Bias Reduction in Logistic Dose-Response Models

In generalized linear models, such as the logistic regression model, maximum likelihood estimators are well known to be biased at smaller sample sizes. When the number of dose levels or replications per dose is small, bias in the maximum likelihood estimates can lead to very misleading results and the model often fails to converge. In order to correct the bias present in the maximum likelihood estimates and the problem of nonconvergence, the penalized maximum likelihood estimator is considered. Simulations compare the fit and empirical confidence levels of inferences made from the maximum likelihood and penalized maximum likelihood based models.