×

Estimating individualized treatment rules using outcome weighted learning. (English) Zbl 1443.62396

Summary: There is increasing interest in discovering individualized treatment rules (ITRs) for patients who have heterogeneous responses to treatment. In particular, one aims to find an optimal ITR that is a deterministic function of patient-specific characteristics maximizing expected clinical outcome. In this article, we first show that estimating such an optimal treatment rule is equivalent to a classification problem where each subject is weighted proportional to his or her clinical outcome. We then propose an outcome weighted learning approach based on the support vector machine framework. We show that the resulting estimator of the treatment rule is consistent. We further obtain a finite sample bound for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed approach is demonstrated via simulation studies and an analysis of chronic depression data.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
68T05 Learning and adaptive systems in artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Bartlett P. L., The Annals of Statistics 33 (4) pp 1497– (2005) · Zbl 1083.62034
[2] Bartlett P. L., Journal of American Statistical Association 101 (473) pp 138– (2006) · Zbl 1118.62330
[3] Blanchard G., The Annals of Statistics 36 pp 489– (2008) · Zbl 1133.62044
[4] Bradley P. S., Proceedings of the 15th International Conference on Machine Learning pp 82– (1998)
[5] Buzdar A. U., The Annals of Oncology 20 pp 993– (2009)
[6] Cai T., Biometrika 97 (2) pp 389– (2010) · Zbl 1205.62161
[7] Cortes C., Machine Learning 20 pp 273– (1995)
[8] Crits-Christoph P., Archives of General Psychiatry 56 pp 493– (1999)
[9] Eagle K. A., Journal of the American Medical Association 291 pp 2727– (2004)
[10] Flume P. A., American Journal of Respiratory and Critical Care Medicine 176 (1) pp 957– (2007)
[11] Grünwald V., Journal of the National Cancer Institute 95 (12) pp 851– (2003)
[12] Hastie T., The Elements of Statistical Learning (2nd ed.) (2009) · Zbl 1273.62005
[13] Insel T. R., Archives of General Psychiatry 66 (2) pp 128– (2009)
[14] Keller M. B., The New England Journal of Medicine 342 (20) pp 1462– (2000)
[15] Laber E. B., Journal of the American Statistical Association 106 pp 904– (2011) · Zbl 1229.62085
[16] Lee Y., Journal of the American Statistical Association 99 pp 67– (2004) · Zbl 1089.62511
[17] Lin Y., Data Mining and Knowledge Discovery 6 pp 259– (2002) · Zbl 05660804
[18] Liu Y., Computational Statistics & Data Analysis 51 (12) pp 6380– (2007) · Zbl 1446.62179
[19] Lugosi G., The Annals of Statistics 32 pp 30– (2004)
[20] Marlowe D. B., Drug and Alcohol Dependence 88 (2) pp S4– (2007)
[21] Moodie E. E. M., Journal of the American Statistical Association 104 (485) pp 155– (2009) · Zbl 06448240
[22] Moodie E. E. M., Biometrics 63 (2) pp 447– (2007) · Zbl 1137.62077
[23] Murphy S. A., Journal of the Royal Statistical Society, Series B 65 pp 331– (2003) · Zbl 1065.62006
[24] Murphy S. A., Journal of the American Statistical Association 96 pp 1410– (2001) · Zbl 1051.62114
[25] Piper W. E., Psychotherapy 32 pp 639– (1995)
[26] Qian M., The Annals of Statistics 39 pp 1180– (2011) · Zbl 1216.62178
[27] Robins J. M., Proceedings of the Second Seattle Symposium on Biostatistics pp 189– (2004) · Zbl 1279.62024
[28] Rosenwald A., The New England Journal of Medicine 346 pp 1937– (2002)
[29] Sargent D. J., Journal of Clinical Oncology 32 pp 2020– (2005)
[30] Steinwart I., IEEE Transactions on Information Theory 51 pp 128– (2005) · Zbl 1304.62090
[31] Steinwart I., The Annals of Statistics 35 pp 575– (2007) · Zbl 1127.68091
[32] Thall P. F., Journal of the American Statistical Association 97 pp 29– (2002) · Zbl 1073.62590
[33] Tsybakov A. B., The Annals of Statistics 32 pp 135– (2004) · Zbl 1105.62353
[34] van’t Veer L. J., Nature 452 pp 564– (2008)
[35] Vapnik V. N., The Nature of Statistical Learning Theory (1995) · Zbl 0833.62008
[36] Vert R., Journal of Machine Learning Research 7 pp 817– (2006)
[37] Wang L., Statistica Sinica 16 pp 617– (2006)
[38] Zhang T., The Annals of Statistics 32 (1) pp 56– (2004) · Zbl 1105.62323
[39] Zhao Y., Biometrics 67 pp 1422– (2011) · Zbl 1274.62922
[40] Zhu J., Neural Information Processing Systems pp 16– (2003)
[41] Zou H., Statistica Sinica 18 pp 379– (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.