Abstract
Let A(t) represent a time-dependent action process as observed on a randomly sampled subject. A general example can be A(t) =(A1(t),A2(t),A3(t),A4(t)), where A1 (t) = I(C ≤ t) jumps to 1 when the subject is right-censored, A2 (t) is a counting process that jumps when the subject is monitored, A3(t) indicates which of the covariates are measured at time t, and A4(t) denotes the treatment that the subject receives at time t. In other words, A(t) can denote both censoring/missingness and treatment actions. Let A be the set of possible sample paths of A(·). For technical reasons and simplicity, we will assume that A(t) only changes values at given time points t = 1, 2, ... , p and that A is finite. We note that this does not diminish the practical applicability of the methods presented in this chapter since one can approximate a continuous action process with an arbitrarily fine discrete approximation. In addition, we will present the formulas in such a way that they can be applied to continuous data as well, although we do not present regularity conditions and proofs
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© 2003 Springer Science+Business Media New York
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van der Laan, M.J., Robins, J.M. (2003). Unified Approach for Causal Inference and Censored Data. In: Unified Methods for Censored Longitudinal Data and Causality. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21700-0_6
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DOI: https://doi.org/10.1007/978-0-387-21700-0_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3055-2
Online ISBN: 978-0-387-21700-0
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