Optimizing occupational exposure measurement strategies when estimating the log-scale arithmetic mean value--an example from the reinforced plastics industry

When assessing occupational exposures, repeated measurements are in most cases required. Repeated measurements are more resource intensive than a single measurement, so careful planning of the measurement strategy is necessary to assure that resources are spent wisely. The optimal strategy depends on the objectives of the measurements. Here, two different models of random effects analysis of variance (ANOVA) are proposed for the optimization of measurement strategies by the minimization of the variance of the estimated log-transformed arithmetic mean value of a worker group, i.e. the strategies are optimized for precise estimation of that value. The first model is a one-way random effects ANOVA model. For that model it is shown that the best precision in the estimated mean value is always obtained by including as many workers as possible in the sample while restricting the number of replicates to two or at most three regardless of the size of the variance components. The second model introduces the 'shared temporal variation' which accounts for those random temporal fluctuations of the exposure that the workers have in common. It is shown for that model that the optimal sample allocation depends on the relative sizes of the between-worker component and the shared temporal component, so that if the between-worker component is larger than the shared temporal component more workers should be included in the sample and vice versa. The results are illustrated graphically with an example from the reinforced plastics industry. If there exists a shared temporal variation at a workplace, that variability needs to be accounted for in the sampling design and the more complex model is recommended.