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.
a Department of Biostatistics , Pfizer , Cambridge , Massachusetts.
Yifang
Y
Li
b Advisory Analytics, Quintiles, Morrisville , North Carolina , USA.
Russell
R
Reeve
D002986:Clinical Trials as Topic; D004305:Dose-Response Relationship, Drug; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical
Chi-squared process; Emax model; Michaelis-Menten; dose response; logistic model; meta-analysis; nonstandard conditions; psoriasis