Regret‐Regression for Optimal Dynamic Treatment Regimes

Abstract

We consider optimal dynamic treatment regime determination in practice. Model building, checking, and comparison have had little or no attention so far in this literature. Motivated by an application on optimal dosage of anticoagulants, we propose a modeling and estimation strategy that incorporates the regret functions of Murphy (2003, Journal of the Royal Statistical Society, Series B 65, 331-366) into a regression model for observed responses. Estimation is quick and diagnostics are available, meaning a variety of candidate models can be compared. The method is illustrated using simulation and the anticoagulation application.

Doubly Robust Estimation of Optimal Dynamic Treatment Regimes

“…It enables us to estimate causal effects from observational data (see Hernán and Robins [11], for a discussion of the exchangeability assumption). We make a third assumption of positivity, that the optimal treatment regime has a positive probability of being observed in the data or, in the case of a continuous treatment, that it is identifiable from the observed data (see Cole and Hernán [4], for a discussion of positivity and Henderson et al [8], for the extension in the continuous case). All three assumptions are standard in causal inference.…”

“…A variety of methods have been proposed for estimation from observational or trial data (e.g. Moodie et al [12]; Almirall et al [2]; Henderson et al [8]; Zhang et al [20]; Zhao et al [21, 22]). Some of these rely on knowledge or assumptions on the process by which decisions on treatment A are reached, which is straightforward for a randomised trial, and some of which rely on modelling the evolution of the states  S as time proceeds.…”

“…A particular case of the former is the g-estimation procedure proposed by Robins [17], and beautifully summarised by Moodie et al [12]. A special case of the latter is the so-called regret-regression approach that was proposed independently by Almirall et al [2] and Henderson et al [8]. These methods all formulate the problem in terms of the structural nested mean models (SNMMs) described by Robins [17].…”

“…65:331–355, 2003). We formulate a doubly robust version of the regret-regression approach of Almirall et al (in Biometrics 66:131–139, 2010) and Henderson et al (in Biometrics 66:1192–1201, 2010) and demonstrate that it is equivalent to a reduced form of Robins’ efficient g-estimation procedure (Robins, in Proceedings of the Second Symposium on Biostatistics. Springer, New York, pp.…”

Model Checking with Residuals for g-estimation of Optimal Dynamic Treatment Regimes

“…One gap that we have identified is that there has been relatively little work on the topic of model checking for this method. Henderson et al (2009) are among the first to have specifically addressed the issue of model checking and diagnostics in the context of optimal dynamic treatment regimes. Their method, which they call regret-regression, incorporates the regret functions of Murphy (2003) into a regression model for observed responses.…”