Electronic Journal of Statistics

Semiparametric single-index model for estimating optimal individualized treatment strategy

Rui Song, Shikai Luo, Donglin Zeng, Hao Helen Zhang, Wenbin Lu, and Zhiguo Li

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Abstract

Different from the standard treatment discovery framework which is used for finding single treatments for a homogenous group of patients, personalized medicine involves finding therapies that are tailored to each individual in a heterogeneous group. In this paper, we propose a new semiparametric additive single-index model for estimating individualized treatment strategy. The model assumes a flexible and nonparametric link function for the interaction between treatment and predictive covariates. We estimate the rule via monotone B-splines and establish the asymptotic properties of the estimators. Both simulations and an real data application demonstrate that the proposed method has a competitive performance.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 364-384.

Dates
Received: February 2016
First available in Project Euclid: 13 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1486976416

Digital Object Identifier
doi:10.1214/17-EJS1226

Mathematical Reviews number (MathSciNet)
MR3608677

Zentralblatt MATH identifier
1356.62220

Subjects
Primary: 62G05: Estimation
Secondary: 62G99: None of the above, but in this section

Keywords
Personalized medicine single index model semiparametric inference

Rights
Creative Commons Attribution 4.0 International License.

Citation

Song, Rui; Luo, Shikai; Zeng, Donglin; Zhang, Hao Helen; Lu, Wenbin; Li, Zhiguo. Semiparametric single-index model for estimating optimal individualized treatment strategy. Electron. J. Statist. 11 (2017), no. 1, 364--384. doi:10.1214/17-EJS1226. https://projecteuclid.org/euclid.ejs/1486976416


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References

  • [1] Chakraborty, B., Murphy, S. and Strecher, V. (2010). Inference for non-regular parameters in optimal dynamic treatment regimes., Statistical methods in medical research 19 317–343.
  • [2] De Boor, C. (1978). A practical guide to splines., Mathematics of Computation.
  • [3] Duan, N. and Li, K.-C. (1991). Slicing regression: a link-free regression method., The Annals of Statistics 505–530.
  • [4] Hardle, W., Hall, P., Ichimura, H. et al. (1993). Optimal smoothing in single-index models., The annals of Statistics 21 157–178.
  • [5] Horowitz, J. L. and Härdle, W. (1996). Direct semiparametric estimation of single-index models with discrete covariates., Journal of the American Statistical Association 91 1632–1640.
  • [6] Hristache, M., Juditsky, A. and Spokoiny, V. (2001). Direct estimation of the index coefficient in a single-index model., Annals of Statistics 595–623.
  • [7] Huang, J. et al. (1996). Efficient estimation for the proportional hazards model with interval censoring., The Annals of Statistics 24 540–568.
  • [8] Ichimura, H. (1993). Semiparametric least squares (SLS) and weighted SLS estimation of single-index models., Journal of Econometrics 58 71–120.
  • [9] Klein, R. W. and Spady, R. H. (1993). An efficient semiparametric estimator for binary response models., Econometrica: Journal of the Econometric Society 387–421.
  • [10] Leitenstorfer, F. and Tutz, G. (2007). Generalized monotonic regression based on B-splines with an application to air pollution data., Biostatistics 8 654–673.
  • [11] Li, K.-C. (1991). Sliced inverse regression for dimension reduction., Journal of the American Statistical Association 86 316–327.
  • [12] Li, K.-C. and Duan, N. (1989). Regression analysis under link violation., The Annals of Statistics 1009–1052.
  • [13] Lu, W., Zhang, H. H. and Zeng, D. (2011). Variable selection for optimal treatment decision., Statistical methods in medical research 0962280211428383.
  • [14] Murphy, S. A. (2003). Optimal dynamic treatment regimes., Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65 331–355.
  • [15] Qian, M. and Murphy, S. A. (2011). Performance guarantees for individualized treatment rules., Annals of statistics 39 1180.
  • [16] Robins, J. M. (2004). Optimal structural nested models for optimal sequential decisions. In, Proceedings of the Second Seattle Symposium in Biostatistics 189–326. Springer.
  • [17] Schumaker, L. (2007)., Spline functions: basic theory. Cambridge University Press.
  • [18] Thall, P. F., Sung, H.-G. and Estey, E. H. (2002). Selecting therapeutic strategies based on efficacy and death in multicourse clinical trials., Journal of the American Statistical Association 97.
  • [19] Thall, P. F., Millikan, R. E., Sung, H.-G. et al. (2000). Evaluating multiple treatment courses in clinical trials., Statistics in medicine 19 1011–1028.
  • [20] Thall, P. F., Wooten, L. H., Logothetis, C. J., Millikan, R. E. and Tannir, N. M. (2007). Bayesian and frequentist two-stage treatment strategies based on sequential failure times subject to interval censoring., Statistics in medicine 26 4687–4702.
  • [21] van der Vaart, A. W. (2000)., Asymptotic statistics 3. Cambridge university press.
  • [22] van der Vaart, A. W. and Wellner, J. A. (1996)., Weak Convergence and Empirical Processes. Springer.
  • [23] Xia, Y. (2006). Asymptotic distributions for two estimators of the single-index model., Econometric Theory 22 1112–1137.
  • [24] Zhang, B., Tsiatis, A. A., Laber, E. B. and Davidian, M. (2012). A robust method for estimating optimal treatment regimes., Biometrics 68 1010–1018.
  • [25] Zhao, Y., Zeng, D., Socinski, M. A. and Kosorok, M. R. (2011). Reinforcement learning strategies for clinical trials in nonsmall cell lung cancer., Biometrics 67 1422–1433.
  • [26] Zhao, Y., Zeng, D., Rush, A. J. and Kosorok, M. R. (2012). Estimating individualized treatment rules using outcome weighted learning., Journal of the American Statistical Association 107 1106–1118.