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We provide additional statistical background for the methodology developed inthe clinical analysis of knee osteoarthritis in "A Precision Medicine Approachto Develop and Internally Validate Optimal Exercise and Weight Loss Treatmentsfor Overweight and Obese Adults with Knee Osteoarthritis" (Jiang et al. 2020).Jiang et al. 2020 proposed a pipeline to learn optimal treatment rules withprecision medicine models and compared them with zero-order models with aZ-test. The model performance was based on value functions, a scalar thatpredicts the future reward of each decision rule. The jackknife (i.e.,leave-one-out cross validation) method was applied to estimate the valuefunction and its variance of several outcomes in IDEA. IDEA is a randomizedclinical trial studying three interventions (exercise (E), dietary weight loss(D), and D+E) on overweight and obese participants with knee osteoarthritis. Inthis report, we expand the discussion and justification with additionalstatistical background. We elaborate more on the background of precisionmedicine, the derivation of the jackknife estimator of value function and itsestimated variance, the consistency property of jackknife estimator, as well asadditional simulation results that reflect more of the performance of jackknifeestimators. We recommend reading Jiang et al. 2020 for clinical application andinterpretation of the optimal ITR of knee osteoarthritis as well as the overallunderstanding of the pipeline and recommend using this article to understandthe underlying statistical derivation and methodology.

Technical Background for "A Precision Medicine Approach to Develop and  Internally Validate Optimal Exercise and Weight Loss Treatments for  Overweight and Obese Adults with Knee Osteoarthritis"