate alone does not resolve this invalidity issue.
- Discretization followed by regression adjustment within intervals yields a valid hypothesis test.
Conclusions:
- Researchers must be cautious when using logistic regression with continuous covariates in observational studies.
- Covariate distribution differences necessitate alternative analytical strategies for valid inference.
- Discretization combined with interval-specific regression adjustment offers a robust solution.
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