Evaluating bias reduction methods in binary Emax model for reliable dose-response estimation

The Binary Emax model is widely employed in dose-response analysis during Phase II clinical studies to identify the optimal dose for subsequence confirmatory trials. The parameter estimation and inference heavily rely on the asymptotic properties of Maximum Likelihood (ML) estimators; however, this approach may be questionable under small or moderate sample sizes and is not robust to violations of model assumptions. To provide a reliable solution, this paper examines three bias-reduction methods: the Cox-Snell bias correction, Firth's score modification, and a maximum penalized likelihood estimator (MPLE) using Jeffreys prior. Through comprehensive simulation studies, we evaluate the performance of these methods in reducing bias and controlling variance, especially when model assumptions are violated. The results demonstrate that both Firth's and MPLE methods provide robust estimates, with MPLE outperforming in terms of stability and lower variance. We further illustrate the practical application of these methods using data from the TURANDOT study, a Phase II clinical trial. Our findings suggest that MPLE with Jeffreys prior offers an effective and reliable alternative to Firth's method, particularly for dose-response relationships that deviate from monotonicity, making it valuable for robust parameter estimation in dose-ranging studies.