Letters to the Editor
On the Detection of Excess Disease Risk in Family Data
To the Editor: Recently, Chakraborty et a1 [1984] and Tarone [1986] have proposed statistics for testing whether disease occurrence in a pedigree differs from disease patterns in a referent population. They assumed that disease outcome, X, for each individual is a Bernoulli random variable and that affection probability, p, is known. In practice, however, p is usually replaced by the "expected" value, e, which is the cumulative disease rate of a standard population, adjusting for year, sex, and race. Since e is a sum of age-specific disease rates, it can, under certain circumstances, exceed unity and thus cannot be a Bernoulli success probability p. If there is no loss to follow-up, then p can and should be explicitly calculated. If there is loss to follow-up, then p cannot usually be determined, since the standard population contains no information on the loss to follow-up distribution. The purpose of this letter is to highlight these points and to suggest that analyses based on the standardized mortality (morbidity) ratio (SMR) and the related Poisson-based test of no association should prove adequate for most purposes.
Suppose a pedigree has N members. For the ith individual, we observe age at response ti and a variable indicating affection (Xi = 1) or not affection ( X i =0) for the disease of interest. Time to event ti includes time to the cause of interest, death from other causes, loss to follow-up, or termination of study. A goal is to evaluate if the