"Poisson Regression for Modeling Count and Frequency Outcomes in Longitudinal Studies of Intimate Partner Violence"

Studies of violence and posttraumatic outcomes often examine questions using outcome variables representing behaviors, such as acts of physical and psychological aggression, or alcohol or drug use, and smoking. Such behavioral outcome variables are typically expressed by a count, frequency, or rate, and therefore may lack a normal distribution. Traditional regression-based statistical procedures, such as structural equation modeling, and multilevel random coefficients regression assume a normally-distributed outcome variable and may not be optimal for modeling count or frequency outcomes. This session will demonstrate the use of Poisson regression, an alternative procedure for modeling count outcomes over time during treatment. Longitudinal application of Poisson regression expresses the natural logarithm of the rate of a person-time outcome variable, y/N, as a linear function of the predictors and the resulting beta coefficients represent the change in the log of the rate of the outcome variable per unit change in the predictor variables. The beta coefficients are usually exponentiated and the result is reported as an incidence density ratio or, more commonly, as a risk ratio. These exponentiated values are typically interpreted as the increased or decreased risk of an event occurring. The seminar will integrate statistical explanation of Poisson regression with hands-on demonstration of application of the method by trauma research psychologists using data from two longitudinal studies. Throughout the seminar, statistical aspects of Poisson regression will be presented by a university school of public health biostatistician. In one study example, Poisson regression will be used to examine physical abuse, psychological abuse, and stalking at five time points during the course of a year among battered women following different relationship courses. The second example will present data examining risk of intimate partner physical and psychological aggression perpetration, at three time points, before, during, and after alcohol treatment. The examples of Poisson models will be demonstrated live using SAS (GENMOD) and HLM software. Output results for each type of software will be explained, particularly interpretation of the estimated coefficients, which may be expressed in logarithmic form, depending upon the type of software used. Statistical questions will be addressed by the lead biostatistician presenter.