Latent variable indirect response modeling of categorical endpoints representing change from baseline

Accurate exposure-response modeling is important in drug development. Methods are still evolving in the use of mechanistic, e.g., indirect response (IDR) models to relate discrete endpoints, mostly of the ordered categorical form, to placebo/co-medication effect and drug exposure. When the discrete endpoint is derived using change-from-baseline measurements, a mechanistic exposure-response modeling approach requires adjustment to maintain appropriate interpretation. This manuscript describes a new modeling method that integrates a latent-variable representation of IDR models with standard logistic regression. The new method also extends to general link functions that cover probit regression or continuous clinical endpoint modeling. Compared to an earlier latent variable approach that constrained the baseline probability of response to be 0, placebo effect parameters in the new model formulation are more readily interpretable and can be separately estimated from placebo data, thus allowing convenient and robust model estimation. A general inherent connection of some latent variable representations with baseline-normalized standard IDR models is derived. For describing clinical response endpoints, Type I and Type III IDR models are shown to be equivalent, therefore there are only three identifiable IDR models. This approach was applied to data from two phase III clinical trials of intravenously administered golimumab for the treatment of rheumatoid arthritis, where 20, 50, and 70% improvement in the American College of Rheumatology disease severity criteria were used as efficacy endpoints. Likelihood profiling and visual predictive checks showed reasonable parameter estimation precision and model performance.