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Combining expert ratings and exposure measurements in occupational epidemiology : a random effect paradigm

 Wild P ¹, E Sauleau ², F Marcenac ³, and J-J Moulin ¹

1. Department of Epidemiology, INRS, Vandoeuvre, France.

2. University of Lyon I, France.

3. Rhoditech, Décines, France.

Introduction

Exposure assessment in occupational studies relies mostly on grouping of subjects considered to experience similar exposure : so-called homogeneous exposure groups (HEG). Often the exposure of these HEGs is characterised by an expert rating into a limited number of semi-quantitative exposure levels. These expert ratings can be obtained either by consensus or by more formal modelling processes. In industry based epidemiology, often some exposure measurements exist in some but not all of the HEGs. However, even in this case, the number of exposure measurements is usually not sufficient to obtain stable exposure estimates. It is therefore usual practice in occupational epidemiology to rely mostly on the exposure ratings for the exposure assessment and use the exposure measurements only as validating tools. We present here a paradigm for combining the exposure measurements and the expert ratings adapted from the standard random effect model.

Methods

The model relies on a hierarchical description of the data. A first step is to make the usual assumption that within each HEG, the exposure concentration measurements, follow a log-normal. Alternatively the log-transformed exposure measurement follows a gaussian (or normal) distribution with corresponding mean mj and standard deviation sWj.

The second step, the so-called random effect, assumes that all HEGj which share a common expert exposure rating k are random samples from the population of all HEGs which share this rating. More specifically, we shall assume that the geometric means of these HEGs again follow a log-normal distribution or equivalently that the log-geometric means mj follow a normal distribution with mean qk and standard deviation sBk, where the B stands for between-HEG standard deviation. We further assume that the within HEG standard deviations do not depend on the exposure rating but can be described by a known statistical distribution from which it is supposed to be a sample. Through this procedure, we obtain on one side an estimate of the typical geometric mean when only ratings are available and, on the other side, a corrected geometric mean for each HEG incorporating the information from the measurements and from the other HEGs with the same rating.

A full analysis of this model requires statistical software, especially when some measurements are below the detection limit 1, but some easily implementable approximate formulae are presented.

We apply this model on 2 data sets. The first is an attempt in a large chemical company to obtain a priori orders of magnitude of exposure from different substances in several industrial sites based on basic characteristics of the work place. This procedure is confronted with actual exposure measurements in 42 exposure groups. The second data set stems from an industry-wide epidemiological study in the French hard metal industry(2,3) for which an expert based Job Exposure Matrix has been developed and for which 47 exposure group had been characterised by actual measurements of the cobalt exposure.

Results

The approximate formulae show how the model performs. The rating specific (log) mean is the mean of the (log) means of the corresponding HEGs. For each HEG the estimated log mean is a linear combination of mean log measurements and the rating specific mean. The information the latter carries is proportional to the between HEG standard deviation. Thus it carries less weight if the exposure variability is large within each rating. Figure 1 shows the first data set. Here the exposure variability is very large within each rating (gsd = 8) so that the rating has little influence on the estimates of the mean exposure in each HEG.

Figure 1. Empirical and model model based estimates of geometric mean exposure with rating specific geometric means.

Table 1 gives the same information for selected HEGs of the second data set. While the between HEG within rating GSD remains rather large, its influence begins to become important in some circumstances as in HEG 5 where the estimated geometric mean (gm=116 mg/m³) is lower than the single exposure measurement (x=171).

Table 1. Exposure ratings and measurements and geometric means in 5 selected HEGs as well as a model based estimate of the geometric mean combining measurements an exposure ratings.

Discussion

Our method presents a way to combine expert ratings and exposure measurements in a quantitative exposure assessment. Its main limitations lie probably in the assumption under which it is valid. The main assumption made here is that the expert ratings are made in absence of knowledge of the exposure measurements, so that both types of information can be considered as independent. Another crucial assumption is that the HEGs, for which measurements were obtained, are typical (random samples) of all the possible HEGs with the same rating. A last hypothesis, that the geometric means follow log-normal distributions seems quite intuitive as it expresses the fact that the error in rating of the experts is best expressed on a multiplicative (log) scale. The results of the analysis of our two data sets (especially in the first example) show that the information is rather weak and that even a single typical exposure measurement gives more information than the prior rating. This was not so in a third (unfortunately confidential) example in which the information coming from expert rating was quite accurate.

Conclusions

We presented a paradigm for combining expert ratings and exposure measurements in quantitative exposure assessment. Its advantages and limitations are discussed.

References

[1] Wild P., Hordan R., Leplay A., Vincent R. Confidence Intervals for probabilities of exceeding TLV with censored log-normal data. Environmetrics, 1996, 7, 247-259

[2] Moulin J.-J., Romazzini S., Lasfargues G., Peltier A., Bozec C., Duguerry P., Pellet F., Wild P., Perdrix A. Elaboration d'une matrice emplois-exposition dans l'industrie productrice de métaux durs. Rev Epidem Santé Publ, 1997, 45, 41-51.

[3] MoulinJ J, Wild P, Romazzini S, Lasfargues G, Perdrix G, Peltier A, Bozec C, Duguerry P, Pellet F. Lung cancer risk in hard metal workers. Am J Epidemiol, 1998, 148, 241-248.

This abstract was presented at at the X2001conference in Gothenburg during June 2001. A fuller version of the work has been submitted to the Annals of Occupational Hygiene.

First published on www.herox.org on 22nd June 2001.

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This paper has not been peer-reviewed and the publisher takes no responsibility for the scientific quality of the work.

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