Inference Methods for Correlated Left Truncated Lifetimes: Parent and Offspring Relations in an Adoption Study |
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Authors: | Liselotte Petersen Thorkild I A Sørensen Gert G Nielsen Per Kragh Andersen |
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Institution: | 1. Danish Epidemiology Science Centre at the Institute of Preventive Medicine, Copenhagen University Hospital, ?ster S?gade 18, 1., DK-1399, Copenhagen K, Denmark 3. Novo Nordisk A/S, DK-2880, Bagsv?rd, Denmark 4. Department of Biostatistics, University of Copenhagen, ?ster Farimagsgade 5, P.O. Box 2099, DK-1014, Copenhagen K, Denmark 2. Danish Epidemiology Science Centre, Statens Serum Institut, Artillerivej 5, DK-2300, Copenhagen S, Denmark
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Abstract: | The associations in mortality of adult adoptees and their biological or adoptive parents have been studied in order to separate
genetic and environmental influences. The 1003 Danish adoptees born 1924–26 have previously been analysed in a Cox regression
model, using dichotomised versions of the parents’ lifetimes as covariates. This model will be referred to as the conditional
Cox model, as it analyses lifetimes of adoptees conditional on parental lifetimes. Shared frailty models may be more satisfactory
by using the entire observed lifetime of the parents. In a simulation study, sample size, distribution of lifetimes, truncation-
and censoring patterns were chosen to illustrate aspects of the adoption dataset, and were generated from the conditional
Cox model or a shared frailty model with gamma distributed frailties. First, efficiency was compared in the conditional Cox
model and a shared frailty model, based on the conditional approach. For data with type 1 censoring the models showed no differences,
whereas in data with random or no censoring, the models had different power in favour of the one from which data were generated.
Secondly, estimation in the shared frailty model by a conditional approach or a two-stage copula approach was compared. Both
approaches worked well, with no sign of dependence upon the truncation pattern, but some sign of bias depending on the censoring.
For frailty parameters close to zero, we found bias when the estimation procedure used did not allow negative estimates. Based
on this evaluation, we prefer to use frailty models allowing for negative frailty parameter estimates. The conclusions from
earlier analyses of the adoption study were confirmed, though without greater precision than using the conditional Cox model.
Analyses of associations between parental lifetimes are also presented. |
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Keywords: | Correlated lifetimes Shared gamma frailty Left truncation Adoption study |
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