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.