A goodness-of-fit test for logistic regression models based on case-control data

We test the logistic regression assumption under a case-control sampling plan. After reparameterisation, the assumed logistic regression model is equivalent to a two-sample semiparametric model in which the log ratio of two density functions is linear in data. By identifying this model with a biased sampling model, we propose a Kolmogorov-Smirnov-type statistic to test the validity of the logistic link function. Moreover, we point out that this test statistic can also be used in mixture sampling. We present a bootstrap procedure along with some results on simulation and on analysis of two real datasets.