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Proportional Odds Models for Survival Data and Estimates Using Ranks

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  • A. N. Pettitt

Abstract

Survival data are analysed where it is assumed that the logarithm of the odds against survival beyond a certain time is equal to a linear term, involving covariates in a regression model, plus a function of time. It is shown that estimates for the regression parameters can be obtained by replacing survival times by their ranks. Comparisons are made with estimates found by Bennett (1983a, b), who used the same model but different techniques of estimation.

Suggested Citation

  • A. N. Pettitt, 1984. "Proportional Odds Models for Survival Data and Estimates Using Ranks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 169-175, June.
    • Handle: RePEc:bla:jorssc:v:33:y:1984:i:2:p:169-175
    DOI: 10.2307/2347443
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    Cited by:

    1. Zhong Guan & Cheng Peng, 2011. "A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness of fit," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 763-780.
    2. Clelia Di Serio & Yosef Rinott & Marco Scarsini, 2009. "Simpson's Paradox in Survival Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 463-480, September.
    3. Zhao, Yichuan, 2010. "Semiparametric inference for transformation models via empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1846-1858, September.
    4. K. F. Lam & Y. W. Lee & T. L. Leung, 2002. "Modeling Multivariate Survival Data by a Semiparametric Random Effects Proportional Odds Model," Biometrics, The International Biometric Society, vol. 58(2), pages 316-323, June.
    5. Pao-sheng Shen & Yi Liu, 2019. "Pseudo maximum likelihood estimation for the Cox model with doubly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1207-1224, August.
    6. Huang, Bin & Wang, Qihua, 2010. "Semiparametric analysis based on weighted estimating equations for transformation models with missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2078-2090, October.
    7. Wang, Qihua & Tong, Xingwei & Sun, Liuquan, 2012. "Exploring the varying covariate effects in proportional odds models with censored data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 168-189.
    8. P. Vellaisamy, 2017. "Collapsibility of some association measures and survival models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1155-1176, October.
    9. Chunpeng Fan & Jason Fine & Jong-Hyeon Jeong, 2012. "Optimal inferences for proportional hazards model with parametric covariate transformations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 715-736, August.
    10. Kin Yau Wong & Yair Goldberg & Jason P. Fine, 2016. "Oracle estimation of parametric models under boundary constraints," Biometrics, The International Biometric Society, vol. 72(4), pages 1173-1183, December.
    11. Jianbo Li & Minggao Gu & Tao Hu, 2012. "General partially linear varying-coefficient transformation models for ranking data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(7), pages 1475-1488, January.
    12. Lu, Wenbin & Liang, Yu, 2006. "Empirical likelihood inference for linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1586-1599, August.
    13. Ying Chen & Su-Chun Cheng, 2004. "Semiparametric Regression Analysis of Mean Residual Life with Censored Survival Data," U.C. Berkeley Division of Biostatistics Working Paper Series 1146, Berkeley Electronic Press.
    14. Matteo Grigoletto & Michael G. Akritas, 1999. "Analysis of Covariance with Incomplete Data Via Semiparametric Model Transformations," Biometrics, The International Biometric Society, vol. 55(4), pages 1177-1187, December.
    15. Zhang, Hao Helen & Lu, Wenbin & Wang, Hansheng, 2010. "On sparse estimation for semiparametric linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1594-1606, August.
    16. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    17. Ronghui Xu & David P. Harrington, 2001. "A Semiparametric Estimate of Treatment Effects with Censored Data," Biometrics, The International Biometric Society, vol. 57(3), pages 875-885, September.
    18. Lin Liu & Jianbo Li & Riquan Zhang, 2014. "General partially linear additive transformation model with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2257-2269, October.
    19. Glenn Heller & Jing Qin, 2001. "Pairwise Rank-Based Likelihood for Estimation and Inference on the Mixture Proportion," Biometrics, The International Biometric Society, vol. 57(3), pages 813-817, September.
    20. Xifen Huang & Chaosong Xiong & Tao Jiang & Junfeng Lu & Jinfeng Xu, 2022. "Efficient Estimation and Inference in the Proportional Odds Model for Survival Data," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    21. Ramesh Gupta & Cheng Peng, 2014. "Proportional odds frailty model and stochastic comparisons," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 897-912, October.
    22. Daniel Rabinowitz & Rebecca A. Betensky & Anastasios A. Tsiatis, 2000. "Using Conditional Logistic Regression to Fit Proportional Odds Models to Interval Censored Data," Biometrics, The International Biometric Society, vol. 56(2), pages 511-518, June.
    23. Ying Qing Chen & Nan Hu & Su-Chun Cheng & Philippa Musoke & Lue Ping Zhao, 2012. "Estimating Regression Parameters in an Extended Proportional Odds Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 318-330, March.

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