Ascertainment-adjusted maximum likelihood estimation for the additive genetic gamma frailty model

Ascertainment correction in frailty models for recurrent events data

In retrospective studies involving recurrent events, it is common to select individuals based on their event history up to the time of selection. In this case, the ascertained subjects might not be representative for the target population, and the analysis should take the selection mechanism into account. The purpose of this paper is two-fold. First, to study what happens when the data analysis is not adjusted for the selection and second, to propose a corrected analysis. Under the Andersen-Gill and shared frailty regression models, we show that the estimators of covariate effects, incidence, and frailty variance can be biased if the ascertainment is ignored, and we show that with a simple adjustment of the likelihood, unbiased and consistent estimators are obtained. The proposed method is assessed by a simulation study and is illustrated on a data set comprising recurrent pneumothoraces. Copyright © 2016 John Wiley & Sons, Ltd.

Score test for age at onset genetic linkage analysis in selected sibling pairs

A new score statistic is derived, which uses information from registries (age-specific incidences) and family studies (sib-sib marginal correlation) to weight affected sibling pairs according to their age at onset. Age at onset of sibling pairs is modelled by a gamma frailty model. From this model we derive a bivariate survival function, which depends on the marginal survival and on the marginal correlation. The score statistic for linkage is a classical nonparametric linkage (NPL) statistic where the identical by descent sharing is weighted by a particular function of the age at onset data. Since the statistic is based on survival models, it can also be applied to discordant and healthy sibling pairs. Simulation studies show that the proposed method is robust and more powerful than standard NPL methods. As illustration we apply the new score statistic to data from a breast cancer study.

Full likelihood analysis of genetic risk with variable age at onset disease--combining population-based registry data and demographic information

Background

In genetic studies of rare complex diseases it is common to ascertain familial data from population based registries through all incident cases diagnosed during a pre-defined enrollment period. Such an ascertainment procedure is typically taken into account in the statistical analysis of the familial data by constructing either a retrospective or prospective likelihood expression, which conditions on the ascertainment event. Both of these approaches lead to a substantial loss of valuable data.

Methodology and Findings

Here we consider instead the possibilities provided by a Bayesian approach to risk analysis, which also incorporates the ascertainment procedure and reference information concerning the genetic composition of the target population to the considered statistical model. Furthermore, the proposed Bayesian hierarchical survival model does not require the considered genotype or haplotype effects be expressed as functions of corresponding allelic effects. Our modeling strategy is illustrated by a risk analysis of type 1 diabetes mellitus (T1D) in the Finnish population-based on the HLA-A, HLA-B and DRB1 human leucocyte antigen (HLA) information available for both ascertained sibships and a large number of unrelated individuals from the Finnish bone marrow donor registry. The heterozygous genotype DR3/DR4 at the DRB1 locus was associated with the lowest predictive probability of T1D free survival to the age of 15, the estimate being 0.936 (0.926; 0.945 95% credible interval) compared to the average population T1D free survival probability of 0.995.

Significance

The proposed statistical method can be modified to other population-based family data ascertained from a disease registry provided that the ascertainment process is well documented, and that external information concerning the sizes of birth cohorts and a suitable reference sample are available. We confirm the earlier findings from the same data concerning the HLA-DR3/4 related risks for T1D, and also provide here estimated predictive probabilities of disease free survival as a function of age.