Estimation of time-varying treatment effects using marginal structural models dependent on partial treatment history

Inverse probability (IP) weighting of marginal structural models (MSMs) can provide consistent estimators of time-varying treatment effects under correct model specifications and identifiability assumptions, even in the presence of time-varying confounding. However, this method has two problems: (i) inefficiency due to IP-weights cumulating all time points and (ii) bias and inefficiency due to the MSM misspecification. To address these problems, we propose (i) new IP-weights for estimating parameters of the MSM that depends on partial treatment history and (ii) closed testing procedures for selecting partial treatment history (how far back in time the MSM depends on past treatments). We derive the theoretical properties of our proposed methods under known IP-weights and discuss their extension to estimated IP-weights. Although some of our theoretical results are derived under additional assumptions beyond standard identifiability assumptions, some of which can be checked empirically from the data. In simulation studies, our proposed methods outperformed existing methods both in terms of performance in estimating time-varying treatment effects and in selecting partial treatment history. Our proposed methods have also been applied to real data of hemodialysis patients with reasonable results.