Comparing approaches to causal inference for longitudinal data: inverse probability weighting versus propensity scores.

In observational studies for causal effects, treatments are assigned to experimental units without the benefits of randomization. As a result, there is the potential for bias in the estimation of the treatment effect. Two methods for estimating the causal effect consistently are Inverse Probability of Treatment Weighting (IPTW) and the Propensity Score (PS). We demonstrate that in many simple cases, the PS method routinely produces estimators with lower Mean-Square Error (MSE). In the longitudinal setting, estimation of the causal effect of a time-dependent exposure in the presence of time-dependent covariates that are themselves affected by previous treatment also requires adjustment approaches. We describe an alternative approach to the classical binary treatment propensity score termed the Generalized Propensity Score (GPS). Previously, the GPS has mainly been applied in a single interval setting; we use an extension of the GPS approach to the longitudinal setting. We compare the strengths and weaknesses of IPTW and GPS for causal inference in three simulation studies and two real data sets. Again, in simulation, the GPS appears to produce estimators with lower MSE.