Chapter

Proceedings of the Second Seattle Symposium in Biostatistics

Volume 179 of the series Lecture Notes in Statistics pp 189-326

Optimal Structural Nested Models for Optimal Sequential Decisions

  • James M. RobinsAffiliated withDepartments of Epidemiology and Biostatistics, Harvard School of Public Health

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Abstract

I describe two new methods for estimating the optimal treatment regime (equivalently, protocol, plan or strategy) from very high dimesional 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 Murphy (2003). 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.