The power to detect linkage disequilibrium with quantitative traits in selected samples

Abstract

Results from power studies for linkage detection have led to many ongoing and planned collections of phenotypically extreme nuclear families. Given the great expense of collecting these families and the imminent availability of a dense diallelic marker map, the families are likely to be used in allelic-association as well as linkage studies. However, optimal selection strategies for linkage may not be equally powerful for association. We examine the power to detect linkage disequilibrium for quantitative traits after phenotypic selection. The results encompass six selection strategies that are in widespread use, including single selection (two designs), affected sib pairs, concordant and discordant pairs, and the extreme-concordant and -discordant design. Selection of sibships on the basis of one extreme proband with high or low trait scores provides as much power as discordant sib pairs but requires the screening and phenotyping of substantially fewer initial families from which to select. Analysis of the role of allele frequencies within each selection design indicates that common trait alleles generally offer the most power, but similarities between the marker- and trait-allele frequencies are much more important than the trait-locus frequency alone. Some of the most widespread selection designs, such as single selection, yield power gains only when both the marker and quantitative trait loci (QTL) are relatively rare in the population. In contrast, discordant pairs and the extreme-proband design provide power for the broadest range of QTL-marker-allele frequency differences. Overall, proband selection from either tail provides the best balance of power, robustness, and simplicity of ascertainment for family-based association analysis.

Figure 1

Differences in selection ratio for various sampling designs. Under truncate selection, any threshold of selection (Z_α) requires screening different numbers of families for each selection strategy. The bars show the number of families phenotyped per family selected for genotyping, for α = .50, .30, .10, and .05.

Figure 2

Effect of marker- and trait-allele frequencies on power (random ascertainment). Power was evaluated for 121 combinations of trait- and marker-allele frequencies. In each case, power is the proportion of 1,000 simulated data sets exceeding the empirical 1% significance level, estimated from 50,000 simulations. Each data set included 180 sib pairs where a diallelic trait-locus allele accounts for 10% of the total trait variance. Trait- and marker-locus allele frequencies were as specified, with θ = .0005 (∼50 kb), and D′ = 0.75. The residual sibling resemblance is .30.

Figure 3

The effect of marker- and trait-allele frequencies on power (under selection). Power was evaluated for 121 combinations of trait- and marker-allele frequencies. In each case, power is the proportion of 1,000 simulated data sets exceeding the empirical 1% significance level, estimated from 50,000 simulations. Each data set included 180 sib-pairs where a diallelic trait-locus allele accounts for 10% of the total trait variance. Trait- and marker-allele frequencies were as specified, with θ= .0005 (∼50 kb), and D′ = .75. The residual sibling resemblance is .30. Thresholds for selection were selected so that ∼1 in 50 families was selected for analysis in all strategies (“proportional” selection). The value shown after each label (e.g., ASP; .08) indicates the approximate tail area used to satisfy the selection ratio of 50.