Identifying the most successful dose (MSD) in dose-finding studies in cancer

For a dose finding study in cancer, the most successful dose (MSD), among a group of available doses, is that dose at which the overall success rate is the highest. This rate is the product of the rate of seeing non-toxicities together with the rate of tumor response. A successful dose finding trial in this context is one where we manage to identify the MSD in an efficient manner. In practice we may also need to consider algorithms for identifying the MSD which can incorporate certain restrictions, the most common restriction maintaining the estimated toxicity rate alone below some maximum rate. In this case the MSD may correspond to a different level than that for the unconstrained MSD and, in providing a final recommendation, it is important to underline that it is subject to the given constraint. We work with the approach described in O'Quigley et al. Biometrics 2001; 57(4):1018-1029]. The focus of that work was dose finding in HIV where both information on toxicity and efficacy were almost immediately available. Recent cancer studies are beginning to fall under this same heading where, as before, toxicity can be quickly evaluated and, in addition, we can rely on biological markers or other measures of tumor response. Mindful of the particular context of cancer, our purpose here is to consider the methodology developed by O'Quigley et al. and its practical implementation. We also carry out a study on the doubly under-parameterized model, developed by O'Quigley et al. but not