Statistical Learning of Origin-Specific Statically Optimal Individualized Treatment Rules

Mark J. van der Laan, Division of Biostatistics, School of Public Health, University of California, Berkeley
Maya L. Petersen, Division of Biostatistics, School of Public Health, University of California, Berkeley

Abstract

Consider a longitudinal observational or controlled study in which one collects chronological data over time on n randomly sampled subjects. The time-dependent process one observes on each randomly sampled subject contains time-dependent covariates, time-dependent treatment actions, and an outcome process or single final outcome of interest. A statically optimal individualized treatment rule (as introduced in van der Laan, Petersen & Joffe (2005), Petersen & van der Laan (2006)) is a (unknown) treatment rule which at any point in time conditions on a user-supplied subset of the past, computes the future static treatment regimen that maximizes a (conditional) mean future outcome of interest, and applies the first treatment action of the latter regimen. In particular, Petersen & van der Laan (2006) clarified that, in order to be statically optimal, an individualized treatment rule should not depend on the observed treatment mechanism. Petersen & van der Laan (2006) further developed estimators of statically optimal individualized treatment rules based on a past capturing all confounding of past treatment history on outcome. In practice, however, one typically wishes to find individualized treatment rules responding to a user-supplied subset of the complete observed history, which may not be sufficient to capture all confounding. The current article provides an important advance on Petersen & van der Laan (2006) by developing locally efficient double robust estimators of statically optimal individualized treatment rules responding to such a user-supplied subset of the past. However, failure to capture all confounding comes at a price; the static optimality of the resulting rules becomes origin-specific. We explain origin-specific static optimality, and discuss the practical importance of the proposed methodology. We further present the results of a data analysis in which we estimate a statically optimal rule for switching antiretroviral therapy among patients infected with resistant HIV virus.