A common error in the ecological regression of cancer incidence on the deprivation index

To determine if introducing age as another explanatory variable in an ecological regression model relating crude rates of cancer incidence and a deprivation index provides better results than the usual practice of using the standard incidence ratio (SIR) as the response variable, introducing the non-standardized index, and not including age in the model.

Relative risks associated with the deprivation index for some locations of cancer in Spain's Girona Health Region were estimated using two different models. Model 1 estimated relative risks with the indirect method, using the SIR as the response variable. Model 2 estimated relative risks using age as an explanatory variable and crude cancer rates as the response variable. Two scenarios and two sub-scenarios were simulated to test the properties of the estimators and the goodness of fit of the two models.

The results obtained from Model 2's estimates were slightly better (less biased) than those from Model 1. The results of the simulation showed that in all cases (two scenarios and two sub-scenarios) Model 2 had a better fit than Model 1. The probability density for the parameter of interest provided evidence that Model 1 leads to biased estimates.

When attempting to explain the relative risk of incidence of cancer using ecological models that control geographic variability, introducing age as another explanatory variable and crude rates as a response variable provides less biased results.