Estimation and evaluation of individualized treatment rules following multiple imputation

An individualized treatment rule (ITR) is a function that inputs patient-level information and outputs a recommended treatment. An important focus of precision medicine is to develop optimal ITRs that maximize a population-level distributional summary. However, guidance for estimating and evaluating optimal ITRs in the presence of missing data is limited. Our work is motivated by the Social Incentives to Encourage Physical Activity and Understand Predictors (STEP UP) study. Participants were randomized to a control or one of three interventions designed to increase physical activity and were given wearable devices to record daily steps as a measure of physical activity. Many participants were missing at least one daily step count during the study period. In the primary analysis of the STEP UP trial, multiple imputation (MI) was used to address missingness in daily step counts. Despite ubiquitous use of MI in practice, it has been given relatively little attention in the context of personalized medicine. We fill this gap by describing two frameworks for estimation and evaluation of an optimal ITR following MI and assessing their performance using simulated data. One framework relies on splitting the data into independent training and testing sets for estimation and evaluation, respectively. The other framework estimates an optimal ITR using the full data and constructs an $m$ -out-of- $n$ bootstrap confidence interval to evaluate its performance. Finally, we provide an illustrative analysis to estimate and evaluate an optimal ITR from the STEP UP data with a focus on practical considerations such as choosing the number of imputations.