Variable Selection for the Propensity Score Model: Beyond Main Effects and Linear Relations

Propensity score methods are frequently used to estimate treatment effects in observational studies. The propensity score is usually estimated using a logistic regression model with additive and linear effects. The limited literature on variable selection for the propensity score model is consistent in its suggestion that the propensity score model should include those variables that are prognostically important for the study outcome. However, the existing literature has focused only on main effects and assumed linear relations between continuous variables and outcomes. We used Monte Carlo simulations to study the impact of omitting quadratic terms and interaction terms from the propensity score model when these terms were prognostically important. We compared two formulations of the propensity score model: a simple formulation that included only main effects and omitted all interactions and quadratic terms and a complex formulation that included main effects in addition to prognostically important interactions and quadratic terms. We examined 168 scenarios defined by the nature of the true treatment-selection model, the nature of the true outcome regression model, and by sample size. In 95% of scenarios, bias in estimated risk differences, along with coverage rates of estimated 95% confidence intervals, did not differ between the two specifications of the propensity score model when using inverse probability of treatment weighting. In only 5% of scenarios was bias substantially higher and coverage rates substantially lower when using the simple specification of the propensity score model compared to when using the complex specification of the propensity score model.