Odds ratio estimation in the presence of complete OR quasi-complete separation in data

In presence of completely or quasi-completely separated data, the maximum likelihood estimates for the logistic regression parameters do not exist. In medical research the question is of great importance because of the need to obtain finite odds ratios. Statistical packages do not solve the estimation problem with non-overlapped dataset. We suggest to apply the hidden logistic regression model and the MEL estimator of Rousseeuw and Christmas (2003) where a unique solution is graphically obtained by the inspection of the ridge trace of regression parameters (IRT). Alternatively, we inroduce a Cross Validation (CV) based method to choose the regularization parameter. A real data-set on oral candidosis affection in considered. Our analysis points out that CV rather that IRT leads to ML estimates with minimum misclassification error rate.