Treatment rules based on individual patient characteristics that are easy to interpret and disseminate are important in clinical practice. Properly planned and conducted randomized clinical trials are used to construct individualized treatment rules. However, it is often a concern that trial participants lack representativeness, so it limits the applicability of the derived rules to a target population. In this work, we use data from a single trial study to propose a two-stage procedure to derive a robust and parsimonious rule to maximize the benefit in the target population. The procedure allows a wide range of possible covariate distributions in the target population, with minimal assumptions on the first two moments of the covariate distribution. The practical utility and favorable performance of the methodology are demonstrated using extensive simulations and a real data application.
References
Audibert, J.-Y., Tsybakov, A. B., et al. “Fast learning rates for plug-in classifiers.”, The Annals of statistics, 35(2):608–633 (2007). 1118.62041 10.1214/009053606000001217 euclid.aos/1183667286Audibert, J.-Y., Tsybakov, A. B., et al. “Fast learning rates for plug-in classifiers.”, The Annals of statistics, 35(2):608–633 (2007). 1118.62041 10.1214/009053606000001217 euclid.aos/1183667286
Biau, G. “Analysis of a random forests model.”, Journal of Machine Learning Research, 13(Apr) :1063–1095 (2012). 1283.62127Biau, G. “Analysis of a random forests model.”, Journal of Machine Learning Research, 13(Apr) :1063–1095 (2012). 1283.62127
Breiman, L. “Random forests.”, Machine learning, 45(1):5–32 (2001). 1007.68152 10.1023/A:1010933404324Breiman, L. “Random forests.”, Machine learning, 45(1):5–32 (2001). 1007.68152 10.1023/A:1010933404324
Brinkley, J., Tsiatis, A., and Anstrom, K. J. “A generalized estimator of the attributable benefit of an optimal treatment regime.”, Biometrics, 66(2):512–522 (2010). 1192.62219 10.1111/j.1541-0420.2009.01282.xBrinkley, J., Tsiatis, A., and Anstrom, K. J. “A generalized estimator of the attributable benefit of an optimal treatment regime.”, Biometrics, 66(2):512–522 (2010). 1192.62219 10.1111/j.1541-0420.2009.01282.x
Buchanan, A. L., Hudgens, M. G., Cole, S. R., Mollan, K., Sax, P. E., Daar, E., Adimora, A. A., Eron, J., and Mugavero, M. “Generalizing evidence from randomized trials using inverse probability of sampling weights.”, Pharmacy Practice Faculty Publications, Paper 77 (2016).Buchanan, A. L., Hudgens, M. G., Cole, S. R., Mollan, K., Sax, P. E., Daar, E., Adimora, A. A., Eron, J., and Mugavero, M. “Generalizing evidence from randomized trials using inverse probability of sampling weights.”, Pharmacy Practice Faculty Publications, Paper 77 (2016).
Cole, S. R. and Stuart, E. A. “Generalizing Evidence From Randomized Clinical Trials to Target Populations The ACTG 320 Trial.”, American journal of epidemiology, 172(1):107–115 (2010).Cole, S. R. and Stuart, E. A. “Generalizing Evidence From Randomized Clinical Trials to Target Populations The ACTG 320 Trial.”, American journal of epidemiology, 172(1):107–115 (2010).
Goldberg, Y. and Kosorok, M. R. “Q-learning with censored data.”, Annals of statistics, 40(1):529 (2012). 1246.62206 10.1214/12-AOS968 euclid.aos/1336396182Goldberg, Y. and Kosorok, M. R. “Q-learning with censored data.”, Annals of statistics, 40(1):529 (2012). 1246.62206 10.1214/12-AOS968 euclid.aos/1336396182
Hastie, T., Tibshirani, R., and Friedman, J. H., The Elements of Statistical Learning. New York: Springer-Verlag New York, Inc., second edition (2009). 1273.62005Hastie, T., Tibshirani, R., and Friedman, J. H., The Elements of Statistical Learning. New York: Springer-Verlag New York, Inc., second edition (2009). 1273.62005
Hayes, D. F., Thor, A. D., Dressler, L. G., Weaver, D., Edgerton, S., Cowan, D., Broadwater, G., Goldstein, L. J., Martino, S., Ingle, J. N., et al. “HER2 and response to paclitaxel in node-positive breast cancer.”, New England Journal of Medicine, 357(15) :1496–1506 (2007).Hayes, D. F., Thor, A. D., Dressler, L. G., Weaver, D., Edgerton, S., Cowan, D., Broadwater, G., Goldstein, L. J., Martino, S., Ingle, J. N., et al. “HER2 and response to paclitaxel in node-positive breast cancer.”, New England Journal of Medicine, 357(15) :1496–1506 (2007).
