Propensity score adjustment of effect estimates in observational studies of treatment is a common technique used to control for bias in treatment assignment. In situations where matching on propensity score is not possible or desirable, regression adjustment and stratification are two options. Regression adjustment is used most often and can be highly efficient, but it can lead to biased results when model assumptions are violated. Validity of the stratification approach depends on fewer model assumptions, but is less efficient than regression adjustment when the regression assumptions hold. To investigate these issues, by simulation we compare stratification and regression adjustments. We consider two stratification approaches; equal frequency classes and an approach the attempts to minimize the mean squared error (MSE) of the treatment effect estimate. The regression approach we consider is a Generalized Additive Model (GAM), that flexibly estimates the relations among propensity score, treatment assignment, and outcome. We find that, under a wide range of plausible data generating distributions, the GAM approach outperforms stratification in treatment effect estimation with respect to bias, variance, and thereby MSE. We illustrate approaches via analysis of data on insurance plan choice and its relation to satisfaction with asthma care.
Statistical Methodology | Statistical Theory
Myers, Jessica A. and Louis, Thomas A., "REGRESSION ADJUSTMENT AND STRATIFICATION BY PROPENSTY SCORE IN TREATMENT EFFECT ESTIMATION" (January 2010). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 203.