Haseman-Elston regression in ascertained samples: importance of dependent variable and mean correction factor selection

Abstract

Objective: One of the first tools for performing linkage analysis, Haseman-Elston regression (HE), has been successfully used to identify linkages to several disease traits. A recent explosion in extensions of HE leaves one faced with the task of choosing a flavor of HE best suited for a given situation. This paper puts this dilemma into perspective and proposes a modification to HE for highly ascertained samples (BLUP-PM).

Methods: Using data simulated for a range of models, we evaluated type I error and power of several dependent variables in HE, including the novel BLUP-PM.

Results: When analyzing a continuous trait, even in highly ascertained samples, type I error is stable and approximately nominal across dependent variables. When analyzing binary traits in highly ascertained samples, type I error is elevated and unstable for all except BLUP-PM. Regardless of trait type, the optimally weighted HE regression and BLUP-PM have the greatest power.

Conclusions: Ascertained samples do not always reflect the population from which they are drawn and therefore choice of dependent variable in HE becomes increasingly important. Our results do not reveal a single, universal choice, but offer criteria by which to choose and demonstrate BLUP-PM performs well in most situations.

Fig. 1

Trait with strong familial correlation. Type I errors of different dependent variables for a continuous trait with different levels and schemes of ascertainment. The abscissa of the vertical line denotes a known population mean of the trait. The ordinates of ‘x’ and ‘+’ denote the type I error of BLUP-PM and Diff, respectively.

Fig. 2

Trait with weak familial correlation. Type I errors of different dependent variables for a continuous trait with different levels and schemes of ascertainment. The abscissa of the vertical line denotes a known population mean of the trait. The ordinates of ‘x’ and ‘+’ denote the type I error of BLUP-PM and Diff, respectively.

Fig. 3

Trait with strong familial correlation. Power of different dependent variables for a continuous trait with different levels and schemes of ascertainment. The power of W3 was not plotted because it was the same as that of W4. The abscissa of the vertical line denotes a known population mean of the trait. The ordinates of ‘x’ and ‘+’ denote the power of BLUP-PM and Diff, respectively.

Fig. 4

Trait with weak familial correlation. Power of different dependent variables for a continuous trait with different levels and schemes of ascertainment. The power of W3 was not plotted because it was the same as that of W4. The abscissa of the vertical line denotes a known population mean of the trait. The ordinates of ‘x’ and ‘+’ denote the power of BLUP-PM and Diff, respectively.

Fig. 5

Type I error of different dependent variables for a binary trait. The solid vertical line is a known population mean and the dashed vertical line is the sample mean, as calculated from the observed data. The ordinates of ‘x’ and ‘+’ denote the power of BLUP-PM and Diff, respectively.

Fig. 6

Power of different dependent variables over a range of μ values for a binary trait with different modes of inheritance and levels of heterogeneity. The solid vertical line denotes the population mean. The ordinates of ‘x’ and ‘+’ denote the power of BLUPPM and Diff, respectively.

Fig. 7

Choice of dependent variable and mean correction factor given various scenarios for a continuous trait.

Fig. 8

Choice of dependent variable and mean correction factor given various scenarios for a binary trait.