Likelihood-based approach to estimating twin concordance for dichotomous traits

Genetic epidemiologists are well aware that the casewise and pairwise twin concordances are two different measures. In determining appropriate estimators for each of these measures, the method of ascertainment must be considered. Here, we derive expressions for the concordance estimators and their asymptotic variances appropriate to different twin ascertainment schemes using a likelihood framework, and apply these formulas to existing data. We emphasize the distinction between concordance measures (i.e., the parameters of interest) and the concordance estimators based on the number of pairs observed. Under random or complete ascertainment the casewise estimator is asymptotically unbiased for the casewise concordance, and the pairwise estimator is asymptotically unbiased for the pairwise concordance. Under incomplete ascertainment, the casewise estimator is biased for the casewise concordance, the pairwise estimator is biased for the pairwise concordance, but the probandwise estimator is asymptotically unbiased for the casewise concordance. One can extend the likelihood equations presented here to allow the concordance parameter of interest to depend on zygosity and, if measured, other factors such as cohabitation status and similarity for genetic markers, while concurrently allowing the disease prevalence to depend on measured covariates.