Regression modeling of ordinal data with nonzero baselines

This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose- response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an EM algorithm for fitting the models. The EM algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.