Estimating morbidity risks with variable age of onset: review of methods and a maximum likelihood approach

Various methods for the estimation of morbidity risk in a disease with late variable onset are described, along with a maximum likelihood approach. It is shown that the Strömgren estimator is nearly as efficient as the maximum likelihood estimator when the true risk is low, but may be significantly less efficient for high morbidity risks. The maximum likelihood estimator offers greater protection against risk estimates greater than or equal to 1, and for small samples, may also be less biased than the Strömgren estimator, especially when risk is high. For reasonable sample sizes both estimates are nearly unbiased. The modified Strömgren estimator is too biased, in general, to be practical. Methods for comparing morbidity risks are also described. If an age-of-onset distribution is estimated from the same sample as morbidity risk, a single maximum likelihood procedure is advocated. The methods are applied to a data set on major affective disorder. The sensitivity of morbidity-risk estimates and tests of hypotheses to the form of onset function assumed is examined.