Statistical Methods in Medical Research

We discuss methods for detecting genetic linkage for quantitative data. The usual LOD score method uses a pseudolikelihood formulation and has optimal power provided all parameters are correctly specified, but can lead to erroneous estimates of the location for the locus influencing a trait under misspecification of parameters describing the variance of the trait. Alternative methods, in which attention focuses upon modelling covariation among relatives as a function of genetic marker, similarity lead to unbiased estimates of the location and major gene heritability of the trait influencing locus. The Haseman-Elston approach uses a regression method to perform linkage analysis and its properties have been widely studied. This method is generally less powerful than variance components procedures, but the maximum likelihood-based variance components procedures require normality of the trait to ensure robustness of the genetic linkage tests (i.e. a correct false positive rate). When samples are non-randomly selected an ascertainment correction is generally required in order to obtain unbiased parameter estimates when applying variance components methods. For quantitative traits, ascertainment corrections usually condition either on the proband exceeding a threshold, or on the trait value of the proband. We summarize simulations that show that both approaches lead to similar efficiencies for estimating genetic effects. Finally, we discuss methods for analysing diseases that include time-to-onset information. A variety of methods are available for the linkage analysis of quantitative traits. Here, we have reviewed the most commonly used methods.

Non-parametric linkage analysis examines similarities among affected relatives in alleles of one or more genetic markers (pieces of DNA at known locations on a chromosome). The objective is to evaluate departures from the null hypothesis that the markers are not near a disease gene. Under the null hypothesis, Mendel's laws give the probabilities that a set of relatives exhibits a particular allele-sharing pattern, and the null hypothesis is rejected if the extent of allele sharing among affected relatives exceeds Mendelian expectation. Because the rationale for allele-sharing methods is intuitively plausible and easily grasped, geneticists have used these methods for more than 30 years, well before the advent of the large sets of polymorphic markers that have made linkage analysis so fruitful today. Here we describe methods for assessing whether the extent of marker allele sharing among affected relatives exceeds Mendelian expectation. We first quantify the notion of allele sharing and the probabilities of allele sharing in various sets of relatives. Then we describe allele sharing methods for affected sibs and more general sets of relatives. We also discuss related issues of test size and power. We conclude with a brief discussion of areas in need of further research.

The past decade produced several proposals for fine-scale gene mapping using linkage disequilibrium data. The suggested methods fall into two main groups, those that rely on pairwise statistics and those that rely on haplotypes. This paper reviews each strategy's development from a chronological perspective.