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Background Given the inherent challenges of conducting randomized phase III trials in older cancer patients, single-arm phase II trials which assess the feasibility of a treatment that has already been shown to be effective in a younger population may provide a compelling alternative. Such an approach would need to evaluate treatment feasibility based on a composite endpoint that combines multiple clinical dimensions and to stratify older patients as fit or frail to account for the heterogeneity of the study population to recommend an appropriate treatment approach. In this context, stratified adaptive two-stage designs for binary or composite endpoints, initially developed for biomarker studies, allow to include two subgroups whilst maintaining competitive statistical performances. In practice, heterogeneity may indeed affect more than one dimension and incorporating co-primary endpoints, which independently assess each individual clinical dimension, would therefore appear quite pertinent. The current paper presents a novel phase II design for co-primary endpoints which takes into account the heterogeneity of a population. Methods We developed a stratified adaptive Bryant & Day design based on the Jones et al. and Parashar et al. algorithm. This two-stage design allows to jointly assess two dimensions (e.g. activity and toxicity) in two different subgroups. The operating characteristics of this new design were evaluated using examples and simulation comparisons with the Bryant & Day design in the context where the study population is stratified according to a pre-defined criterion. Results Simulation results demonstrated that the new design minimized the expected and maximum sample sizes as compared to parallel Bryant & Day designs (one in each subgroup), whilst controlling type I error rates and maintaining a competitive statistical power as well as a high probability of detecting heterogeneity. Conclusions In a heterogeneous population, this two-stage stratified adaptive phase II design provides a useful alternative to classical one and allows to identify a subgroup of interest without dramatically increasing sample size. As heterogeneity is not limited to older populations, this new design may also be relevant to other study populations such as children or adolescents and young adults or the development of targeted therapies based on a biomarker.