Variable selection for propensity score models

Abstract

Despite the growing popularity of propensity score (PS) methods in epidemiology, relatively little has been written in the epidemiologic literature about the problem of variable selection for PS models. The authors present the results of two simulation studies designed to help epidemiologists gain insight into the variable selection problem in a PS analysis. The simulation studies illustrate how the choice of variables that are included in a PS model can affect the bias, variance, and mean squared error of an estimated exposure effect. The results suggest that variables that are unrelated to the exposure but related to the outcome should always be included in a PS model. The inclusion of these variables will decrease the variance of an estimated exposure effect without increasing bias. In contrast, including variables that are related to the exposure but not to the outcome will increase the variance of the estimated exposure effect without decreasing bias. In very small studies, the inclusion of variables that are strongly related to the exposure but only weakly related to the outcome can be detrimental to an estimate in a mean squared error sense. The addition of these variables removes only a small amount of bias but can increase the variance of the estimated exposure effect. These simulation studies and other analytical results suggest that standard model-building tools designed to create good predictive models of the exposure will not always lead to optimal PS models, particularly in small studies.

Figure 1

The causal diagram for Simulation Experiment 1.

Figure 2

Variance of unadjusted estimator ${\widehat{\gamma }}_0$ and PS adjusted estimator ${\widehat{\gamma }}_1$ for different values of β₁ for n = 500 and n = 2500.

Figure 3

Contours of the MSE of the PS adjusted estimator relative to the unadjusted estimator, $\text{MSE}({\widehat{\gamma }}_1) / \text{MSE}({\widehat{\gamma }}_0)$.