LIKELIHOOD-BASED INFERENCE FOR THE GENETIC RELATIVE RISK-BASED ON AFFECTED-SIBLING-PAIR MARKER DATA

Using genetic marker data from affected sibling pairs, we study likeli hood-based linkage analysis under quasi-recessive, quasi-dominant, and general single-locus models. We use an epidemiologic parameterization under a model where the marker locus is closely linked to the putativ e disease susceptibility gene. This model and parameterization allow i nferences about the relative risk associated with the susceptible geno type. We base inferences on approximate likelihoods that focus on the affected siblings in the sibship and, using these likelihoods, we deri ve closed-form maximum likelihood estimators for model parameters and closed-form Likelihood ratio statistics for tests that the relative ri sk associated with the susceptible genotype is one. Under the general single-locus model, our likelihood ratio test is the same as the itera tively computed triangle test proposed by Holmans (1993, American Jour nal of Human Genetics 52, 362-374) for the case where marker identity- by-descent is known; our derivation gives a closed form for the test s tatistic. We present quartiles of the distribution of parameter estima tes and critical values for the exact null distribution of our likelih ood ratio test statistics; we also give large-sample approximations to their null distributions. We show that the powers of our likelihood r atio tests exceed the powers of more commonly used nonparametric affec ted-sibling-pair tests when the data meet the inheritance model assump tions used to derive the test; we also show that our tests' powers are robust to violation of model assumptions. We conclude that our model- based inferences provide a practical alternative to more common affect ed-sibling-pal tests when investigators have some knowledge about the mode of inheritance of a disease and that our methods may sometimes be useful for comparing the genetic relative risk with environmental rel ative risks.