A regression tree approach to identifying subgroups with differential treatment effects

Statistics in Medicine

Volumn 34, Issue 11, 2015, Pages 1818-1833

  Loh, Wei Yin ^a   He, Xu ^b   Man, Michael ^c  

^a University of Wisconsin   (United States)

^b CHINESE ACADEMY OF SCIENCES   (China)

^c ELI LILLY AND COMPANY   (United States)

Author keywords

Bootstrap; Missing values; Proportional hazards; Selection bias

Indexed keywords

ALGORITHM; ARTICLE; BOOTSTRAPPING; CALCULATION; CLASSIFICATION; CONTINGENCY TABLE; EFFECT SIZE; GENERALIZED UNBIASED INTERACTION DETECTION AND ESTIMATION; HORMONAL THERAPY; HUMAN; KAPLAN MEIER METHOD; LINEAR SYSTEM; MATHEMATICAL COMPUTING; MEASUREMENT ACCURACY; POISSON DISTRIBUTION; PROBABILITY; PROPORTIONAL HAZARDS MODEL; QUALITATIVE ANALYSIS; REGRESSION ANALYSIS; SCORING SYSTEM; SIMULATION; STATISTICAL MODEL; SURVIVAL TIME; THERAPY EFFECT; TREATMENT RESPONSE; CHI SQUARE DISTRIBUTION; CONFIDENCE INTERVAL; NEOPLASMS; RANDOMIZED CONTROLLED TRIAL (TOPIC); SELECTION BIAS;

ALGORITHMS; CHI-SQUARE DISTRIBUTION; CONFIDENCE INTERVALS; HUMANS; MODELS, STATISTICAL; NEOPLASMS; POISSON DISTRIBUTION; RANDOMIZED CONTROLLED TRIALS AS TOPIC; REGRESSION ANALYSIS; SELECTION BIAS;

EID: 84926513964     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6454     Document Type: Article

References (41)

