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Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data

Author

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  • Chyong-Mei Chen

    (National Yang-Ming University)

  • Pao-Sheng Shen

    (Tunghai University)

Abstract

Left-truncated data often arise in epidemiology and individual follow-up studies due to a biased sampling plan since subjects with shorter survival times tend to be excluded from the sample. Moreover, the survival time of recruited subjects are often subject to right censoring. In this article, a general class of semiparametric transformation models that include proportional hazards model and proportional odds model as special cases is studied for the analysis of left-truncated and right-censored data. We propose a conditional likelihood approach and develop the conditional maximum likelihood estimators (cMLE) for the regression parameters and cumulative hazard function of these models. The derived score equations for regression parameter and infinite-dimensional function suggest an iterative algorithm for cMLE. The cMLE is shown to be consistent and asymptotically normal. The limiting variances for the estimators can be consistently estimated using the inverse of negative Hessian matrix. Intensive simulation studies are conducted to investigate the performance of the cMLE. An application to the Channing House data is given to illustrate the methodology.

Suggested Citation

  • Chyong-Mei Chen & Pao-Sheng Shen, 2018. "Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 250-272, April.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:2:d:10.1007_s10985-016-9385-9
    DOI: 10.1007/s10985-016-9385-9
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    References listed on IDEAS

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    1. Micha Mandel & Rebecca A. Betensky, 2007. "Testing Goodness of Fit of a Uniform Truncation Model," Biometrics, The International Biometric Society, vol. 63(2), pages 405-412, June.
    2. Pao-sheng Shen, 2011. "Semiparametric analysis of transformation models with left-truncated and right-censored data," Computational Statistics, Springer, vol. 26(3), pages 521-537, September.
    3. Yu-Jen Cheng & Chiung-Yu Huang, 2014. "Combined estimating equation approaches for semiparametric transformation models with length-biased survival data," Biometrics, The International Biometric Society, vol. 70(3), pages 608-618, September.
    4. Jane Paik Kim & Wenbin Lu & Tony Sit & Zhiliang Ying, 2013. "A Unified Approach to Semiparametric Transformation Models Under General Biased Sampling Schemes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 217-227, March.
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    8. Wei Pan & Rick Chappell, 2002. "Estimation in the Cox Proportional Hazards Model with Left-Truncated and Interval-Censored Data," Biometrics, The International Biometric Society, vol. 58(1), pages 64-70, March.
    9. Qian, Jing & Betensky, Rebecca A., 2014. "Assumptions regarding right censoring in the presence of left truncation," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 12-17.
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    Cited by:

    1. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    2. Prabhashi W. Withana Gamage & Christopher S. McMahan & Lianming Wang, 2023. "A flexible parametric approach for analyzing arbitrarily censored data that are potentially subject to left truncation under the proportional hazards model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 188-212, January.

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