A robust method for estimating optimal treatment regimes

Abstract

A treatment regime is a rule that assigns a treatment, among a set of possible treatments, to a patient as a function of his/her observed characteristics, hence "personalizing" treatment to the patient. The goal is to identify the optimal treatment regime that, if followed by the entire population of patients, would lead to the best outcome on average. Given data from a clinical trial or observational study, for a single treatment decision, the optimal regime can be found by assuming a regression model for the expected outcome conditional on treatment and covariates, where, for a given set of covariates, the optimal treatment is the one that yields the most favorable expected outcome. However, treatment assignment via such a regime is suspect if the regression model is incorrectly specified. Recognizing that, even if misspecified, such a regression model defines a class of regimes, we instead consider finding the optimal regime within such a class by finding the regime that optimizes an estimator of overall population mean outcome. To take into account possible confounding in an observational study and to increase precision, we use a doubly robust augmented inverse probability weighted estimator for this purpose. Simulations and application to data from a breast cancer clinical trial demonstrate the performance of the method.

Figure 1

Empirical cdfs across 1000 Monte Carlo data sets using correct and incorrect propensity score (PS) models of the quantities $Q({\widehat{\eta }}^{\mathit{\text{opt}}})/E\{Y^{*}(g_{\eta }^{\mathit{\text{opt}}})\}$ for the first simulation scenario. RGt and RGm denote the regression estimator with correct and misspecified model μ(A, X; β), respectively; AIPWEt and AIPWEm denote the estimator based on (3) with correct and misspecified model μ(A, X; β), respectively; and IPWE denotes the estimator based on (2).

Figure 2

Empirical cdfs across 1000 Monte Carlo data sets using correct and incorrect propensity score (PS) models of the quantities $Q({\widehat{\eta }}^{\mathit{\text{opt}}})/E\{Y^{*}(g_{\eta }^{\mathit{\text{opt}}})\}$ for each estimator for the second simulation scenario. RG1 and RG2 denote the regression estimator using incorrect models μ₁(A, X; β) and μ₂(A, X; β), respectively; AIPWE1 and AIPWE2 denote the estimator based on (3) using μ₁(A, X; β) and μ₂(A, X; β), respectively; and IPWE denotes the estimator based on (2).

Figure 3

(a) Estimated optimal treatment regimes of the form I(age ≥ η₀+η₁LPR) using the regression estimator (RG), the estimator based on (2) (IPWE), and the estimator based on (3) (AIPWE). (b) The regime identified by Fisher et al., (1983) and Gail and Simon (1985) (solid lines) and optimal regimes of the form 1 − I(age < η₀ and PR < η₁) estimated based on (2) (dotted-dashed lines) and (3) (long dashed lines).