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We have 3 areas, with varying rate ratios for smoking. After standardization, the SMR is 5 and this is equal to the crude rate ratio of 5 (in the Total column). Therefore, there is no confounding using the individual level data. The ecological regression analysis, using % smokers and the cancer rate, shows an inverse relationship (intercept of 9 and slope of -3), and this is due to the differences in rate differences between groups.

   Ecological regression rate  = 9 - 3 * %   In the absence of individual data above

   Estimated ecological rate ratio = 0.67 (1 - 3/9)

   From Greenland and Morgenstern, Int J Epidem 1989; 18: 269-74