Properties of the geometrically averaged ratio, an alternative standardized measure

In epidemiology, the comparative mortality figure and the standardized mortality ratio are standardized measures in common use. Both are weighted averages of rate ratios (or observed/expected death count ratios) on the arithmetic scale. I propose a new standardized measure, the geometrically averaged ratio (GAR), which is defined through simple averaging on the logarithmic scale. I show that, in addition to providing a valid comparison between populations, the geometrically averaged ratio possesses the following desirable properties: (1) invertibility and invariance of standardized sex ratios and (2) interpopulational comparability with different standards.