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Abstract:
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Suppose that the probability of a categorical outcome is determined by its predictor according to a given model, but the marginal distributions of the outcome and the predictor are both unknown. From an outcome-dependent enriched sample, which corresponds to the combination of a cohort data and a case-control data, one can estimate the model parameter consistently and with small variance via either the weighted-likelihood (WL) or profile-likelihood (PL) method. This study develops the likelihood-ratio, Wald and Score tests of a composite hypothesis for these two methods. In addition, we construct the likelihood-ratio tests of model goodness-of-fit for the case when the predictor is discrete. Connection between the likelihood-based and contingency-table-based analyses is made through the WL method. Performance of the proposed tests is evaluated via a simulation study.
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