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"

We provide additional statistical background for the methodology developed in the clinical analysis of knee osteoarthritis in "A Precision Medicine Approach to Develop and Internally Validate Optimal Exercise and Weight Loss Treatments for Overweight and Obese Adults with Knee Osteoarthritis" (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. IDEA is a randomized clinical trial studying three interventions (exercise (E), dietary weight loss (D), and D+E) on 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.

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

We proposed a precision medicine approach to determine the optimal treatment regime for participants in an exercise (E), dietary weight loss (D), and D+E trial for knee osteoarthritis (KOA) that would have maximized their expected outcomes. Using data from 343 participants of the Intensive Diet and Exercise for Arthritis (IDEA) trial, we applied 24 machine-learning models to develop individualized treatment rules on seven outcomes: SF-36 physical component score, weight loss, WOMAC pain/function/stiffness scores, compressive force, and IL-6. The optimal model was selected based on jackknife value function estimates that indicate improvement in the outcome(s) if future participants follow the estimated decision rule compared against the optimal single, fixed treatment model. Multiple outcome random forest was the optimal model for the WOMAC outcomes. For the other outcomes, list-based models were optimal. For example, the estimated optimal decision rule for weight loss assigns the D+E intervention to participants with baseline weight not exceeding 109.35 kg and waist circumference above 90.25 cm, and assigns D to all other participants except those with history of a heart attack. If applied to future participants, the optimal rule for weight loss is estimated to increase average weight loss to 11.2 kg at 18 months, contrasted with 9.8 kg if all received D+E (p = 0.01). The precision medicine models supported the overall findings from IDEA that the D+E intervention was optimal for most participants, but there was evidence that a subgroup of participants would likely benefit more from diet alone for two outcomes.