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February 2011 Causal inference for continuous-time processes when covariates are observed only at discrete times
Mingyuan Zhang, Marshall M. Joffe, Dylan S. Small
Ann. Statist. 39(1): 131-173 (February 2011). DOI: 10.1214/10-AOS830


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.


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Mingyuan Zhang. Marshall M. Joffe. Dylan S. Small. "Causal inference for continuous-time processes when covariates are observed only at discrete times." Ann. Statist. 39 (1) 131 - 173, February 2011.


Published: February 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1209.62214
MathSciNet: MR2797842
Digital Object Identifier: 10.1214/10-AOS830

Primary: 62P10
Secondary: 62M99

Keywords: Causal inference , continuous-time process , deterministic model , diarrhea , g-estimation , longitudinal data , structural nested model

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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