SCORE TEST FOR FAMILIAL AGGREGATION IN PROBANDS STUDIES - APPLICATIONTO ALZHEIMERS-DISEASE

When studying familial aggregation of a disease, the following two-sta ge design is often used: first select index subjects (cases and contro ls); then record data on their relatives. The likelihood corresponding to this design is derived and a score test of homogeneity is proposed for testing the hypothesis of no-aggregation. This test takes into ac count the selection procedure and allows adjustment to be made for exp lanatory variables. It appears as the sum of three terms: a pure test of homogeneity, a test of comparison of observed minus expected cases in the two groups, and a term which adjusts for the possible unequal p robabilities of disease of the index subjects. Asymptotic efficiency a nd a simulation study show that the proposed test is superior to eithe r the pure homogeneity test or tests based on the comparison of number s of affected in the two groups. The test statistic, which has an asym ptotically standard normal distribution, is applied to a study of fami lial aggregation of early-onset Alzheimer's disease for which a highly significant value (9.46) is obtained: this is the highest value among the three tests compared, in agreement with the simulation study. A l ogistic normal model is fitted to the data, taking account of the sele ction procedure: it allows to estimate the regression parameters and t he variance of the random effect; the likelihood ratio test for famili al aggregation seems less powerful than the score test.