Testing goodness-of-fit in logistic case-control studies

We present a goodness-of-fit test for the logistic regression model under case-control sampling. The test statistic is constructed via a discrepancy between two competing kernel density estimators of the underlying conditional distributions given case-control status. The proposed goodness-of-fit test is shown to compare very favourably with previously proposed tests for case-control sampling in terms of power. The test statistic can be easily computed as a quadratic form in the residuals from a prospective logistic regression maximum likelihood fit. In addition, the proposed test is affine invariant and has an alternative representation in terms of empirical characteristic functions.