Effects of Exposure Misspecification in Log-Linear Models for Rates

John W. McDonald, University of Southampton
Peter W.F. Smith, University of Southampton

Log-linear models are used in demography and epidemiology to model rates cross-classified by explanatory variables. A rate is defined as the ratio of the number of events of interest to the exposure. For example, for mortality rates, the exposure is total person-years at risk. The rates are not modelled directly, but a table of counts of events of interest and a table of exposures are required. Often, the true exposure is unknown and an estimate of exposure is used. The problem we study in this paper is the effects of misspecification of the exposures on inferences drawn from a log-linear model for rates. Our literature review suggests that the effects of this type of misspecification have not been investigated. In particular, we investigate how this type of rates model misspecification affects parameter estimates, estimated standard errors, confidence intervals, test statistics, etc.