Supplementary Material for: Variance Components Linkage Analysis with Repeated Measurements

Background: When subjects are measured multiple times, linkage analysis needs to appropriately model these repeated measures. A number of methods have been proposed to model repeated measures in linkage analysis. Here, we focus on assessing the impact of repeated measures on the power and cost of a linkage study. Methods: We describe three alternative extensions of the variance components approach to accommodate repeated measures in a quantitative trait linkage study. We explicitly relate power and cost through the number of measures for different designs. Based on these models, we derive general formulas for optimal number of repeated measures for a given power or cost and use analytical calculations and simulations to compare power for different numbers of repeated measures across several scenarios. We give rigorous proof for the results under the balanced design. Results: Repeated measures substantially improve power and the proportional increase in LOD score depends mostly on measurement error and total heritability but not much on marker map, the number of alleles per marker or family structure. When measurement error takes up 20% of the trait variability and 4 measures/subject are taken, the proportional increase in LOD score ranges from 38% for traits with heritability of ~20% to 63% for traits with heritability of ~80%. An R package is provided to determine optimal number of repeated measures for given measurement error and cost. Variance component and regression based implementations of our methods are included in the MERLIN package to facilitate their use in practical studies.