Application of sample survey methods for modelling ratios to incidence densities

We describe ratio estimation methods for multivariately analysing incidence densities from prospective epidemiologic studies. Commonly used in survey data analysis, these ratio methods require minimal distributional assumptions and take into account the random variability in the at-risk periods. We illustrate their application with data from a study of lower respiratory illness (LRI) in children during the first year of life. One question of interest is whether children with passive exposure to tobacco smoke have a higher rate of LRI, on average, than those with no exposure and in a setting where age of child and season are taken into account. A second question is whether the relationship persists after adjusting for background variables such as family's socioeconomic status, crowding in the home, race, and type of feeding. The basic strategy consists of a two-step process in which we first estimate subgroup-specific incidence densities and their covariance matrix via a first-order Taylor series approximation. These estimates are used to test for differences in marginal rates of LRI between children exposed to tobacco smoke and those not exposed. We then fit a log-linear model to the estimated ratios in order to test for significant covariate effects. The ability to produce direct estimates of adjusted incidence density ratios for risk factors of interest is an important advantage of this approach. For comparison purposes and to address the limitations of the ratio method with respect to the number of covariates that can be controlled simultaneously, we consider survey logistic regression methods for the example data as well as logistic and Poisson regression models fitted via generalized estimating equation methods. Although the analysis strategy is illustrated with illness data from an epidemiologic study, the context of application is broader and includes, for example, data on adverse events from a clinical trial.