Methods to estimate proportion and number of nonexposed cases in a population

Abstract

National mortality statistics commonly provide disease-specific absolute and relative frequencies of death by sex and age, but not by exposure status. However, it is often of interest to know how many of the diseased individuals, that is the cases, were exposed or not exposed to a specific risk factor. We present two methods to estimate the proportion and the number of exposed and nonexposed cases, both of which require an estimate of the exposure prevalence in the nondiseased population. Method I additionally requires an estimate of the relative effect of exposure, that is a relative risk function if the exposure has a continuous distribution, or a relative risk estimate for each category if the exposure is categorical. Method II additionally requires an estimate of the disease rate among the nonexposed. We provide theoretical justifications, discuss practical limitations, and provide an R script to calculate the probability for nonexposure among the diseased, and compare the approaches. Both methods are subsequently applied to the estimation of the number of never smokers among lung cancer deaths. The two suggested methods rely on the availability of specific data sources and might therefore be applicable in different research settings. Both methods yield unbiased estimates of the number of nonexposed cases, given that the respective underlying assumptions are fulfilled.