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Optimal structural nested models for optimal sequential decisions. (English) Zbl 1279.62024
Lin, D. Y. (ed.) et al., Proceedings of the second Seattle symposium in biostatistics. Analysis of correlated data, Seattle, WA, USA, November 20–21, 2000. New York, NY: Springer (ISBN 0-387-20862-3/pbk). Lecture Notes in Statistics 179, 189-326 (2004).
Summary: I describe two new methods for estimating the optimal treatment regime (equivalently, protocol, plan or strategy) from very high dimensional observational and experimental data: (i) g-estimation of an optimal double-regime structural nested mean model (drSNMM) and (ii) g-estimation of a standard single regime SNMM combined with sequential dynamic-programming (DP) regression. These methods are compared to certain regression methods found in the sequential decision and reinforcement learning literatures and to the regret modelling methods of S. A. Murphy [J. R. Stat. Soc., Ser. B, Stat. Methodol. 65, No. 2, 331–366 (2003; Zbl 1065.62006)]. I consider both Bayesian and frequentist inference. In particular, I propose a novel “Bayes-frequentist compromise” that combines honest subjective non- or semiparametric Bayesian inference with good frequentist behavior, even in cases where the model is so large and the likelihood function so complex that standard (uncompromised) Bayes procedures have poor frequentist performance.
For the entire collection see [Zbl 1058.62104].

62C05 General considerations in statistical decision theory
62-07 Data analysis (statistics) (MSC2010)
62C99 Statistical decision theory
62P10 Applications of statistics to biology and medical sciences; meta analysis
90C90 Applications of mathematical programming
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