Effects of Misspecification of the Propensity Score on Estimators of Treatment Effect
Biometrics, 49 (4):
1231--1236 (1993)Abstract
A comparison was carried out between the propensity score
and prognostic models in estimating treatment effects from
observational studies. One issue investigated was the
effect of estimating the propensity score on estimators of
treatment effect. It was found that estimating the
propensity score introduced no additional bias. A second
question addressed comparisons of the propensity score and
prognostic approach when a confounder is omitted. The
results indicate that biases due to omitted covariates are
large and of the same magnitude. Third, misspecifications
of the propensity score were compared to misspecified
response models. Here it was found that estimators obtained
from incorrect response models had much larger biases than
estimators from incorrectly estimated propensity scores. In
all cases there were two types of models, one involving a
continuous and one a binary response. Least squares
estimators for the continuous response were compared to
stratified mean differences between treatment groups. For
the binary response maximum likelihood estimators of the
odds ratio were compared to Mantel-Haenszel estimators. In
both cases the strata were based on the quintiles of the
true and estimated propensity scores.