On the lod score method in linkage analysis

Genetic epidemiology deals with the interaction of environmental and genetic determinants in common diseases. Linkage analysis is an important branch of this field. The current practice of claiming linkage between two genetic loci when the maximum lod score z(theta) exceeds 3 has not received theoretical justification, whether considered as a sequential or as a fixed sample size test. Within the framework of significance testing, Wald's (1947) formulae are not applicable to allow this procedure a sequential interpretation. Considered as a fixed sample size test, we find that a chi 2 approximation would instead be very adequate. Since repeated significance testing is performed on linkage data, the nominal significance level should be more stringent for each test than the overall level. Some recent developments in group sequential trials by Pocock (1977) and in repeated significance testing by Woodroofe (1979) seem to indicate that the critical value of the maximum lod score should lie roughly between 0.9 and 3.3, depending on the maximum number of repetitions anticipated, on whether the significance level is desired to be 0.05, 0.01 or 0.001, and on whether the test is derived from a one-sided or a two-sided consideration. In terms of the group sequential approach, if a maximum of twenty repetitions is allowed, if z(theta) greater than log10 A is considered as a one-sided test and assumed to be symmetric when linkage is absent, then the type I error is approximately given by 1/A. We also treat the confidence interval approach for exclusion of unlikely recombination values.