Expected loss functions as additional measures to assess performance of multiple testing procedures for combination drug dose finding.

There are several measures that are commonly used to assess performance of a multiple testing procedure (MTP). These measures include power, overall error rate (family-wise error rate), and lack of power. In settings where the MTP is used to estimate a parameter, for example, the minimum effective dose, bias is of interest. In some studies, the parameter has a set-like structure, and thus, bias is not well defined. Nevertheless, the accuracy of estimation is one of the essential features of an MTP in such a context. In this paper, we propose several measures based on the expected values of loss functions that resemble bias. These measures are constructed to be useful in combination drug dose response studies when the target is to identify all minimum efficacious drug combinations. One of the proposed measures allows for assigning different penalties for incorrectly overestimating and underestimating a true minimum efficacious combination. Several simple examples are considered to illustrate the proposed loss functions. Then, the expected values of these loss functions are used in a simulation study to identify the best procedure among several methods used to select the minimum efficacious combinations, where the measures take into account the investigator's preferences about possibly overestimating and/or underestimating a true minimum efficacious combination. The ideas presented in this paper can be generalized to construct measures that resemble bias in other settings. These measures can serve as an essential tool to assess performance of several methods for identifying set-like parameters in terms of accuracy of estimation.