A dynamic regime is a function that takes treatment and covariate history and baseline covariates as inputs and returns a decision to be made. Murphy (2003, Journal of the Royal Statistical Society, Series B 65, 331-366) and Robins (2004, Proceedings of the Second Seattle Symposium on Biostatistics, 189-326) have proposed models and developed semiparametric methods for making inference about the optimal regime in a multi-interval trial that provide clear advantages over traditional parametric approaches. We show that Murphy's model is a special case of Robins's and that the methods are closely related but not equivalent. Interesting features of the methods are highlighted using the Multicenter AIDS Cohort Study and through simulation.
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