Comparing methods for estimating the variation of risks of cancer between small areas

Analysing the geographical variation of cancer incidence is an important issue in epidemiological research. It might suggest new aetiologic hypotheses, provide guidelines for the design of new surveys and give ideas for preventive campaigns.

Four different methods for estimating the variation of cancer risks between small areas and three homogeneity tests were evaluated by simulation. In three of the methods the systematic variation of the relative risks (RR) was estimated by subtracting the expected Poisson variation from the total variation. The last method assumes that RR are gamma distributed and the maximum likelihood estimate (MLH) of the systematic variation parameter is calculated. A likelihood ratio test (LRT) of heterogeneity of RR based on this method is also evaluated, and compared with an ordinary chi2 test and the Potthoff and Whittinghill test (P&W).

For most of the simulated data-sets, the estimates obtained by MLH are most precise, even if the assumption of gamma distribution of RR is violated. The LRT and P&W tests of homogeneity are also shown to perform better than the chi2 test. Most of the real cancer data-sets exhibited at least some geographical variation. Cancer of the lung, melanoma and other skin cancers, and cancers of the urinary bladder, pancreas and stomach, have the highest systematic variation.

The study suggests that likelihood-based approaches are suitable, both for estimating the variation between small areas and for testing the null hypothesis of equal RR. Such geographical analyses might suggest new aetiological hypothesis.