Artificial Insemination by Donor: Discrete time survival data with crossed and nested random effects

  • David Clayton
  • René Ecochard
Part of the Lecture Notes in Statistics book series (LNS, volume 123)


A discrete time survival problem arising in studies of artificial insemination by donor is described. This problem involves two levels of “ frailty” effect to model heterogeneity of female fecundability, together with a further two nested sets of random effects for sperm donor and donation. Parametric and non-parametric approaches to modelling such data are discussed, and computational difficulties highlighted. Attention is also drawn to the relationship of such problems to the extensive literature on generalised linear mixed models.


Generalize Linear Mixed Model Artificial Insemination Sperm Quality Frailty Model Logit Scale 
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  1. [AF95]
    M. Aitkin and B.J. Francis. GLIM4 macros for nonparametric maximum likelihood estimation with overdispersion and variance component models in the exponential family. The GLIM Newsletter (submitted), 1995.Google Scholar
  2. [BC93]
    N.E. Breslow and D. Clayton. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88:9–25, 1993.CrossRefMATHGoogle Scholar
  3. [BR92]
    A.S. Bryke and S.W. Raudenbush. Hierarchical Linear Models: Applications and Data Analysis Methods. Sage publications, Newbury Park, 1992.Google Scholar
  4. [Cla78]
    D. Clayton. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65:141–151, 1978.MathSciNetCrossRefMATHGoogle Scholar
  5. [Cla94]
    D. Clayton. Generalized linear mixed models. In W.R. Gilks, S. Richardson, and D. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice. Chapman and Hall, London, 1994.Google Scholar
  6. [Con90]
    M.R. Conoway. A random effects model for binary data. Biometrics, 46:317–328, 1990.MathSciNetCrossRefGoogle Scholar
  7. [Cox72]
    D.R. Cox. Regression models and life tables (with discussion). Journal of the Royal Statistical Society, Series B, 34:187–220, 1972.MATHGoogle Scholar
  8. [CR82]
    R.J. Carroll and D. Ruppert. Robust estimation in heteroscedastic linear models. Annals of Statistics, 10:429–441, 1982.MathSciNetCrossRefMATHGoogle Scholar
  9. [G0186]
    H. Goldstein. Multilevel mixed linear model analysis using iterative generalized least squares. Biometrika, 73:43–56, 1986.MathSciNetCrossRefMATHGoogle Scholar
  10. [Hou84]
    P. Hougaard. Life table methods for heterogeneous populations: distributions describing the heterogeneity. Biometrika, 71:75–83, 1984.MathSciNetCrossRefMATHGoogle Scholar
  11. [Hub67]
    P.J. Huber. The behaviour of maximum likelihood estimates under non-standard conditions. In Proceedings of the Fifth Berkely Symposium on Mathematical Statistics and Probability, I, pages 221–223. 1967.Google Scholar
  12. [HW90a]
    J.J. Heckmann and J.R. Walker. Estimating fecundability from data on waiting times to first conception. Journal of the American Statistical Association, 85:283–295, 1990.CrossRefGoogle Scholar
  13. [HW90b]
    J.P. Hinde and A.T.A. Wood. Binomial variance component models with a non-parametric assumption concerning random effects. In R. Crouchley, editor, Longitudinal data analysis. Avebury, Aldershot, Hants, 1990.Google Scholar
  14. [Irw49]
    J.O. Irwin. A note on the subdivision of X 2 into componenents. Biometrika,36:130, 1949.MathSciNetMATHGoogle Scholar
  15. [Lan49]
    H.O. Lancaster. The derivation and partition of X 2 in certain discrete distributions. Biometrika,36:117, 1949.MathSciNetMATHGoogle Scholar
  16. [LN96]
    Y. Lee and J.A. Neider. Hierarchical generalized linear models. Journal of the Royal Statistical Society, Series B, 58:1, 1964.Google Scholar
  17. [LR87]
    J.A. Little and D.B. Rubin. Statistical Analysis with Missing Data. Wiley Series in Probability and Mathematical Statistics. Wiley, New York, 1987.MATHGoogle Scholar
  18. [LZ86]
    K.Y. Liang and S.L. Zeger. Longitudinal data analysis using generalized linear models. Biometrika, 73:13–22, 1986.MathSciNetCrossRefMATHGoogle Scholar
  19. [MA91]
    C.A. McGilchrist and C.W. Aisbett. Regression with frailty in survival analysis. Biometrics, 47:461–466, 1991.CrossRefGoogle Scholar
  20. [McG93]
    C.A. McGilchrist. REML estimation for survival models with frailty. Biometrics, 49:221–225, 1993.CrossRefGoogle Scholar
  21. [Oak82]
    D. Oakes. A model for association in bivariate survival data. Journal of the Royal Statistical Society, Series B, 44:414–422, 1982.MathSciNetMATHGoogle Scholar
  22. [Oak86]
    D. Oakes. Semi-parametric inference in a model for association in bivariate survival time data. Biometrika, 73:353–361, 1986.MathSciNetMATHGoogle Scholar
  23. [She64]
    M.C. Sheps. On the time required for conception. Population Studies, 17:85–97, 1964.Google Scholar
  24. [SM73]
    M.C. Sheps and J. A. Menken. Mathematical models of conception and birth. University of Chicago Press, Chicago, 1973.Google Scholar
  25. [WBW94]
    C.R. Weinberg, D.D. Baird, and A.J. Wilcox. Sources of bias in studies of time to pregnancy. Statistics in Medicine, 13:671–681, 1994.CrossRefGoogle Scholar
  26. [WG86]
    C.R. Weinberg and B.C. Gladen. The beta-geometric distribution applied to comparatitive fecundability studies. Biometrics, 42:547–560, 1986.CrossRefGoogle Scholar
  27. [Whi80]
    H. White. A heteroskedasticity-consistent covariance matrix estimate and a direct test for heteroskedasticity. Econometrika, 48:817–830, 1980.CrossRefMATHGoogle Scholar
  28. [YI95]
    A.I. Yashin and I.A. Iachine. Genetic analysis of durations: correlated frailty model applied to survival of Danish twins. Genetic Epidemiology, 12:529–538, 1995.CrossRefGoogle Scholar
  29. [ZK91]
    S.L. Zeger and M.R. Karim. Generalized linear models with random effects; a gibbs sampling approach. Journal of the American Statistical Association, 86:79–86, 1991.MathSciNetCrossRefGoogle Scholar

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© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • David Clayton
  • René Ecochard

There are no affiliations available

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