Causal Inference for Continuous-Time Processes When Covariates Are Observed Only at Discrete Times
Penn collection
Degree type
Discipline
Subject
continuous-time process
deterministic model
diarrhea
g-estimation
longitudinal data
structural nested model
Statistical Methodology
Statistics and Probability
Vital and Health Statistics
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Contributor
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.