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Effect of frailty on marginal regression estimates in survival analysis

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  • R. Henderson
  • P. Oman

Abstract

Unexplained heterogeneity in univariate survival data and association in multivariate survival can both be modelled by the inclusion of frailty effects. This paper investigates the consequences of ignoring frailty in analysis, fitting misspecified Cox proportional hazards models to the marginal distributions. Regression coefficients are biased towards 0 by an amount which depends in magnitude on the variability of the frailty terms and the form of frailty distribution. The bias is reduced when censoring is present. Fitted marginal survival curves can also differ substantially from the true marginals.

Suggested Citation

  • R. Henderson & P. Oman, 1999. "Effect of frailty on marginal regression estimates in survival analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 367-379, April.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:2:p:367-379
    DOI: 10.1111/1467-9868.00182
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    Cited by:

    1. Marcelo Resende & Vicente Cardoso & Luis Otávio Façanha, 2016. "Determinants of survival of newly created SMEs in the Brazilian manufacturing industry: an econometric study," Empirical Economics, Springer, vol. 50(4), pages 1255-1274, June.
    2. Yang-Jin Kim, 2006. "Regression Analysis of Doubly Censored Failure Time Data with Frailty," Biometrics, The International Biometric Society, vol. 62(2), pages 458-464, June.
    3. repec:gig:joupla:v:6:y:2014:i:2:p:3-38 is not listed on IDEAS
    4. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    5. Alex Mota & Eder A. Milani & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Oilson G. Junior & Vera L. D. Tomazella & Francisco Louzada, 2023. "A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 883-909, September.
    6. Elizabeth Wrigley-Field, 2020. "Multidimensional Mortality Selection: Why Individual Dimensions of Frailty Don’t Act Like Frailty," Demography, Springer;Population Association of America (PAA), vol. 57(2), pages 747-777, April.
    7. Robin Henderson & Ralitsa Mihaylova & Paul Oman, 2019. "A dual frailty model for lifetime analysis in maritime transportation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 739-756, October.
    8. Bowles, Roger Arthur & Florackis, Chrisostomos, 2007. "Duration of the time to reconviction: Evidence from UK prisoner discharge data," Journal of Criminal Justice, Elsevier, vol. 35(4), pages 365-378.
    9. Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    10. Niels Keiding & Katrine Lykke Albertsen & Helene Charlotte Rytgaard & Anne Lyngholm Sørensen, 2019. "Prevalent cohort studies and unobserved heterogeneity," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 712-738, October.
    11. Yu, Binbing & Peng, Yingwei, 2008. "Mixture cure models for multivariate survival data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1524-1532, January.
    12. María-Dolores Huete-Morales & Esteban Navarrete-Álvarez & María-Jesús Rosales-Moreno & María-José Del-Moral-Ávila & José-Manuel Quesada-Rubio, 2020. "Modelling the survival function of the Spanish population by the Wong–Tsui model with the incorporation of frailty and covariates," Letters in Spatial and Resource Sciences, Springer, vol. 13(2), pages 151-163, August.
    13. Hendrik Koffijberg & Gabriel Rinkel & Erik Buskens, 2009. "Do Intraindividual Variation in Disease Progression and the Ensuing Tight Window of Opportunity Affect Estimation of Screening Benefits?," Medical Decision Making, , vol. 29(1), pages 82-90, January.
    14. Virginia Zarulli, 2016. "Unobserved Heterogeneity of Frailty in the Analysis of Socioeconomic Differences in Health and Mortality," European Journal of Population, Springer;European Association for Population Studies, vol. 32(1), pages 55-72, February.
    15. Lei Liu & Xuelin Huang, 2009. "Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 65-81, February.
    16. Andreas Wienke, 2003. "Frailty models," MPIDR Working Papers WP-2003-032, Max Planck Institute for Demographic Research, Rostock, Germany.

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