title: CAUSAL INFERENCE FOR CONTINUOUS-TIME PROCESSES WHEN COVARIATES ARE OBSERVED ONLY AT DISCRETE TIMES.
abstract: 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.
authors: University of Pennsylvania.
authors: Mingyuan
authors: M
authors: Zhang
authors: Marshall M
authors: MM
authors: Joffe
authors: Dylan S
authors: DS
authors: Small
keywords: Causal inference; continuous-time process; deterministic model; diarrhea; g-estimation; longitudinal data; structural nested model