Causal inference for continuous-time processes when covariates are observed only at discrete times

TL;DR

This paper addresses causal inference in continuous-time processes with discrete observations, proposing methods that improve upon traditional g-estimation when assumptions are violated, demonstrated through simulations and real data from Bangladesh.

Contribution

It introduces a controlling-the-future method for causal inference in continuous-time models observed discretely, relaxing assumptions needed for g-estimation and ensuring consistency in broader scenarios.

Findings

Controlling-the-future method performs well when g-estimation fails.

Methods are validated on simulated data and real flood-related health data.

Proposed approach offers more reliable causal estimates under less restrictive assumptions.

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.