Date of this Version
The Annals of Statistics
Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set collected following a massive flood in Bangladesh, estimating the effect of diarrhea on children’s height. Results from different methods are compared in both simulation and the real application.
casual inference, continuous-time process, deterministic model, diarrhea, g-estimation, longitudinal data, structural nested model
Zhang, M., Joffe, M. M., & Small, D. S. (2011). Causal Inference for Continuous-Time Processes When Covariates Are Observed Only at Discrete Times. The Annals of Statistics, 39 (1), 131-173. http://dx.doi.org/10.1214/10-AOS830
Date Posted: 27 November 2017
This document has been peer reviewed.