# Robust Emax model fitting: Addressing nonignorable missing binary outcome in dose–response analysis

## TL;DR

This paper introduces a new method to handle missing data in dose-response studies, improving accuracy and reducing bias in drug development analysis.

## Contribution

A novel penalized likelihood-based method is proposed to address nonignorable missing data and separation issues in dose-response analysis.

## Key findings

- The proposed method outperforms existing approaches like non-responder imputation in simulation studies.
- The method is successfully applied to real-world Phase II clinical trial data.
- A new R package, ememax, is developed to implement the proposed method.

## Abstract

The Binary Emax model is widely employed in dose–response analysis during drug development, where missing data often pose significant challenges. Addressing nonignorable missing binary responses—where the likelihood of missing data is related to unobserved outcomes—is particularly important, yet existing methods often lead to biased estimates. This issue is compounded when using the regulatory-recommended ‘‘imputing as treatment failure’’ approach, known as non-responder imputation (NRI). Moreover, the problem of separation, where a predictor perfectly distinguishes between outcome classes, can further complicate likelihood maximization. In this paper, we introduce a penalized likelihood-based method that integrates a modified expectation-maximization (EM) algorithm in the spirit of Ibrahim and Lipsitz to effectively manage both nonignorable missing data and separation issues. Our approach applies a noninformative Jeffreys’ prior to the likelihood, reducing bias in parameter estimation. Simulation studies demonstrate that our method outperforms existing methods, such as NRI, and the superiority is further supported by its application to data from a Phase II clinical trial. Additionally, we have developed an R package, ememax (https://github.com/Celaeno1017/ememax), to facilitate the implementation of the proposed method.