Searching for an adequate dose : Combining Multiple Comparisons and Modeling

The search for an adequate dose involves some of the most complex series of decisions to be made in developing a clinically viable product. Typically decisions based on such dose-finding studies reside in two domains: the first being one of “proof” that the treatment provides evidence of effectiveness. The second concerns the need to choose dose(s) for further development. The analysis of dose response studies has long been divided according to two major strategies: multiple comparison procedures and model-based approaches. The modelbased approach assumes a functional relationship between the response and the dose, taken as a quantitative factor, according to a pre-specified parametric model, such as a logistic, an Emax or a linear log-dose model. The fitted model is then used to estimate an adequate dose to achieve a desired response. Such an approach provides flexibility in investigating the effect of doses not used in the actual study. However, the validity of its conclusions will highly depend on the correct choice of the dose-response model, which is of course a priori unknown. This creates a dilemma in practice, because, within the regulated environment in which drug development takes place, it is required to have the analysis methods (including the choice of the dose-response model) defined prior to the study. Multiple comparison procedures, on the other hand, regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. The primary goal is often to identify the minimum effective dose that is statistically significant and produces a clinically relevant effect. One approach is to evaluate the significance of contrasts between different dose levels, while preserving the familywise error rate. Such procedures are relatively robust to the underlying dose-response shape, but they are not designed for extrapolation of information beyond the observed dose levels. Inference is thus confined to the selection of the target dose among the dose levels under investigation. In this paper, we describe a unified strategy to the analysis of data from doseresponse studies which combines multiple comparison and modeling techniques. We assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying doseresponse curve. We first evaluate the significance of the individual models in terms of corresponding single contrast tests. If none of the contrast tests are significant, no further steps towards identifying adequate doses are pursued. Otherwise, in the second step, a good candidate model is chosen as the one with the most significant contrast test. Such a procedure allows the selection of the most adequate dose-response model within the candidate set, while preserving the familywise error rate. The selected model is then used to provide inference on adequate doses and we propose three different rules for the dose estimation step. The methodology is illustrated with data from a phase II dose-finding study. A simulation study is performed to evaluate and compare the performance of the proposed methods. keywords: contrast test, dose finding, dose ranging, MED, MTD, multiple testing, proof-of-concept.