Family data are used extensively in quantitative genetic studies to disentangle the genetic and environmental contributions to various diseases. Many family studies based their analysis on population-based registers containing a large number of individuals composed of small family units. For binary trait analyses, exact marginal likelihood is a common approach, but, due to the computational demand of the enormous data sets, it allows only a limited number of effects in the model. This makes it particularly difficult to perform joint estimation of variance components for a binary trait and the potential confounders. We have developed a data-reduction method of ascertaining informative families from population-based family registers. We propose a scheme where the ascertained families match the full cohort with respect to some relevant statistics, such as the risk to relatives of an affected individual. The ascertainment-adjusted analysis, which we implement using a pseudo-likelihood approach, is shown to be efficient relative to the analysis of the whole cohort and robust to mis-specification of the random effect distribution.