Mathematics – Statistics Theory
Scientific paper
2011-03-08
Annals of Statistics 2011, Vol. 39, No. 1, 131-173
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/10-AOS830 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
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.
Joffe Marshall M.
Small Dylan S.
Zhang Mingyuan
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