Score Test for Linkage in Generalized Linear Models

Score tests for exploring complex models: application to HIV dynamics models

In biostatistics, more and more complex models are being developed. This is particularly the case in system biology. Fitting complex models can be very time-consuming, since many models often have to be explored. Among the possibilities are the introduction of explanatory variables and the determination of random effects. The particularity of this use of the score test is that the null hypothesis is not itself very simple; typically, some random effects may be present under the null hypothesis. Moreover, the information matrix cannot be computed, but only an approximation based on the score. This article examines this situation with the specific example of HIV dynamics models. We examine the score test statistics for testing the effect of explanatory variables and the variance of random effect in this complex situation. We study type I errors and the statistical powers of this score test statistics and we apply the score test approach to a real data set of HIV-infected patients.

Testing for genetic association in the presence of linkage and gene-covariate interactions

In order to study family-based association in the presence of linkage, we extend a generalized linear mixed model proposed for genetic linkage analysis (Lebrec and van Houwelingen (2007), Human Heredity 64, 5-15) by adding a genotypic effect to the mean. The corresponding score test is a weighted family-based association tests statistic, where the weight depends on the linkage effect and on other genetic and shared environmental effects. For testing of genetic association in the presence of gene-covariate interaction, we propose a linear regression method where the family-specific score statistic is regressed on family-specific covariates. Both statistics are straightforward to compute. Simulation results show that adjusting the weight for the within-family variance structure may be a powerful approach in the presence of environmental effects. The test statistic for genetic association in the presence of gene-covariate interaction improved the power for detecting association. For illustration, we analyze the rheumatoid arthritis data from GAW15. Adjusting for smoking and anti-cyclic citrullinated peptide increased the significance of the association with the DR locus.

New score tests for age-at-onset linkage analysis in general pedigrees

Our aim is to develop methods for mapping genes related to age at onset in general pedigrees. We propose two score tests, one derived from a gamma frailty model with pairwise likelihood and one derived from a log-normal frailty model with approximated likelihood around the null random effect. The score statistics are weighted nonparametric linkage statistics, with weights depending on the age at onset. These tests are correct under the null hypothesis irrespective of the weight used. They are simple, robust, computationally fast, and can be applied to large, complex pedigrees. We apply these methods to simulated data and to the Genetic Analysis Workshop 16 Framingham Heart Study data set. We investigate the time to the first of three events: hard coronary heart disease, diabetes, or death from any cause. We use a two-step procedure. In the first step, we estimate the population parameters under the null hypothesis of no linkage. In the second step, we apply the score tests, using the population parameters estimated in the first step.

Robust age at onset linkage analysis in nuclear families

OBJECTIVE

Standard methods for linkage analysis ignore the phenotype of the parents when they are not genotyped. However, this information can be useful for gene mapping. In this paper we propose methods for age at onset genetic linkage analysis in sibling pairs, taking into account parental age at onset.

METHODS

Two new score statistics are derived, one from an additive gamma frailty model and one from a log-normal frailty model. The score statistics are classical non-parametric linkage (NPL) statistics weighted by a function of the age at onset of the four family members. The weight depends on information from registries (age-specific incidences) and family studies (sib-sib and father-mother correlation).

RESULTS

In order to investigate how age at onset of sibs and their parents affect the information for linkage analysis the weight functions were studied for rare and common disease models, realistic models for breast cancer and human lifespan. We studied the performance of the weighted NPL methods by simulations. As illustration, the score statistics were applied to the GAW12 data. The results show that it is useful to include parental age at onset information in genetic linkage analysis.

Adjusting for sex and anti-CCP levels in linkage analysis of rheumatoid arthritis

We incorporate population effects of sex and antibodies directed against cyclic citrullinated peptides (anti-CCP) into the linkage analysis of rheumatoid arthritis (RA) with microsatellites data provided by the North American Rheumatoid Arthritis Consortium in Genetic Analysis Workshop 15.

The method stems from a generalized linear mixed model that incorporates the marginal population effects of important covariates. The resulting test for linkage is based on a score test in a pseudo-likelihood of this model. The mathematical derivation is given elsewhere but the test has a simple and appealing form: it assigns weights to excess identity-by-descent sharing between pairs of related individuals depending on the individual-specific values of the covariates and phenotypes.

Although RA is three times more prevalent in women than in men, the weights derived for male-male, female-male, and female-female affected sib pairs turn out to be very similar and the sex-adjusted analysis hardly differs from an unadjusted analysis. High anti-CCP levels are known to strongly predict RA. Our test assigns very small weights to pairs whose anti-CCP levels are high for the two siblings, sib pairs with two low anti-CCP levels are those most contributing to the evidence for linkage. Comparison of the unadjusted and the anti-CCP-adjusted analyses identifies persisting peaks mapping to regions that can be attributed to a 'dimension' of RA independent of anti-CCP.