Mortality odds ratio, proportionate mortality ratio, and healthy worker effect

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Abstract
The standardized proportionate mortality ratio (PMRi) and the mortality odds ratio (MORi) are two statistics used to approximate the cause specific standardized mortality ratio (SMRi) when death data are available but the population at risk is not known. When there is a healthy worker effect, the MORi will always overestimate the SMRi and will always be greater than the PMRi. The PMRi is influenced by the relative frequency of the cause of death. For rare causes, such as brain cancer or leukemia, the PMRi will overestimate the SMRi to essentially the same degree as the MORi. For more common conditions, such as lung cancer, the PMRi will overestimate or underestimate the SMRi depending on the magnitude of the healthy worker effect. When the SMRi = 1 and there is a healthy worker effect, both the PMRi and MORi are in excess of one (1) regardless of the disease rate. As the SMRi increases it is more likely to be bounded by the PMRi (lower) and the MORi (upper). We therefore recommend that each statistic be derived when death certificates are the only source of data used to assess risk due to occupational exposures.

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