A Study on Reproducibility and the Reliability of the Hosmer-Lemeshow Test in Published Research

This paper discusses two elements of reproducibility in published research. First, it examines whether published results are reproducible with author-supplied data: specifically, whether the authors publish their data, whether authors respond to requests for data when data are claimed to be available upon reasonable request, and whether data provided are usable to reproduce the authors’ results. Second, we seek to substantiate the currently mostly theoretical concerns about the Hosmer-Lemeshow goodness-of-fit test’s lack of power by investigating its usage in practice: in published research, by authors aiming to validate their models. By using the authors’ data to build larger alternative models and doing hypothesis testing to show that the smaller models—validated by Hosmer-Lemeshow—do not adequately capture information that is available in the data, we demonstrate that the Hosmer-Lemeshow goodness of fit test is often incapable of detecting inadequacies in models.