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**A robust method for estimating optimal treatment regimes.**
*(English)*
Zbl 1258.62116

Summary: A treatment regime is a rule that assigns a treatment, among a set of possible treatments, to a patient as a function of his/her observed characteristics, hence “personalizing” treatments to the patient. The goal is to identify the optimal treatment regime that, if followed by the entire population of patients, would lead to the best outcome on average. Given data from a clinical trial or observational study, for a single treatment decision, the optimal regime can be found by assuming a regression model for the expected outcome conditional on treatment and covariates, where, for a given set of covariates, the optimal treatment is the one that yields the most favorable expected outcome. However, treatment assignments via such a regime is suspect if the regression model is incorrectly specified. Recognizing that, even if misspecified, such a regression model defines a class of regimes, we instead consider finding the optimal regime within such a class by finding the regime that optimizes an estimator of overall population mean outcomes. To take into account possible confounding in an observational study and to increase precision, we use a doubly robust augmented inverse probability weighted estimator for this purpose. Simulations and application to data from a breast cancer clinical trial demonstrate the performance of the method.

### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

92C50 | Medical applications (general) |

65C60 | Computational problems in statistics (MSC2010) |

### Keywords:

doubly robust estimator; inverse probability weighting; outcome regression; personalized medicine; potential outcomes; propensity score### Software:

rgenoud
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\textit{B. Zhang} et al., Biometrics 68, No. 4, 1010--1018 (2012; Zbl 1258.62116)

### References:

[1] | Bang, Doubly robust estimation in missing data and causal inference models, Biometrics 61 pp 962– (2005) · Zbl 1087.62121 |

[2] | Brinkley, A generalized estimator of the attributable benefit of an optimal treatment regime, Biometrics 21 pp 512– (2009) · Zbl 1192.62219 |

[3] | Cao, Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data, Biometrika 96 pp 723– (2009) · Zbl 1170.62007 |

[4] | Fisher, Influence of tumor estrogen and progesterone receptor levels on the response to Tamoxifen and chemotherapy in primary breast cancer, Journal of Clinical Oncology 1 pp 227– (1983) |

[5] | Gail, Testing for qualitative interactions between treatment effects and patient subsets, Biometrics 41 pp 361– (1985) · Zbl 0614.62140 |

[6] | Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. (1989) · Zbl 0721.68056 |

[7] | Gunter, Journal of Biopharmaceutical Statistics 21 pp 1063– (2011) |

[8] | Henderson, Regret-regression for optimal dynamic treatment regimes, Biometrics 66 pp 1192– (2010) · Zbl 1233.62180 |

[9] | Mebane, Genetic optimization using derivatives: The rgenoud package for R, Journal of Statistical Software 42 pp 1– (2011) |

[10] | Moodie, Demystifying optimal dynamic treatment regimes, Biometrics 63 pp 447– (2007) · Zbl 1137.62077 |

[11] | Murphy, Optimal dynamic treatment regimes (with discussion), Journal of the Royal Statistical Society, Series B 65 pp 331– (2003) · Zbl 1065.62006 |

[12] | Orellana, Dynamic regime marginal structural mean models for estimation of optimal treatment regimes, part I: Main content, International Journal of Biostatistics 6 (2010) |

[13] | Qian, Performance guarantees for individualized treatment rules, Annals of Statistics 39 pp 1180– (2011) · Zbl 1216.62178 |

[14] | Robins, Estimation and extrapolation of optimal treatment and testing strategies, Statistics in Medicine 27 pp 4678– (2008) |

[15] | Robins, Proceedings of the Second Seattle Symposium on Biostatistics pp 189– (2004) · Zbl 1279.62024 |

[16] | Robins, Estimation of regression coefficients when some regressors are not always observed, Journal of the American Statistical Association 89 pp 846– (1994) · Zbl 0815.62043 |

[17] | Robins, Marginal structural models and causal inference in epidemiology, Epidemiology 11 pp 550– (2000) |

[18] | Rubin , D. B 1974 Estimating causal effects of treatments in |

[19] | Rubin, Bayesian inference for causal effects: The role of randomization, Annals of Statistics 6 pp 34– (1978) · Zbl 0383.62021 |

[20] | Stefanski, The calculus of M-estimation, The American Statistician 56 pp 29– (2002) |

[21] | Zhao, Reinforcement learning design for cancer clinical trials, Statistics in Medicine 28 pp 3294– (2009) |

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