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Modelling heterogeneity for bivariate survival data by the log-normal distribution

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  • Hanagal, David D.

Abstract

We propose a bivariate Weibull regression model with heterogeneity (frailty or random effect) which is generated by log-normal distribution. We assume that the bivariate survival data follow bivariate Weibull of [Hanagal, D.D., 2004. Parametric bivariate regression analysis based on censored samples: A Weibull model. Economic Quality Control 19, 83--90]. There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both monozygotic and dizygotic) where genetic behaviour (which is unknown and random) of patients follows known frailty distribution. These are the situations which motivate to study this particular model. We propose two-stage maximum likelihood estimation for hierarchical likelihood in the proposed model. We present a small simulation study to compare these estimates with the true value of the parameters and it is observed that these estimates are very close to the true values of the parameters. We also compare theoretical standard errors with Monte Carlo standard errors and theoretical coverage probabilities with Monte Carlo coverage probabilities.

Suggested Citation

  • Hanagal, David D., 2008. "Modelling heterogeneity for bivariate survival data by the log-normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1101-1109, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1101-1109
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    References listed on IDEAS

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    1. Hanagal David D., 2004. "Parametric Bivariate Regression Analysis Based on Censored Samples: A Weibull Model," Stochastics and Quality Control, De Gruyter, vol. 19(1), pages 83-90, January.
    2. Hanagal David D., 2006. "Weibull Extension of Bivariate Exponential Regression Model with Gamma Frailty for Survival Data," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 261-270, January.
    3. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    1. Hanagal, David D., 2010. "Modeling heterogeneity for bivariate survival data by the compound Poisson distribution with random scale," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1781-1790, December.

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