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Semiparametric analysis of survival data with left truncation and right censoring

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  • Shen, Pao-sheng

Abstract

Let T, C and V denote the lifetime, censoring and truncation variables, respectively. Assume that (C,V) is independent of T and P(C>=V)=1. Let F, Q and G denote the common distribution functions of T, C and V, respectively. For left-truncated and right-censored (LTRC) data, one can observe nothing if T =V. For LTRC data, the truncation product-limit estimate is the maximum likelihood estimate (MLE) for nonparametric models. If the distribution of V is parameterized as G(x;[theta]) and the distributions of T and C are left unspecified, the product-limit estimate is not the MLE for this semiparametric model. In this article, for LTRC data, two semiparametric estimates are proposed for the semiparametric model. A simulation study is conducted to compare the performances of the two semiparametric estimators against that of . The proposed semiparametric method is applied to a Channing House data.

Suggested Citation

  • Shen, Pao-sheng, 2009. "Semiparametric analysis of survival data with left truncation and right censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4417-4432, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4417-4432
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    References listed on IDEAS

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    1. Asgharian M. & MLan C.E. & Wolfson D. B., 2002. "Length-Biased Sampling With Right Censoring: An Unconditional Approach," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 201-209, March.
    2. Shen, Pao-sheng, 2009. "Hazards regression for length-biased and right-censored data," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 457-465, February.
    3. Hwang, Yi-Ting & Wang, Chun-chao, 2008. "A goodness of fit test for left-truncated and right-censored data," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2420-2425, October.
    4. de Una-Alvarez, Jacobo & Rodriguez-Casal, Alberto, 2007. "Nonparametric estimation from length-biased data under competing risks," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2653-2669, February.
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    Cited by:

    1. 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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