gms | German Medical Science

National mortality statistics commonly provide disease-specific absolute and relative frequencies and rates 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, i.e. the cases, were exposed or not exposed to a specific risk factor.

For many risk factors a proportion of the population is not exposed, and among the exposed exposure has a continuous distribution, for example smoking or alcohol consumption. These variables are called semi-continuous or spike at zero variables.

We present a method to estimate the proportion and subsequently the absolute number of exposed and non-exposed cases. The method requires an estimate of the exposure prevalence in the non-diseased population and an estimate of the relative effect of the exposure. The latter is either a relative risk function given X has a continuous distribution for X>0, or a set of risk estimates for all exposure categories given X is categorical. In the continuous case, an estimate for the proportion of non-exposed cases (p₀₁) is given by p₀₁ = p₀₀ / (p₀₀ + ∫ R(x) f(x) dx), where p₀₀ is the proportion of the non-exposed in the non-diseased, R(x) is the risk function denoting the relative risk given dose x compared to dose 0, and f(x) is the density function of X in the non-diseased.

We provide theoretical justification for the method and suggest approaches for sensitivity analyses. The method is applied to the estimation of the proportion and number of never smokers among lung cancer deaths in Germany.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.