Mixed exposures are often combined into single exposure measures using weighting factors. An example of this arises in radiation epidemiology where doses of distinct forms of ionising radiation (such as alpha, beta, and gamma radiation) are combined based on knowledge of their biological effectiveness relative a reference form of radiation (most often gamma). Similar pooling of mixed exposures may occur with multiple congeners or air pollutants to develop more parsimonious models. The weights used for combining exposures are determined from experimental animal and cellular research, but not observational research. In this work, we show that these weights, which are the ratio of two normally distributed variables, cannot be reliably estimated from observational research. We propose an alterative approach for estimating differences in effectiveness of distinct exposures based on their excess effectiveness compared to a reference exposure. This alternative provides reliable estimates of differences in effectiveness of distinct exposures.
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