The likelihood function represents statistical evidence given data and a model. The evidential paradigm (EP), an alternative to Bayesian and Frequentist paradigms, provides considerable theory demonstrating evidence strength for different parameter values via the ratio of likelihoods at different parameter values; thus, enabling inference directly from the likelihood function. The likelihood function, however, can be difficult to compute; for example, in genetic association studies with a binary outcome in large pedigrees. Composite likelihood (CL) is an alternative when the real likelihood is intractable. We show CLs have the two large sample properties of the EP for reliable evidence interpretation: (1) CL supports the true value over a false value by an arbitrarily large factor; and (2) the probability of favouring a false value over the true value is small and bounded. Using simulation, and in a genetic association analysis of reading disability (RD) in large rolandic epilepsy pedigrees, we show that the CL approach yields valid statistical inference and identifies RD associated variants. When compared to analyses using generalized estimating equations, results show a similar prioritization of SNPs, although the CL approach provides additional complementary information, and more intuitive solutions to the multiple hypothesis testing problem.
Keywords: correlated binary data; family data; reading disorder; statistical evidence; the evidential paradigm.
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