Bias associated with using the estimated propensity score as a regression covariate

Area of Science:

• Biostatistics
• Epidemiology
• Health Services Research

Background:

• Propensity score methods are widely used in public health and medical research to address selection bias in observational studies.
• A common practice involves using the propensity score as a covariate in regression models.

Purpose of the Study:

• To investigate the bias in treatment effect estimation when propensity scores are used as covariates in nonlinear regression models.
• To compare the performance of different propensity score adjustment methods through simulation.

Main Methods:

• A Monte Carlo simulation study was conducted.
• Evaluated bias in linear and nonlinear regression models (logistic, Cox proportional hazards).
• Compared covariate adjustment with propensity score stratification, matching, inverse probability of treatment weighting, and spline-based nonparametric estimation.

Main Results:

• Bias in treatment effect estimation was demonstrated when using estimated propensity scores as covariates, even in linear regression.
• Propensity score matching performed well when the treated group was a subset of the control group.
• Model-based adjustment showed advantages when covariate overlap between groups was limited.

Conclusions:

• Adjusting for propensity scores via stratification or matching, followed by regression or spline methods, is a practical and effective strategy.
• The choice of method depends on the degree of covariate overlap between treatment groups.