Causal inference in early phase clinical trials: Variance decomposition and order of patient inclusion

Causal inference tools, in particular those of variance decomposition, hierarchical data structures and counterfactuals, are applied to the study of the methodology of dose-finding studies in oncology. A detailed variance decomposition brings into a much sharper focus the relative performance of different designs. We develop and present new results on the role played by the order of patient inclusions into a sequential dose-finding study. These results make it clear why, previously, authors could easily be misled into a conclusion that different designs enjoy similar performances. This is not so and we show how to avoid making that mistake. We highlight our findings via both theoretical and numerical studies.