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.

[1]  H. Chipman,et al.  BART: Bayesian Additive Regression Trees , 2008, 0806.3286.

[2]  Andy Liaw,et al.  Classification and Regression by randomForest , 2007 .

[3]  M. H. Quenouille.  Approximate tests of correlation in time-series 3 , 1949, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  Trevor Hastie,et al.  Regularization Paths for Generalized Linear Models via Coordinate Descent. , 2010, Journal of statistical software.

[5]  S. Murphy,et al.  PERFORMANCE GUARANTEES FOR INDIVIDUALIZED TREATMENT RULES. , 2011, Annals of statistics.

[6]  P. Burman.  A comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods , 1989 .

[7]  M. Kramer,et al.  Estimating Response-Maximized Decision Rules With Applications to Breastfeeding , 2009 .

[8]  Purushottam W. Laud,et al.  Nonparametric survival analysis using Bayesian Additive Regression Trees (BART) , 2016, Statistics in medicine.

[9]  Donglin Zeng,et al.  Estimating Individualized Treatment Rules Using Outcome Weighted Learning , 2012, Journal of the American Statistical Association.

[10]  Eric B. Laber,et al.  A Robust Method for Estimating Optimal Treatment Regimes , 2012, Biometrics.

[11]  Inbal Nahum-Shani,et al.  Optimization of behavioral dynamic treatment regimens based on the sequential, multiple assignment, randomized trial (SMART) , 2014, Clinical trials.

[12]  Yichi Zhanga,et al.  Estimation of Optimal Treatment Regimes Using Lists , 2018 .

[13]  S. Murphy,et al.  Optimal dynamic treatment regimes , 2003 .

[14]  James M. Robins,et al.  Optimal Structural Nested Models for Optimal Sequential Decisions , 2004 .

[15]  J. Robins,et al.  Estimation of Regression Coefficients When Some Regressors are not Always Observed , 1994 .

[16]  Nema Dean,et al.  Q-Learning: Flexible Learning About Useful Utilities , 2013, Statistics in Biosciences.

[17]  Michael R Kosorok,et al.  Residual Weighted Learning for Estimating Individualized Treatment Rules , 2015, Journal of the American Statistical Association.

[18]  Arkadiusz Paterek,et al.  Improving regularized singular value decomposition for collaborative filtering , 2007 .

[19]  M. Kosorok.  Introduction to Empirical Processes and Semiparametric Inference , 2008 .

[20]  James M. Robins,et al.  Semiparametric Regression for Repeated Outcomes With Nonignorable Nonresponse , 1998 .

[21]  Wenting Cheng,et al.  Reader reaction to “A robust method for estimating optimal treatment regimes” by Zhang et al. (2012) , 2015, Biometrics.

[22]  Peter Bühlmann,et al.  MissForest - non-parametric missing value imputation for mixed-type data , 2011, Bioinform..

[23]  L. Breiman.  Heuristics of instability and stabilization in model selection , 1996 .

[24]  Donglin Zeng,et al.  Reinforcement Learning Trees , 2015, Journal of the American Statistical Association.

[25]  B. W. Yap,et al.  Comparisons of various types of normality tests , 2011 .

[26]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[27]  Yuhong Yang,et al.  Cross-validation for selecting a model selection procedure , 2015 .

[28]  Crystal T. Nguyen,et al.  Characterizing the weight-glycemia phenotypes of type 1 diabetes in youth and young adulthood , 2020, BMJ Open Diabetes Research & Care.

[29]  Yoshua Bengio,et al.  Série Scientifique Scientific Series No Unbiased Estimator of the Variance of K-fold Cross-validation No Unbiased Estimator of the Variance of K-fold Cross-validation , 2022 .