Assessing changes in ages at onset over successive generation: an application to breast cancer

Decreased age at onset in successive generations has been observed for a number of diseases. Two nonparametric matched and unmatched test statistics are proposed, taking into account not only current age or age at death for unaffected individuals and age at disease onset for affected individuals, but also possible correlations among family members. Both are asymptotically normal with readily estimated variances from the data. A simulation study is conducted to compare the proposed tests with the commonly used paired t-test and log-rank test. It has been shown that the proposed test statistics yield valid conclusions in assessing genetic anticipation under all situations considered. However, the paired t-test is valid only when the censoring distributions are comparable between two generations, whereas the log-rank test is valid when the correlation among family members is weak. As expected, the matched test is most powerful when the data are heterogeneous, and the unmatched and the log-rank tests are most powerful when the data are homogeneous and the correlation is weak. Lastly, a population-based family study of breast cancer conducted at the Fred Hutchinson Cancer Research Center is used for illustration of the proposed and the log-rank tests. The preliminary analysis suggests that there appears a decreased age at onset over the successive generations in breast cancer.