002 - Causal inference with cross-temporal design

We propose a cross-temporal design that uses a time-related variable as an instrumental variable for evaluating studies where the treatment is not directly controlled, and important confounders cannot be adjusted due to data limitations. Over time, the rising accessibility of a particular treatment has prompted certain people to take the treatment. In other words, if it were before, they would not have used the treatment. By taking advantage of this rise over time, we formulate an encouragement design using subjects observed from two-time points and partition them into three strata: always-takers, never-takers, and compliers, based on their potential receipt of the treatment at different time points. Because the time may impact the potential outcomes regardless of the receipt of treatment, the usual exclusion restrictions assumptions are violated. Therefore, we introduce the common trends assumption and the weakly identifying assumption to identify the temporal effect and separate it from the desired treatment effect among compliers. The weakly identifying assumption allows the temporal effects of each stratum to be different and correlated. It introduces a hierarchical structure to the data so that the temporal effect of compliers can be estimated through borrowing information from the other two strata. In estimation, we present two approaches for identifying stratification: the cross-temporal matching and the data augmentation (DA) algorithm, and model the data using Bayesian analysis. The simulation results show that the DA with the common trends assumption provides robust estimation performance even when the assumption is violated. Further, given the growth in the Medicare Advantage program (MA) enrollment, we applied the proposed method on estimating the effect of MA on the risk of nursing home residents who were admitted from acute hospital being re-hospitalized in the 30 days after their hospital discharge as compared to the traditional program.

causal inference

observational study

cross-temporal design

difference-in-difference

Bayesian analysis 

Mid-Level

Knowledge

International Conference on Health Policy Statistics 2023