The likelihood ratio test for the Hill model.

The Hill model is used to describe many biological phenomena to specify the dose-response relationship in clinical trials and other applications. When testing the null hypothesis of no curve versus the Hill model, the likelihood ratio test (LRT) does not exhibit the appropriate Type I error rate. We describe the reason for the failure of the LRT and then proceed to show that a chi-squared approximation with about 1.6 degrees of freedom works well. We then extend the results to analyses of data from published literature.