Tests of the Null Hypothesis in Case-Control Studies

The relative merits of the likelihood ratio statistic, the Wald statistic, and the score statistic are examined by an empirical evaluation based on matched case-control data. A mixture model for the relative-odds function is used. The likelihood ratio statistic is relatively constant for reasonable values of the mixture parameter, but the Wald statistic is unstable. The score statistic is shown to be independent of the mixture parameter. An exact expression is derived for the change in the score statistic upon deletion of risk sets, and an approximation is numerically evaluated.