  The likelihood function represents statistical evidence in the context of
data and a probability model. Considerable theory has demonstrated that
evidence strength for different parameter values can be interpreted from the
ratio of likelihoods at different points on the likelihood curve. The
likelihood function can, however, be unknown or difficult to compute; e.g. for
genetic association studies with a binary outcome in large multi-generational
families. Composite likelihood is a convenient alternative to using the real
likelihood and here we show composite likelihoods have valid evidential
interpretation. We show that composite likelihoods, with a robust adjustment,
have two large sample performance properties that enable reliable evaluation of
relative evidence for different values on the likelihood curve: (1) The
composite likelihood function will support the true value over the false value
by an arbitrarily large factor; and (2) the probability of favouring a false
value over a true value with high probability is small and bounded. Using an
extensive simulation study, and in a genetic association analysis of reading
disability in large complex pedigrees, we show that the composite approach
yields valid statistical inference. Results are compared to analyses using
generalized estimating equations and show similar inference is obtained,
although the composite approach results in a full likelihood solution that
provides additional complementary information.
