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Survival Analysis on Pedigrees: A Marked Point Process Model

Published online by Cambridge University Press:  09 August 2013

Angus S. Macdonald
Angus S. Macdonald*
Affiliation:
Department of Actuarial Mathematics and Statistics, and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom, Tel.: +44(0)131-451-3209, Fax: +44(0)131-451-3249, E-mail: A.S.Macdonald@ma.hw.ac.uk
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Abstract

Regulation of insurers' use of genetic information means actuaries are interested in age-at-onset of genetic disorders. Arjas & Haara (1984) suggested marked point processes (MPPs) as useful models for life history data with complex covariates. Age-at-onset distributions (or equivalently, hazard rates) in respect of inherited disorders are often estimated from pedigrees, which are life histories with unusually complex covariates, as well as strong dependencies induced by shared genes. Since Elston (1973) parametric models have often been used, conditioning the likelihood on known genotypes. However, a genotype identii ed by a presymptomatic genetic test is a form of internal covariate (Kalbfleisch & Prentice, 2002). We propose a very general MPP model of a pedigree, including presymptomatic genetic testing, (‘the full model’) and show under what circumstances the partial model leading to Elston's likelihood is valid. In practice, pedigrees are often ascertained retrospectively. Many such events can be modelled by augmenting the natural filtration of the MPP. We show that, except in simple special cases, the partial model is no longer valid, and the resulting likelihoods appear to be intractable. In particular, ascertainment interacts even with independent censoring so that likelihoods no longer factorize. For one simple special case — studies of sibships — we generalise a classical result to age-at-onset data. We conclude that the study of genetic conditions with variable age at onset gains insights from the underlying principles of survival analysis in their modern form, but that great care is needed in translating epidemiological studies into actuarial models.

Keywords

AscertainmentInsuranceInternal CovariateMarked Point ProcessPedigreePresymptomatic Genetic TestRate of OnsetSurvival Analysis
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 35 - 64
Copyright
Copyright © International Actuarial Association 2010

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References

Aalen, O.O., Borgan, Ø., Keiding, N. and Thormann, J. (1980) Interaction between life history events. Nonparametric analysis for prospective and retrospective data in the presence of censoring, Scandinavian Journal of Statistics, 7, 161–171.Google Scholar
Andersen, P.K., Borgan, Ø., Gill, R.D. and Keiding, N. (1993) Statistical models based on counting processes, Springer-Verlag, New York.CrossRefGoogle Scholar
Arjas, E. (1989) Survival models and martingale dynamics, Scandinavian Journal of Statistics, 16, 177–225.Google Scholar
Arjas, E. and Haara, P. (1984) A marked point process approach to censored failure data with complicated covariates, Scandinavian Journal of Statistics, 11, 193–209.Google Scholar
Cannings, C. and Thompson, E.A. (1977) Ascertainment in the sequential sampling of pedigrees, Clinical Genetics, 12, 208–212.Google Scholar
Elston, R.C. (1973) Ascertainment and age at onset in pedigree analysis, Human Heredity, 23, 105–112.CrossRefGoogle ScholarPubMed
Elston, R.C. (1995) 'Twixt cup and lip: How intractable is the ascertainment problem?, American Journal of Human Genetics, 56, 15–17.Google Scholar
Espinosa, C. and Macdonald, A.S. (2007) A correction for ascertainment bias in estimating rates of onset of highly penetrant genetic disorders, ASTIN Bulletin, 37, 429–452.Google Scholar
Fisher, R.A. (1934) The effects of methods of ascertainment upon the estimation of frequencies, Annals of Human Genetics, 50, 399–402.Google Scholar
George, V.T. and Elston, R.C. (1991) Ascertainment: An overview of the classical segregation analysis model for independent sibships, Biometric Journal, 33, 741–753.Google Scholar
Hodge, S.E. (2002) Ascertainment, Biostatistical genetics and genetic epidemiology, Elston, R., Olson, J. and Palmer, L., Wiley, John.Google Scholar
Hoem, J.M. (1969) Purged and partial Markov chains, Skandinavisk Aktuarietidskrift, 1969, 146–155.Google Scholar
Kalbfleisch, J.D. and Prentice, R.L. (2002) The statistical analysis of failure time data (second edition), John Wiley, New Jersey.Google Scholar
Langholz, B., Ziogas, A., Thomas, D.C., Faucett, C., Huberman, M. and Goldstein, L. (1999) Ascertainment correction in rate ratio estimation from case-sibling control studies of variable age-at-onset diseases, Biometrics, 55, 1129–1136.CrossRefGoogle Scholar
Li, H. (2007) Survival analysis methods in genetic epidemiology, Current topics in human genetics: Studies of complex diseases, Deng, H.-W., Shen, H., Liu, Y. and Hu, H., World Scientific Publishing, Singapore.Google Scholar
Lu, L., Macdonald, A.S. and Waters, H.R. (2008) Sampling distributions of critical illness insurance premium rates: Breast and ovarian cancer, ASTIN Bulletin, 38, 527–542.CrossRefGoogle Scholar
Lu, L., Macdonald, A.S. and Wekwete, C.T. (2008) Premium rates based on genetic studies: How reliable are they?, Insurance: Mathematics and Economics, 42, 319–331.Google Scholar
Macdonald, A.S., Waters, H.R., and Wekwete, C.T. (2003) The genetics of breast and ovarian cancer II: A model of critical illness insurance, Scandinavian Actuarial Journal, 1, 28–50.Google Scholar
Morton, N.E. (1959) Genetic tests under incomplete ascertainment, American Journal of Human Genetics, 11, 1–16.Google ScholarPubMed
Newcombe, R.G. (1981) A life table for onset of Huntington's Chorea, Annals of Human Genetics, 45, 375–385.Google Scholar
Thompson, E.A. (1993) Sampling and ascertainment in genetic epidemiology: A tutorial review, Technical Report 243, Department of Statistics, University of Washington.Google Scholar
Vieland, V.J. and Hodge, S.E. (1995) Inherent intractability of the ascertainment problem for pedigree data: A general likelihood framework, American Journal of Human Genetics, 56, 33–43.Google Scholar