LESSONS LEARNED Designed Experiments with Binary Responses

A crucial part of designing an experimental protocol is selecting an adequately large number of replicate results prior to running the experiment. An investigator should ensure that statistical tests are adequately powered to detect meaningful differences between experimental conditions. The cost of additional replicates is not easily avoided and is even higher for studies that address binary response variables (e.g., “yes/no”) over those with quantitative response variables. An example of this takes place during protein formulation development. An important response variable with a dichotomous response is detecting the presence or absence of visible particles (“present/not present”). Here the application of Formal Experimental Design 1 may lead to substantial cost savings over one-factor-at-a-time (OFAT) experimentation because of the inherent property of “hidden replication.” Consider the low and high levels of three predictor variables of interest (A, B ,a ndC) to be coded as –1 and +1. This is a 2 3 or “2 to the 3” factorial design, where the two represents the number of levels (low and high), and three the number of predictor variables. The resulting eight combinations can be represented in a cube, as shown in Figure 1.