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A class of semiparametric models for bivariate survival data

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  • Walmir Reis Miranda Filho

    (Federal University of Ouro Preto)

  • Fábio Nogueira Demarqui

    (Federal University of Minas Gerais)

Abstract

We propose a new class of bivariate survival models based on the family of Archimedean copulas with margins modeled by the Yang and Prentice (YP) model. The Ali-Mikhail-Haq (AMH), Clayton, Frank, Gumbel-Hougaard (GH), and Joe copulas are employed to accommodate the dependency among marginal distributions. Baseline distributions are modeled semiparametrically by the Piecewise Exponential (PE) distribution and the Bernstein polynomials (BP). Inference procedures for the proposed class of models are based on the maximum likelihood (ML) approach. The new class of models possesses some attractive features: i) the ability to take into account survival data with crossing survival curves; ii) the inclusion of the well-known proportional hazards (PH) and proportional odds (PO) models as particular cases; iii) greater flexibility provided by the semiparametric modeling of the marginal baseline distributions; iv) the availability of closed-form expressions for the likelihood functions, leading to more straightforward inferential procedures. The properties of the proposed class are numerically investigated through an extensive simulation study. Finally, we demonstrate the versatility of our new class of models through the analysis of survival data involving patients diagnosed with ovarian cancer.

Suggested Citation

  • Walmir Reis Miranda Filho & Fábio Nogueira Demarqui, 2025. "A class of semiparametric models for bivariate survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(1), pages 102-125, January.
    • Handle: RePEc:spr:lifeda:v:31:y:2025:i:1:d:10.1007_s10985-024-09642-x
    DOI: 10.1007/s10985-024-09642-x
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    References listed on IDEAS

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    1. Petti, Danilo & Eletti, Alessia & Marra, Giampiero & Radice, Rosalba, 2022. "Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    2. Song Yang & Ross Prentice, 2005. "Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data," Biometrika, Biometrika Trust, vol. 92(1), pages 1-17, March.
    3. Guoqing Diao & Donglin Zeng & Song Yang, 2013. "Efficient Semiparametric Estimation of Short-Term and Long-Term Hazard Ratios with Right-Censored Data," Biometrics, The International Biometric Society, vol. 69(4), pages 840-849, December.
    4. Joe, H., 1993. "Parametric Families of Multivariate Distributions with Given Margins," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 262-282, August.
    5. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
    6. I‐Shou Chang & Chao A. Hsiung & Yuh‐Jenn Wu & Che‐Chi Yang, 2005. "Bayesian Survival Analysis Using Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 447-466, September.
    7. Osman, Muhtarjan & Ghosh, Sujit K., 2012. "Nonparametric regression models for right-censored data using Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 559-573.
    8. Giampiero Marra & Rosalba Radice, 2020. "Copula Link-Based Additive Models for Right-Censored Event Time Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(530), pages 886-895, April.
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