Extension of the generalized disequilibrium test to polytomous phenotypes and two-locus models

Polyunphased: an extension to polytomous outcomes of the Unphased package for family-based genetic association analysis

Polytomous phenotypes arise when a disease has multiple subtypes or when two dichotomous phenotypes are analyzed simultaneously. Few software programs offer the option to analyze such phenotypes in family studies, and none implements conditional polytomous logistic regression for within-family analysis robust to population stratification. We introduce Polyunphased, an extension to polytomous phenotypes of the Unphased package, a flexible software tool for genetic association analysis in nuclear families. Like Unphased, Polyunphased is written in C++ and runs from the command line or from a Java graphical user interface. Most Unphased options remain available in Polyunphased, including those handling missing parental genotypes while preserving robustness to population stratification, and the modelling options. Simulation studies confirmed the expected statistical behaviour of the maximum likelihood estimates of the association parameters of the conditional logistic regression model when the corresponding association parameters in the parental term of the likelihood function are set to 0, but revealed convergence problems when estimating these parental association parameters separately. The former approach is thus recommended with polytomous phenotypes.

When Is an Endophenotype Useful to Detect Association to a Disease? Exploring the Relationships between Disease Status, Endophenotype and Genetic Polymorphisms

OBJECTIVES

To investigate the conditions and analysis strategies required so that endophenotypes related to a disease help discover genetic variants involved in the disease.

METHODS

The association with disease susceptibility variants is examined as a function of the relationships between disease status, endophenotype values and the genotype at another disease or endophenotype susceptibility locus assumed to be previously known, using approximate linear models of allele frequencies as a function of these variables and simulations in the context of family studies when the endophenotype is dichotomous.

RESULTS

Under genetic mechanisms where the risk allele of the tested locus has an effect exclusively in subjects with the endophenotype, the risk allele frequency differences between affected and unaffected subjects are much greater in the subset of subjects with an endophenotype impairment than in those without such an impairment, and power gains are obtained when testing the association under a joint disease-endophenotype model, both with two-locus or single-locus tests. However, with moderate main effect on the risk of disease or endophenotype impairment, testing directly the association between risk allele and disease or endophenotype is more powerful than testing under a joint disease-endophenotype model.

CONCLUSIONS

Joint modeling of disease and endophenotype should be used only in parallel with standard disease association testing.

On the validity of within-nuclear-family genetic association analysis in samples of extended families

Splitting extended families into their component nuclear families to apply a genetic association method designed for nuclear families is a widespread practice in familial genetic studies. Dependence among genotypes and phenotypes of nuclear families from the same extended family arises because of genetic linkage of the tested marker with a risk variant or because of familial specificity of genetic effects due to gene-environment interaction. This raises concerns about the validity of inference conducted under the assumption of independence of the nuclear families. We indeed prove theoretically that, in a conditional logistic regression analysis applicable to disease cases and their genotyped parents, the naive model-based estimator of the variance of the coefficient estimates underestimates the true variance. However, simulations with realistic effect sizes of risk variants and variation of this effect from family to family reveal that the underestimation is negligible. The simulations also show the greater efficiency of the model-based variance estimator compared to a robust empirical estimator. Our recommendation is therefore, to use the model-based estimator of variance for inference on effects of genetic variants.

Estimating genetic effect sizes under joint disease-endophenotype models in presence of gene-environment interactions

Effects of genetic variants on the risk of complex diseases estimated from association studies are typically small. Nonetheless, variants may have important effects in presence of specific levels of environmental exposures, and when a trait related to the disease (endophenotype) is either normal or impaired. We propose polytomous and transition models to represent the relationship between disease, endophenotype, genotype and environmental exposure in family studies. Model coefficients were estimated using generalized estimating equations and were used to derive gene-environment interaction effects and genotype effects at specific levels of exposure. In a simulation study, estimates of the effect of a genetic variant were substantially higher when both an endophenotype and an environmental exposure modifying the variant effect were taken into account, particularly under transition models, compared to the alternative of ignoring the endophenotype. Illustration of the proposed modeling with the metabolic syndrome, abdominal obesity, physical activity and polymorphisms in the NOX3 gene in the Quebec Family Study revealed that the positive association of the A allele of rs1375713 with the metabolic syndrome at high levels of physical activity was only detectable in subjects without abdominal obesity, illustrating the importance of taking into account the abdominal obesity endophenotype in this analysis.