Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight‐Loss Treatments for Overweight and Obese Adults With Knee Osteoarthritis: Data From a Single‐Center Randomized Trial

Abstract

This technical report provides additional statistical background for the methodology developed in the clinical analysis of knee osteoarthritis in Jiang et al. (2020). Jiang et al. (2020) proposed a pipeline to learn optimal treatment rules with precision medicine models and compared them with zero-order models with a Z-test. The model performance was based on value functions, a scalar that predicts the future reward of each decision rule. The jackknife (i.e., leave-one-out cross validation) method was applied to estimate the value function and its variance of several outcomes in IDEA, a randomized clinical trial studying overweight and obese participants with knee osteoarthritis. In this report, we expand the discussion and justification with additional statistical background. We elaborate more on the background of precision medicine, the derivation of the jackknife estimator of value function and its estimated variance, the consistency property of jackknife estimator, as well as additional simulation results that reflect more of the performance of jackknife estimators. We recommend reading Jiang et al. (2020) for clinical application and interpretation of the optimal ITR of knee osteoarthritis as well as the overall understanding of the pipeline and recommend using this article to understand the underlying statistical derivation and methodology.

Inflammatory phenotype of osteoarthritis and its potential therapies

“…The marked variations in disease expression and pathobiological manifestations in OA suggest the significant value of personalized and precision medicine from the therapeutic perspective 12,69,72 . Personalized medicine is used to treat patients on the basis of their individual clinical characteristics, taking account of the diversity of symptoms, severity, and genetic defects 73 . In precision medicine, molecular information maximizes the accuracy of patient classification and treatment, typically applying large amounts of data for the identification of patient phenotypes that share specific relevant characteristics to predict diagnosis, progression, or treatment response and utilize appropriate therapeutic targets 74,75 .…”

Model Selection for Survival Individualized Treatment Rules Using the Jackknife Estimator

“…Through proofs and simulations Jiang et al [7] showed consistency and asymptotic normality of the proposed jackknife estimator of the value function. Note that we are ignoring the contribution to the limiting distribution due to estimating the propensity scores.…”

“…The selected approach is then evaluated via cross-validation techniques for assessing the value function associated with the estimated treatment rule. Jiang et al [7] proposed a LOOCV or jackknife estimator for the value function for continuous outcomes. The approach requires weak assumptions, namely that the data are independent and identically distributed.…”

“…We build a test to compare optimal treatment rules from two estimation approaches. Similarly to Jiang et al [7], the test statistic is expressed as:…”

“…Assuming independent or conditionally independent censoring, these methods generally perform well for a small to moderate proportion of censored observations. In this paper, we extend the jackknife method proposed by Jiang et al [7] for a binary treatment and a right-censored survival outcome. Our extension of the jackknife method uses the inverse probability of censoring weighting (IPCW) to mitigate the bias induced by the censored observations.…”