Stable inverse probability weighting estimation for longitudinal studies

We consider estimation of the average effect of time-varying dichotomous exposure on outcome using inverse probability weighting (IPW) under the assumption that there is no unmeasured confounding of the exposure-outcome association at each time point. Despite the popularity of IPW, its performance is often poor due to instability of the estimated weights. We develop an estimating equation-based strategy for the nuisance parameters indexing the weights at each time point, aimed at preventing highly volatile weights and ensuring the stability of IPW estimation. Our proposed approach targets the estimation of the counterfactual mean under a chosen treatment regime and requires fitting a separate propensity score model at each time point. We discuss and examine extensions to enable the fitting of marginal structural models using one propensity score model across all time points. Extensive simulation studies demonstrate adequate performance of our approach compared with the maximum likelihood propensity score estimator and the covariate balancing propensity score estimator.