Estimating Individualized Treatment Regimes from Crossover Designs

Personalized medicine is the practice of tailoring treatment to account for patient heterogeneity (Chakraborty and Murphy, 2014). Health care providers have practiced personalized medicine by adjusting doses or prescriptions based on a patient’s medical history or demographics for centuries (Ashley, 2015). Precision medicine is an emerging field that aims to support personalized medicine decisions with reproducible research (Collins and Varmus, 2015). Such research is imperative, particularly when diseases are expressed with great heterogeneity across patients. A topic of interest in precision medicine is the individualized treatment regime (ITR): a set of decision rules for one or more decision time points that can be used to assign patients to treatment that is tailored by their patient-specific factors (Lavori and Dawson, 2014). One objective in precision medicine is to estimate the optimal ITR, or the ITR that maximizes the mean of some desirable outcome (Kosorok and Moodie, 2015). Crossover clinical trials are uniquely suited to precision medicine, because they allow for observing responses to multiple treatments for each patient. This paper introduces a method to estimate optimal ITRs using data from a crossover study by extending generalized outcome weighted learning (GOWL) (Chen et al., 2018) to deal with correlated outcomes. In a crossover study, patients are randomized to a sequence of treatments rather than a single treatment. Thus, multiple outcomes are observed, one per subject from each treatment period, and each subject acts as his or her own control for reduced between-subject variability (Wellek and Blettner, 2012). Such designs are popular in pilot studies, where only a small sample of individuals is available and/or affordable, because crossover designs at a lower sample size are able achieve the same level of power as a parallel design with a larger sample size. To concurrently address precision medicine aims with aims of hypothesis testing, it is imperative that ITR estimation methods be broadened to crossover designs in an accessible and easy to implement way in order to better take advantage of the additional data available in such crossover studies. There have been many developments in machine learning methods for answering precision medicine questions from parallel study designs. For example, Qian and Murphy (2011) indirectly estimate the decision rule using L1 penalized least squares; Zhang et al. (2012a) maximize a doubly robust augmented inverse probability weighted estimator for the population mean outcome; Athey and Wager (2017) maximize a doubly robust score that may take into account instrumental variables; Kallus (2018) employs a weighting algorithm similar to inverse probability weighting but minimize the worst case mean square error; Laber and Zhao (2015) propose the use of decision trees, which prove to be both flexible and easily interpretable; Zhao et al. (2012), Zhang et al. (2012b), Zhou et al. (2017), and Chen et al. (2018) directly estimate the decision rule by viewing the problem from a weighted classification standpoint. However, little work has been done to develop precision medicine methods that handle correlated observations in the single-stage decision setting such as those that arise from crossover designs. Kulasekera and Siriwardhana (2019) propose a weighted ranking algorithm to estimate a decision rule that maximizes either the expected outcome or the probability of selecting the best treatment, but they assume that there are no carryover effects present. Because the intended effect of the washout period can be difficult to achieve in practice (Wellek and Blettner, 2012), it is imperative that methods for crossover designs can be applied when carryover effects are present. In this paper, we show that the difference in response to two treatments from a 2 × 2 crossover trial can be used as the reward in the generalized outcome weighted learning (GOWL) objective function to estimate an optimal ITR. We introduce a plug-in estimator that can be used with the proposed method to account for carryover effects. Additionally, we show that using a crossover design with the proposed method results in improvements in misclassification rate and estimated value when compared to standard methods for a parallel design at the same sample size. As a clinical example, consider nutritional recommendations surrounding the intake of dietary fiber for the purpose of weight loss. Although increased fiber is recommended across the population for a myriad of health benefits (US Department of Agriculture, 2010), evidence of the impact of the consumption of dietary fiber for improved satiety and reduction in body weight is mixed (Halliday et al., 2018). Heterogeneity in response to dietary fiber may be leveraged to develop targeted fiber interventions to promote feelings of satiety. We use data from a crossover study in which Hispanic and African American adolescents who are overweight and obese were fed breakfast and lunch under a typical Western high sugar diet condition, and a high fiber diet condition. From these data, we estimate a decision rule with which clinical care providers can input patient characteristics, including demographics and clinical measures, and receive a recommendation to maximize the change in measures of perceived satiety from before breakfast to after lunch. This type of analysis could be useful in identifying a subgroup of at-risk adolescents for which targeting specific dietary recommendations is expected to lead to an increase in patient-reported satiety, thereby helping to decrease caloric intake in a population with great clinical need for effective, non-invasive weight loss strategies. The rest of this paper is organized as follows. In Section 2, we review outcome weighted learning (OWL) (Zhao et al., 2012) and present the proposed method for estimating an optimal ITR from a crossover study regardless of the presence of carryover effects. Section 3 establishes Fisher and global consistency. Section 4 demonstrates the performance of the proposed method in simulation studies, with results on misclassification rate and estimated value. Section 5 displays an analysis of data from a feeding trial with overweight and obese Hispanic and African American adolescents, and we conclude with a discussion in Section 6. Additional simulation results, feeding trial results and their discussion, and theoretical derivations may be found in the web based supporting materials.