An Algorithm for Generating Individualized Treatment Decision Trees and Random Forests

ABSTRACT With new treatments and novel technology available, precision medicine has become a key topic in the new era of healthcare. Traditional statistical methods for precision medicine focus on subgroup discovery through identifying interactions between a few markers and treatment regimes. However, given the large scale and high dimensionality of modern datasets, it is difficult to detect the interactions between treatment and high-dimensional covariates. Recently, novel approaches have emerged that seek to directly estimate individualized treatment rules (ITR) via maximizing the expected clinical reward by using, for example, support vector machines (SVM) or decision trees. The latter enjoys great popularity in clinical practice due to its interpretability. In this article, we propose a new reward function and a novel decision tree algorithm to directly maximize rewards. We further improve a single tree decision rule by an ensemble decision tree algorithm, ITR random forests. Our final decision rule is an average over single decision trees and it is a soft probability rather than a hard choice. Depending on how strong the treatment recommendation is, physicians can make decisions based on our model along with their own judgment and experience. Performance of ITR forest and tree methods is assessed through simulations along with applications to a randomized controlled trial (RCT) of 1385 patients with diabetes and an EMR cohort of 5177 patients with diabetes. ITR forest and tree methods are implemented using statistical software R (https://github.com/kdoub5ha/ITR.Forest). Supplementary materials for this article are available online.

[1]  B. Wolffenbuttel,et al.  DURAbility of Basal Versus Lispro Mix 75/25 Insulin Efficacy (DURABLE) Trial 24-Week Results , 2009, Diabetes Care.

[2]  Xin Yan,et al.  Facilitating score and causal inference trees for large observational studies , 2012, J. Mach. Learn. Res..

[3]  F. Cognetti,et al.  HER2 and response to paclitaxel in node-positive breast cancer. , 2008, The New England journal of medicine.

[4]  Eric B. Laber,et al.  Tree-based methods for individualized treatment regimes. , 2015, Biometrika.

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

[6]  I. van Mechelen,et al.  Qualitative interaction trees: a tool to identify qualitative treatment–subgroup interactions , 2014, Statistics in medicine.

[7]  Marie Davidian,et al.  Using decision lists to construct interpretable and parsimonious treatment regimes , 2015, Biometrics.

[8]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[9]  J. Morgan,et al.  Problems in the Analysis of Survey Data, and a Proposal , 1963 .

[10]  J. M. Taylor,et al.  Subgroup identification from randomized clinical trial data , 2011, Statistics in medicine.

[11]  J. Weinstein,et al.  Biomarkers in Cancer Staging, Prognosis and Treatment Selection , 2005, Nature Reviews Cancer.

[12]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

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

[14]  G. Meininger,et al.  Efficacy and safety of canagliflozin over 52 weeks in patients with type 2 diabetes on background metformin and pioglitazone , 2014, Diabetes, obesity & metabolism.

[15]  R. Bergenstal,et al.  Type 2 diabetes: assessing the relative risks and benefits of glucose-lowering medications. , 2010, The American journal of medicine.

[16]  Peter Doyle,et al.  The Use of Automatic Interaction Detector and Similar Search Procedures , 1973 .

[17]  L. Tian,et al.  Analysis of randomized comparative clinical trial data for personalized treatment selections. , 2011, Biostatistics.

[18]  G. Tutz,et al.  An introduction to recursive partitioning: rationale, application, and characteristics of classification and regression trees, bagging, and random forests. , 2009, Psychological methods.

[19]  Min Zhang,et al.  Estimating optimal treatment regimes from a classification perspective , 2012, Stat.

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

[21]  Lu Tian,et al.  Effectively Selecting a Target Population for a Future Comparative Study , 2013, Journal of the American Statistical Association.

[22]  L. Wood,et al.  The General Practice Research Database , 2004, Drug safety.

[23]  G. Ginsburg,et al.  The path to personalized medicine. , 2002, Current opinion in chemical biology.

[24]  D H Lawson,et al.  The General Practice Research Database. Scientific and Ethical Advisory Group. , 1998, QJM : monthly journal of the Association of Physicians.

[25]  Hansheng Wang,et al.  Subgroup Analysis via Recursive Partitioning , 2009, J. Mach. Learn. Res..

[26]  F. Collins,et al.  The path to personalized medicine. , 2010, The New England journal of medicine.

[27]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[28]  Leo Breiman,et al.  Random Forests , 2001, Machine Learning.

[29]  Wei-Yin Loh,et al.  Classification and regression trees , 2011, WIREs Data Mining Knowl. Discov..

[30]  Haoda Fu,et al.  Estimating optimal treatment regimes via subgroup identification in randomized control trials and observational studies , 2016, Statistics in medicine.

[31]  Menggang Yu,et al.  Regularized outcome weighted subgroup identification for differential treatment effects , 2015, Biometrics.

[32]  Honghua H. Jiang,et al.  Comparison of insulin lispro protamine suspension versus insulin glargine once daily added to oral antihyperglycaemic medications and exenatide in type 2 diabetes: a prospective randomized open-label trial , 2013, Diabetes, obesity & metabolism.

[33]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[34]  Luc Van Gaal,et al.  Exenatide once weekly versus insulin glargine for type 2 diabetes (DURATION-3): 3-year results of an open-label randomised trial. , 2014, The lancet. Diabetes & endocrinology.

[35]  K. Imai,et al.  Estimation of Heterogeneous Treatment Effects from Randomized Experiments, with Application to the Optimal Planning of the Get-Out-the-Vote Campaign , 2011, Political Analysis.

[36]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[37]  Roland A Matsouaka,et al.  Evaluating marker‐guided treatment selection strategies , 2014, Biometrics.

[38]  A. Kitabchi,et al.  Management of type 2 diabetes: evolving strategies for the treatment of patients with type 2 diabetes. , 2011, Metabolism: clinical and experimental.

[39]  I. Lipkovich,et al.  Subgroup identification based on differential effect search—A recursive partitioning method for establishing response to treatment in patient subpopulations , 2011, Statistics in medicine.

[40]  Ilya Lipkovich,et al.  Local control for identifying subgroups of interest in observational research: persistence of treatment for major depressive disorder , 2013, International journal of methods in psychiatric research.

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

[42]  W. Loh,et al.  REGRESSION TREES WITH UNBIASED VARIABLE SELECTION AND INTERACTION DETECTION , 2002 .

[43]  D. M. Grant,et al.  The Art and Science of Personalized Medicine , 2007, Clinical pharmacology and therapeutics.

[44]  Dag Aarsland,et al.  Effects of rivastigmine in Alzheimer's disease patients with and without hallucinations. , 2010, Journal of Alzheimer's disease : JAD.

[45]  Bruce H. R. Wolffenbuttel,et al.  The DURABLE Trial 24-week Results: Safety and Efficacy of Insulin Lispro Mix 75/25 Versus Insulin Glargine Added to Oral Antihyperglycemic Drugs in Patients with Type 2 Diabetes , 2009 .