Sample size needed to detect gene-gene interactions using linkage analysis

Causal models for investigating complex genetic disease: II. what causal models can tell us about penetrance for additive, heterogeneity, and multiplicative two-locus models

BACKGROUND/AIMS

Statistical geneticists commonly use certain two-locus penetrance models because these models are familiar and mathematically tractable. We investigate whether and under what circumstances these two-locus penetrance models correspond to models of causation.

METHODS

We describe a sufficient component cause model for a hypothetical disease with two genetic causes. We then use the potential outcomes framework to determine the expected two-locus penetrances from this causal model and contrast them with commonly used two-locus penetrance models (additive, heterogeneity, and multiplicative penetrance models, as formulated by Risch [Am J Hum Genet 1990;46:222-228]).

RESULTS

Conventional additive and multiplicative models can correspond to any two-locus causal model only when certain very specific algebraic relationships hold. The heterogeneity model corresponds to a two-locus causal model only if the model stipulates that no disease cases are caused by the combined presence of the causal genotypes at both loci (i.e. only when there is no causal gene-gene interaction). Hence the heterogeneity model provides a valid test of the null hypothesis of no gene-gene interaction, whereas the additive and multiplicative models do not.

CONCLUSION

We suggest that causal principles should provide the basis for statistical modeling in genetics.

Methods for detecting interactions between imprinted genes and environmental exposures using birth cohort designs with mother-offspring pairs

Genomic imprinting is a form of epigenetic regulation in mammals in which the same allele of a gene is expressed differently depending on the parental origin of the allele. Traditionally, the detection of imprinted genes that affect complex diseases has been focused on linkage designs with pedigrees or case-parent designs with case-parent trios. In the past two decades, the birth cohort design with mother-offspring pairs has been applied to understand better the effect of environmental influences during pregnancy and beginning of life on the growth and development of children. No work has been done on the detection of imprinted genes using birth cohort designs. Moreover, although the importance of imprinting has been well recognized, no study has looked at how environmental exposures modify the effects of imprinted genes. In this study, we show that the proposed imprinting test using the birth cohort design with mother-offspring pairs is an efficient test for testing the interactions between imprinted genes and environmental exposures. Through extensive simulation studies and a real data application, the proposed imprinting test has demonstrated much improved power in detecting gene-environment interactions than that of a test assuming the Mendelian dominant model when the true underlying genetic model is imprinting.

Methods for detecting interactions between genetic polymorphisms and prenatal environment exposure with a mother-child design

Prenatal exposures such as polycyclic aromatic hydrocarbons and early postnatal environmental exposures are of particular concern because of the heightened susceptibility of the fetus and infant to diverse environmental pollutants. Marked inter-individual variation in response to the same level of exposure was observed in both mothers and their newborns, indicating that susceptibility might be due to genetic factors. With the mother-child pair design, existing methods developed for parent-child trio data or random sample data are either not applicable or not designed to optimally use the information. To take full advantage of this unique design, which provides partial information on genetic transmission and has both maternal and newborn outcome status collected, we developed a likelihood-based method that uses both the maternal and the newborn information together and jointly models gene-environment interactions on maternal and newborn outcomes. Through intensive simulation studies, the proposed method has demonstrated much improved power in detecting gene-environment interactions. The application on a real mother-child pair data from a study conducted in Krakow, Poland, suggested four significant gene-environment interactions after multiple comparisons adjustment.

Searching for epistasis and linkage heterogeneity by correlations of pedigree-specific linkage scores

Recognizing that multiple genes are likely responsible for common complex traits, statistical methods are needed to rapidly screen for either interacting genes or locus heterogeneity in genetic linkage data. To achieve this, some investigators have proposed examining the correlation of pedigree linkage scores between pairs of chromosomal regions, because large positive correlations suggest interacting loci and large negative correlations suggest locus heterogeneity (Cox et al. [1999]; Maclean et al. [1993]). However, the statistical significance of these extreme correlations has been difficult to determine due to the autocorrelation of linkage scores along chromosomes. In this study, we provide novel solutions to this problem by using results from random field theory, combined with simulations to determine the null correlation for syntenic loci. Simulations illustrate that our new methods control the Type-I error rates, so that one can avoid the extremely conservative Bonferroni correction, as well as the extremely time-consuming permutational method to compute P-values for non-syntenic loci. Application of these methods to prostate cancer linkage studies illustrates interpretation of results and provides insights into the impact of marker information content on the resulting statistical correlations, and ultimately the asymptotic P-values.