Dimension of model parameter space and operating characteristics in adaptive dose-finding studies

Adaptive, model-based, dose-finding methods, such as the continual reassessment method, have been shown to have good operating characteristics. One school of thought argues in favor of the use of parsimonious models, not modeling all aspects of the problem, and using a strict minimum number of parameters. In particular, for the standard situation of a single homogeneous group, it is common to appeal to a one-parameter model. Other authors argue for a more classical approach that models all aspects of the problem. Here, we show that increasing the dimension of the parameter space, in the context of adaptive dose-finding studies, is usually counter productive and, rather than leading to improvements in operating characteristics, the added dimensionality is likely to result in difficulties. Among these are inconsistency of parameter estimates, lack of coherence in escalation or de-escalation, erratic behavior, getting stuck at the wrong level, and, in almost all cases, poorer performance in terms of correct identification of the targeted dose. Our conclusions are based on both theoretical results and simulations.