Hernán, M. A. and Robins, J. M. “Estimating causal effects from epidemiological data.”, Journal of epidemiology and community health, 60(7):578–586 (2006).Hernán, M. A. and Robins, J. M. “Estimating causal effects from epidemiological data.”, Journal of epidemiology and community health, 60(7):578–586 (2006).
Huang, X., Ning, J., and Wahed, A. S. “Optimization of individualized dynamic treatment regimes for recurrent diseases.”, Statistics in medicine, 33(14) :2363–2378 (2014).Huang, X., Ning, J., and Wahed, A. S. “Optimization of individualized dynamic treatment regimes for recurrent diseases.”, Statistics in medicine, 33(14) :2363–2378 (2014).
Ishwaran, H., Kogalur, U. B., Blackstone, E. H., and Lauer, M. S. “Random survival forests.”, The annals of applied statistics, 2:841–860 (2008). 1149.62331 10.1214/08-AOAS169 euclid.aoas/1223908043Ishwaran, H., Kogalur, U. B., Blackstone, E. H., and Lauer, M. S. “Random survival forests.”, The annals of applied statistics, 2:841–860 (2008). 1149.62331 10.1214/08-AOAS169 euclid.aoas/1223908043
Kang, C., Janes, H., and Huang, Y. “Combining biomarkers to optimize patient treatment recommendations.”, Biometrics, 70(3):695–707 (2014). 1299.62125 10.1111/biom.12191Kang, C., Janes, H., and Huang, Y. “Combining biomarkers to optimize patient treatment recommendations.”, Biometrics, 70(3):695–707 (2014). 1299.62125 10.1111/biom.12191
Kosorok, M. R., Introduction to empirical processes and semiparametric inference. New York: Springer-Verlag (2008). 1180.62137Kosorok, M. R., Introduction to empirical processes and semiparametric inference. New York: Springer-Verlag (2008). 1180.62137
Lanckriet, G. R., Ghaoui, L. E., Bhattacharyya, C., and Jordan, M. I. “A robust minimax approach to classification.”, The Journal of Machine Learning Research, 3:555–582 (2003). 1084.68657Lanckriet, G. R., Ghaoui, L. E., Bhattacharyya, C., and Jordan, M. I. “A robust minimax approach to classification.”, The Journal of Machine Learning Research, 3:555–582 (2003). 1084.68657
Lara, P. N., Ely, B., Quinn, D. I., Mack, P. C., Tangen, C., Gertz, E., Twardowski, P. W., Goldkorn, A., Hussain, M., Vogelzang, N. J., et al. “Serum biomarkers of bone metabolism in castration-resistant prostate cancer patients with skeletal metastases: results from SWOG 0421.”, JNCI: Journal of the National Cancer Institute, 106(4) (2014).Lara, P. N., Ely, B., Quinn, D. I., Mack, P. C., Tangen, C., Gertz, E., Twardowski, P. W., Goldkorn, A., Hussain, M., Vogelzang, N. J., et al. “Serum biomarkers of bone metabolism in castration-resistant prostate cancer patients with skeletal metastases: results from SWOG 0421.”, JNCI: Journal of the National Cancer Institute, 106(4) (2014).
Marshall, A. W. and Olkin, I. “Multivariate chebyshev inequalities.”, The Annals of Mathematical Statistics, 31(4) :1001–1014 (1960). 0244.60013 10.1214/aoms/1177705673 euclid.aoms/1177705673Marshall, A. W. and Olkin, I. “Multivariate chebyshev inequalities.”, The Annals of Mathematical Statistics, 31(4) :1001–1014 (1960). 0244.60013 10.1214/aoms/1177705673 euclid.aoms/1177705673
Orellana, L., Rotnitzky, A., and Robins, J. M. “Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, part I: main content.”, The International Journal of Biostatistics, 6(2) (2010).Orellana, L., Rotnitzky, A., and Robins, J. M. “Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, part I: main content.”, The International Journal of Biostatistics, 6(2) (2010).
Qian, M. and Murphy, S. A. “Performance Guarantees for Individualized Treatment Rules.”, The Annals of Statistics, 39 :1180–1210 (2011). 1216.62178 10.1214/10-AOS864 euclid.aos/1304947047Qian, M. and Murphy, S. A. “Performance Guarantees for Individualized Treatment Rules.”, The Annals of Statistics, 39 :1180–1210 (2011). 1216.62178 10.1214/10-AOS864 euclid.aos/1304947047
Quinn, D. I., Tangen, C. M., Hussain, M., Lara, P. N., Goldkorn, A., Moinpour, C. M., Garzotto, M. G., Mack, P. C., Carducci, M. A., Monk, J. P., et al. “Docetaxel and atrasentan versus docetaxel and placebo for men with advanced castration-resistant prostate cancer (SWOG S0421): a randomised phase 3 trial.”, The Lancet Oncology, 14(9):893–900 (2013).Quinn, D. I., Tangen, C. M., Hussain, M., Lara, P. N., Goldkorn, A., Moinpour, C. M., Garzotto, M. G., Mack, P. C., Carducci, M. A., Monk, J. P., et al. “Docetaxel and atrasentan versus docetaxel and placebo for men with advanced castration-resistant prostate cancer (SWOG S0421): a randomised phase 3 trial.”, The Lancet Oncology, 14(9):893–900 (2013).
