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A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity


  • Congdon, Peter


For certain life cycle events a non-susceptible fraction of subjects will never undergo the event. In demographic applications, examples are provided by marriage and age at first maternity. A model for survival data allowing a permanent survival fraction, non-monotonic failure rates and unobserved frailty is considered here. Regressions are used to explain both the failure time and permanent survival mechanisms and additive correlated errors are included in the general linear models defining these regressions. AÂ hierarchical Bayesian approach is adopted with likelihood conditional on the random frailty effects and a second stage prior defining the bivariate density of those effects. The gain in model fit, and potential effects on inference, from adding frailty is demonstrated in a case study application to age at first maternity in Germany.

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  • Congdon, Peter, 2008. "A bivariate frailty model for events with a permanent survivor fraction and non-monotonic hazards; with an application to age at first maternity," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4346-4356, May.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4346-4356

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    1. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    2. Tutz, Gerhard & Kauermann, Goran, 2003. "Generalized linear random effects models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 13-28, May.
    3. FFF1Michaela NNN1Kreyenfeld, 2004. "Fertility Decisions in the FRG and GDR: An Analysis with Data from the German Fertility and Family Survey," Demographic Research Special Collections, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 3(11), pages 275-318, April.
    4. Schmidt, Peter & Witte, Ann Dryden, 1989. "Predicting criminal recidivism using 'split population' survival time models," Journal of Econometrics, Elsevier, vol. 40(1), pages 141-159, January.
    5. Chib, Siddhartha & Winkelmann, Rainer, 2001. "Markov Chain Monte Carlo Analysis of Correlated Count Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 428-435, October.
    6. Jaap H. Abbring & Gerard J. Van Den Berg, 2007. "The unobserved heterogeneity distribution in duration analysis," Biometrika, Biometrika Trust, vol. 94(1), pages 87-99.
    7. Gordana Colby & Paul Rilstone, 2007. "Simplified estimation of multivariate duration models with unobserved heterogeneity," Computational Statistics, Springer, vol. 22(1), pages 17-29, April.
    8. Siv Gustafsson, 2001. "Optimal age at motherhood. Theoretical and empirical considerations on postponement of maternity in Europe," Journal of Population Economics, Springer;European Society for Population Economics, vol. 14(2), pages 225-247.
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