Analysis of count data from before-after control-impact studies

Before-after control-impact (BACI) studies are common observational studies conducted to determine environmental impacts of accidents or potential disturbances. In this paper, we present a practical guide to analysis of BACI studies when response variables are counts. Two commonly used analyses and one less common, but more appropriate, analysis are covered. The two common analyses fundamentally compare differences of differences, one using original units, the other using log-transformed units. The third analysis, which is less common, consists of estimating interaction effects in a quasi-likelihood generalized linear model with correlated errors (i.e., a generalized linear mixed model). We conclude that the two common analyses are of marginal utility when analyzing count data due to questions regarding interpretation of parameter estimates and treatment of zeros. These questions do not arise under the quasi-likelihood generalized linear model method, and it is the recommended approach. We illustrate the three techniques by analyzing data similar to that collected by an observational study of seabird counts on oiled and unoiled sites before and after the Exxon Valdez oil spill. Example data and SAS(r) code to conduct the three analyses are given.