Robins, J. M., Hernán, M. Á., and Brumback, B. “Marginal structural models and causal inference in epidemiology.”, Epidemiology, 11(5):550–560 (2000).Robins, J. M., Hernán, M. Á., and Brumback, B. “Marginal structural models and causal inference in epidemiology.”, Epidemiology, 11(5):550–560 (2000).
Rubin, D. B. “Bayesian Inference for Causal Effects: The Role of Randomization.”, The Annals of Statistics, 6:34–58 (1978). 0383.62021 10.1214/aos/1176344064 euclid.aos/1176344064Rubin, D. B. “Bayesian Inference for Causal Effects: The Role of Randomization.”, The Annals of Statistics, 6:34–58 (1978). 0383.62021 10.1214/aos/1176344064 euclid.aos/1176344064
Tsybakov, A. B. “Optimal aggregation of classifiers in statistical learning.”, Annals of Statistics, 32:135–166 (2004). 1105.62353 10.1214/aos/1079120131 euclid.aos/1079120131Tsybakov, A. B. “Optimal aggregation of classifiers in statistical learning.”, Annals of Statistics, 32:135–166 (2004). 1105.62353 10.1214/aos/1079120131 euclid.aos/1079120131
van der Vaart, A., Asymptotic Statistics. New York: Cambridge University Press (1998). 0910.62001van der Vaart, A., Asymptotic Statistics. New York: Cambridge University Press (1998). 0910.62001
Vapnik, V., Golowich, S. E., and Smola, A. “Support vector method for function approximation, regression estimation, and signal processing.”, Advances in neural information processing systems, 281–287 (1997).Vapnik, V., Golowich, S. E., and Smola, A. “Support vector method for function approximation, regression estimation, and signal processing.”, Advances in neural information processing systems, 281–287 (1997).
Zhang, B., Tsiatis, A. A., Laber, E. B., and Davidian, M. “A robust method for estimating optimal treatment regimes.”, Biometrics, 68(4) :1010–1018 (2012). 1258.62116 10.1111/j.1541-0420.2012.01763.xZhang, B., Tsiatis, A. A., Laber, E. B., and Davidian, M. “A robust method for estimating optimal treatment regimes.”, Biometrics, 68(4) :1010–1018 (2012). 1258.62116 10.1111/j.1541-0420.2012.01763.x
Zhao, Y.-Q., Zeng, D., Laber, E. B., Song, R., Yuan, M., and Kosorok, M. R. “Doubly robust learning for estimating individualized treatment with censored data.”, Biometrika, 102(1):151–168 (2015). 1345.62092 10.1093/biomet/asu050Zhao, Y.-Q., Zeng, D., Laber, E. B., Song, R., Yuan, M., and Kosorok, M. R. “Doubly robust learning for estimating individualized treatment with censored data.”, Biometrika, 102(1):151–168 (2015). 1345.62092 10.1093/biomet/asu050
Zhao, Y. Q., Zeng, D., Rush, A. J., and Kosorok, M. R. “Estimating Individualized Treatment Rules using Outcome Weighted Learning.”, Journal of American Statistical Association, 107 :1106–1118 (2012). 06104679 10.1080/01621459.2012.695674Zhao, Y. Q., Zeng, D., Rush, A. J., and Kosorok, M. R. “Estimating Individualized Treatment Rules using Outcome Weighted Learning.”, Journal of American Statistical Association, 107 :1106–1118 (2012). 06104679 10.1080/01621459.2012.695674
Zhao, Y. Q., Zeng, D., Tangen, C. M., and LeBlanc, M. L. Supplementary Materials for “Robustifying Trial-Derived Optimal Treatment Rules for A Target Population”, (2019) DOI:, 10.1214/19-EJS1540SUPP 07056162 10.1214/19-EJS1540Zhao, Y. Q., Zeng, D., Tangen, C. M., and LeBlanc, M. L. Supplementary Materials for “Robustifying Trial-Derived Optimal Treatment Rules for A Target Population”, (2019) DOI:, 10.1214/19-EJS1540SUPP 07056162 10.1214/19-EJS1540
