Quintile stratification based on a misspecified propensity score in longitudinal treatment effectiveness analyses of ordinal doses

The propensity adjustment provides a strategy to reduce the bias in treatment effectiveness analyses that compare non-equivalent groups such as seen in observational studies [Rosenbaum P.R., Rubin D.B., 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 41–55]. The objective of this simulation study is to examine the effect of omitting confounding variables from the propensity score on the quintile-stratified propensity adjustment in a longitudinal study. The primary focus was the impact of a misspecified propensity score on bias. Three features of the omitted confounding variables were examined: type of predictor variable (binary vs. continuous), constancy over time (time-varying vs. time-invariant), and magnitude of the association with treatment and outcome (null, small, and large odds ratios). The simulation results indicate that omission of continuous, time-varying confounders that are strongly associated with treatment and outcome (i.e., an odds ratio of 1.75) adversely impacts bias, coverage, and type I error. Omitted time-varying continuous variables had somewhat more effect on bias than omitted binary variables. Time-invariant confounding variables that are not included in the propensity score have a much less effect on results. This evaluation only examined continuous treatment effectiveness outcomes and the propensity scores used for stratification included just four variables. Relative to the use of the propensity adjustment in applied settings that typically comprise numerous potential confounding variables, the impact of one omitted continuous, time-varying confound in this simulation study could be overstated.