Rejoinder on "ascertainment adjustment in complex diseases"

Behavioral and Molecular Genetics of Reading-Related AM and FM Detection Thresholds

Auditory detection thresholds for certain frequencies of both amplitude modulated (AM) and frequency modulated (FM) dynamic auditory stimuli are associated with reading in typically developing and dyslexic readers. We present the first behavioral and molecular genetic characterization of these two auditory traits. Two extant extended family datasets were given reading tasks and psychoacoustic tasks to determine FM 2 Hz and AM 20 Hz sensitivity thresholds. Univariate heritabilities were significant for both AM (h 2  = 0.20) and FM (h 2  = 0.29). Bayesian posterior probability of linkage (PPL) analysis found loci for AM (12q, PPL = 81 %) and FM (10p, PPL = 32 %; 20q, PPL = 65 %). Bivariate heritability analyses revealed that FM is genetically correlated with reading, while AM was not. Bivariate PPL analysis indicates that FM loci (10p, 20q) are not also associated with reading.

Fitting ACE structural equation models to case-control family data

Investigators interested in whether a disease aggregates in families often collect case-control family data, which consist of disease status and covariate information for members of families selected via case or control probands. Here, we focus on the use of case-control family data to investigate the relative contributions to the disease of additive genetic effects (A), shared family environment (C), and unique environment (E). We describe an ACE model for binary family data; this structural equation model, which has been described previously, combines a general-family extension of the classic ACE twin model with a (possibly covariate-specific) liability-threshold model for binary outcomes. We then introduce our contribution, a likelihood-based approach to fitting the model to singly ascertained case-control family data. The approach, which involves conditioning on the proband's disease status and also setting prevalence equal to a prespecified value that can be estimated from the data, makes it possible to obtain valid estimates of the A, C, and E variance components from case-control (rather than only from population-based) family data. In fact, simulation experiments suggest that our approach to fitting yields approximately unbiased estimates of the A, C, and E variance components, provided that certain commonly made assumptions hold. Further, when our approach is used to fit the ACE model to Austrian case-control family data on depression, the resulting estimate of heritability is very similar to those from previous analyses of twin data.