Modelling of mortality data from a multi-centre study in Japan by means of Poisson regression with error in variables

Death rates of particular categories in epidemiological studies are often based on a small number of occurrences which can be well described by a Poisson distribution.

We applied this model for the analysis of a multi-centre study in five Japanese counties where the death rates of stomach cancer (ICD-9 code 151) in four age groups are known. In our example some covariates of the cases (e.g. plasma lycopene levels) are unknown values and are estimated from a randomly chosen collective. Therefore these values are subject to a sampling error. The inclusion of errors in variables (e-i-v) into the statistical model can adequately describe such a situation. The model is estimated in a Bayesian framework by means of resampling techniques.

Based on the posterior distribution of the parameters the relative risk of stomach cancer is 0.46 (95% confidence interval: 0.23-0.79) comparing the maximum of the population medians of lycopene with the minimum. The estimated overdispersion is close to zero indicating only minor interference with other possible explanatory variables. In addition, we show that inclusion of e-i-v can give more accurate estimates of the parameters even from small sample sizes.

Appropriate statistical methods allow the accurate estimation of relative risks from small sample sizes and from low number of cases. Lycopene plasma levels are good predictors for stomach cancer.