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A nonparametric maximum likelihood approach for survival data with observed cured subjects, left truncation and right-censoring

Author

Listed:
  • Jue Hou

    (University of California)

  • Christina D. Chambers

    (University of California
    University of California)

  • Ronghui Xu

    (University of California
    University of California)

Abstract

We consider observational studies in pregnancy where the outcome of interest is spontaneous abortion (SAB). This at first sight is a binary ‘yes’ or ‘no’ variable, albeit there is left truncation as well as right-censoring in the data. Women who do not experience SAB by gestational week 20 are ‘cured’ from SAB by definition, that is, they are no longer at risk. Our data is different from the common cure data in the literature, where the cured subjects are always right-censored and not actually observed to be cured. We consider a commonly used cure rate model, with the likelihood function tailored specifically to our data. We develop a conditional nonparametric maximum likelihood approach. To tackle the computational challenge we adopt an EM algorithm making use of “ghost copies” of the data, and a closed form variance estimator is derived. Under suitable assumptions, we prove the consistency of the resulting estimator which involves an unbounded cumulative baseline hazard function, as well as the asymptotic normality. Simulation results are carried out to evaluate the finite sample performance. We present the analysis of the motivating SAB study to illustrate the advantages of our model addressing both occurrence and timing of SAB, as compared to existing approaches in practice.

Suggested Citation

  • Jue Hou & Christina D. Chambers & Ronghui Xu, 2018. "A nonparametric maximum likelihood approach for survival data with observed cured subjects, left truncation and right-censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 612-651, October.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:4:d:10.1007_s10985-017-9415-2
    DOI: 10.1007/s10985-017-9415-2
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    References listed on IDEAS

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    1. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    2. Jing Ning & Jing Qin & Yu Shen, 2010. "Non‐parametric tests for right‐censored data with biased sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 609-630, November.
    3. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    4. Zeng, Donglin & Yin, Guosheng & Ibrahim, Joseph G., 2006. "Semiparametric Transformation Models for Survival Data With a Cure Fraction," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 670-684, June.
    5. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    6. Li, Chin-Shang & Taylor, Jeremy M. G. & Sy, Judy P., 2001. "Identifiability of cure models," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 389-395, October.
    7. Li, Yi & Lin, Xihong, 2006. "Semiparametric Normal Transformation Models for Spatially Correlated Survival Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 591-603, June.
    8. Wei Pan, 2000. "A Multiple Imputation Approach to Cox Regression with Interval-Censored Data," Biometrics, The International Biometric Society, vol. 56(1), pages 199-203, March.
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    Cited by:

    1. Zhang, Feipeng & Yang, Jiejing & Ye, Min, 2020. "A nonparametric maximum likelihood estimation for biased-sampling data with zero-inflated truncation," Economics Letters, Elsevier, vol. 194(C).

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