Two-stage global search designs for linkage analysis using pairs of affected relatives

We investigate the two-stage procedure proposed by Elston [(1992) Proceedings of the XVIth International Biometric Conference, Hamilton, New Zealand, December 7-11, 1992, pp 39-51, and (1994) "Genetic Approaches to Mental Disorders." Washington, DC: American Psychiatric Press, pp 3-21] for performing a global search of the genome to locate disease genes by linkage analysis using affected relative pairs. The optimal design depends on the type of pairs studied, the effect of the disease locus, the relative costs of recruiting affected persons and typing markers, how informative the markers are, and the amount of genetic heterogeneity. It is specified by the initial number of markers to use, the number of affected relative pairs to study, the initial significance level alpha* to use at the first stage, and the number of flanking markers to use at the second stage around markers significant at the first stage. Asymptotically, the optimal design does not depend separately on either the desired final significance level or power, but rather on a function of the two. Both as the effect of the disease locus increases and as the relative cost of recruiting a subject increases, the optimal number of initial markers increases and the optimal number of pairs decreases. The expected cost of the study decreases as the effect of the disease locus increases, but increases as the relative cost of recruiting a subject increases. The optimal initial number of markers decreases but the number of pairs increases when there is genetic heterogeneity present; conversely, the optimal initial number of markers increases when markers are less than fully informative. Compared to a one-stage procedure, a two-stage procedure typically halves the cost of a study.