Estimation of the twin concordance rate for a disease often requires two stages. First, the disease is ascertained in a population or in a population sample, and such twins as are found with the disease become probands. Second, twin pairs with only one proband are further investigated and additional concordant pairs are thus discovered. A mathematical model is presented that allows for continuous variation in completeness of ascertainment in both stages, for correlation within pairs in the primary ascertainment process, and for correlation within pairs in occurrence of the disease. The concordance rate can be estimated by the proband method if secondary ascertainment is complete; other measures of concordance are accurate only if primary ascertainment is complete. A parameter analogous to the concordance rate but related to correlation in primary ascertainment can be estimated from the same data.
