Aggregation of exposure level and probability into a single metric in job-exposure matrices creates bias

Job-exposure matrices (JEMs) are often used in occupational epidemiological studies to provide an exposure estimate for a typical person in a 'job' during a particular time period. A JEM can produce exposure estimates on a variety of scales, such as (but not limited to) binary assessments of presence or absence of exposure, ordinal ranking of exposure level and frequency, and quantitative exposure estimates of exposure intensity and frequency. Specifically, one popular approach to construct a JEM, engendered in a Finnish job exposure matrix (FINJEM), provides a probability that a worker within an occupational group is exposed and an estimate of intensity of exposure among the exposed workers within this occupation. Often the product of the probability and intensity (aka level) is used to obtain the estimate of exposure for the epidemiological analyses. This procedure aggregates exposure across exposed and non-exposed individuals and the effect of this particular procedure on epidemiological analyses has never been studied. We developed a theoretical framework for understanding how these aggregate exposure estimates relate to true exposure (either unexposed or log-normally distributed for 'exposed'), assuming that there is no uncertainty about estimates of level and probability of exposure. Theoretical derivations show that multiplying occupation-specific exposure level and probability of non-zero exposure results in both systematic and differential measurement errors. Simulations demonstrated that under certain conditions bias in odds ratios in a cohort study away from the null are possible and that this bias is smaller when (a) arithmetic rather than geometric mean is used to assess exposure level and (b) exposure level and prevalence are positively correlated. We illustrate the potential impact of using the specified JEM in a simulation based on a case-control study of non-Hodgkin lymphoma and exposure to ionizing and non-ionizing radiation. Inflation of standard errors in the log-odds was observed as well as bias away from null for two out of three specific exposures/data structures. Overall, it is clear that influence of the phenomenon we studied on epidemiological results is complex and difficult to predict, being influenced a great deal by the structure of data. We recommend exploring the influence of JEMs that use the product of exposure level and probability in epidemiological analyses through simulations during planning of such studies to assess both the expected extent of the potential bias in risk estimates and impact on power. The SAS and R code required to implement such simulations are provided. All our calculations are either theoretical or based on simulated data.