1. Ciampi A, Negassa A, Lou Z. Tree-structured prediction for censored survival data and the Cox model. Journal of Clinical Epidemiology 1995; 48:675-689.
2. Foster JC, Taylor JMG, Ruberg SJ. Subgroup identification from randomized clinical trial data. Statistics in Medicine 2011; 30:2867-2880.
3. Lipkovich I, Dmitrienko A, Denne J, Enas G. Subgroup identification based on differential effect search - a recursive partitioning method for establishing response to treatment in patient subpopulations. Statistics in Medicine 2011; 30:2601-2621.
4. Schmoor C, Olschewski M, Schumacher M. Randomized and non-randomized patients in clinical trials: experiences with comprehensive cohort studies. Statistics in Medicine 1996; 15:263-271.
5. Peters A, Hothorn T. Improved predictors, 2012. R package version 0.8-13.
6. Schumacher M, Baster G, Bojar H, Hübner K, Olschewski M, Sauerbrei W, Schmoor C, Beyerle C, Newmann RLA, Rauschecker HF. Randomized 2 × 2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. Journal of Clinical Oncology 1994; 12:2086-2093.
7. Sauerbrei W, Royston P. Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. Journal of the Royal Statistical Society, Series A 1999; 162:71-94.
8. Everitt BS, Hothorn T. A Handbook of Statistical Analyses Using R. Chapman and Hall/CRC: New York, 2006.
9. Mehta S, Shelling A, Muthukaruppan A, Lasham A, Blenkiron C, Laking G, Print C. Predictive and prognostic molecular markers for cancer medicine. Therapeutic Advances in Medical Oncology 2010; 2(2):125-148.
10. Italiano A. Prognostic or predictive? It's time to get back to definitions! Journal of Clinical Oncology 2011; 29:4718.
11. Su XG, Kang J, Fan J, Levine R, Yan X. Facilitating score and causal inference trees for large observational data. Journal of Machine Learning Research 2012; 13:2955-2994.
12. Negassa A, Ciampi A, Abrahamowicz M, Shapiro S, Boivin JR. Tree-structured subgroup analysis for censored survival data: validation of computationally inexpensive model selection criteria. Statistics and Computing 2005; 15:231-239.
13. Su X, Zhou T, Yan X, Fan J, Yang S. Interaction trees with censored survival data. International Journal of Biostatistics 2008; 4. Article 2. DOI: 10.2202/1557-4679.1071.
14. Su X, Tsai CL, Wang H, Nickerson DM, Bogong L. Subgroup analysis via recursive partitioning. Journal of Machine Learning Research 2009; 10:141-158.
15. Breiman L. Random forests. Machine Learning 2001; 45:5-32.
16. Therneau TM, Atkinson B. Rpart: recursive partitioning, 2012. R package version 3.1-51.
17. Dusseldorp E, VanMechelen I. Qualitative interaction trees: a tool to identify qualitative treatment-subgroup interactions. Statistics in Medicine 2014; 33:219-237.
18. Loh WY, Shih YS. Split selection methods for classification trees. Statistica Sinica 1997; 7:815-840.
19. Loh WY. Regression trees with unbiased variable selection and interaction detection. Statistica Sinica 2002; 12:361-386.
20. Loh WY. Fifty years of classification and regression trees (with discussion). International Statistical Review 2014; 34:329-370.
21. Kass GV. An exploratory technique for investigating large quantities of categorical data. Applied Statistics 1980; 29:119-127.
22. Loh WY. Improving the precision of classification trees. Annals of Applied Statistics 2009; 3:1710-1737.
23. Kim H, Loh WY. Classification trees with unbiased multiway splits. Journal of the American Statistical Association 2001; 96:589-604.
24. Hothorn T, Hornik K, Strobl C, Zeileis A. Party: a laboratory for recursive partytioning, 2012. R package version 1.0-1.
25. Zeileis A, Hothorn T, Hornik K. Model-based recursive partitioning. Journal of Computational and Graphical Statistics 2008; 17:492-514.
26. Wilson EB, Hilferty MM. The distribution of chi-square. Proceedings of the National Academy of Sciences of the United States of America 1931; 17:684-688.
27. Breiman L, Friedman JH, Olshen RA, Stone CJ. Classification and Regression Trees. Wadsworth: Belmont, California, 1984.
28. Weisberg S. Applied Linear Regression 2nded. Wiley: New York, 1985.
29. Ahn H, Loh WY. Tree-structured proportional hazards regression modeling. Biometrics 1994; 50:471-485.
30. Aitkin M, Clayton D. The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics 1980; 29:156-163.
31. Laird N, Olivier D. Covariance analysis of censored survival data using log-linear analysis techniques. Journal of the American Statistical Association 1981; 76:231-240.
32. Chaudhuri P, Lo WD, Loh WY, Yang C-C. Generalized regression trees. Statistica Sinica 1995; 5:641-666.
33. Loh WY. Regression tree models for designed experiments. In Second E. L. Lehmann Symposium, Rojo J (ed.), Institute of Mathematical Statistics Lecture Notes-Monograph Series, vol.49. 2006; 210-228.
34. Agresti A. An Introduction to Categorical Data Analysis 2nded. Wiley, 2007.
35. Aalen OO. Nonparametric inference for a family of counting processes. Annals of Statistics 1978; 6:701-726.
36. Breslow N. Contribution to the discussion of regression models and life tables by D. R. Cox. Journal of the Royal Statistical Society, Ser. B 1972; 34:216-217.
37. Lawless JF. Statistical Models and Methods for Lifetime Data. Wiley: New York, 1982.
38. Loh WY. Variable selection for classification and regression in large p, small n problems. In Probability Approximations and Beyond, Barbour A, Chan HP, Siegmund D (eds), Lecture Notes in Statistics-Proceedings, vol.205. Springer, New York, 2012; 133-157.
39. Satterthwaite FE. An approximate distribution of estimates of variance components. Biometrics Bulletin 1946; 2:110-114.
40. Strobl C, Boulesteix AL, Zeileis A, Hothorn T. Bias in random forest variable importance measures: illustrations, sources and a solution. BMC Bioinformatics 2007; 8:25. DOI: 10.1186/1471-2105-8-25.
41. Ding Y, Simonoff JS. An investigation of missing data methods for classification trees applied to binary response data. Journal of Machine Learning Research 2010; 11:131-170.