Estimating mean exposures from censored data: exposure to benzene in the Australian petroleum industry

Abstract

A retrospective assessment of exposure to benzene was carried out for a nested case control study of lympho-haematopoietic cancers, including leukaemia, in the Australian petroleum industry. Each job or task in the industry was assigned a Base Estimate (BE) of exposure derived from task-based personal exposure assessments carried out by the company occupational hygienists. The BEs corresponded to the estimated arithmetic mean exposure to benzene for each job or task and were used in a deterministic algorithm to estimate the exposure of subjects in the study. Nearly all of the data sets underlying the BEs were found to contain some values below the limit of detection (LOD) of the sampling and analytical methods and some were very heavily censored; up to 95% of the data were below the LOD in some data sets. It was necessary, therefore, to use a method of calculating the arithmetic mean exposures that took into account the censored data. Three different methods were employed in an attempt to select the most appropriate method for the particular data in the study. A common method is to replace the missing (censored) values with half the detection limit. This method has been recommended for data sets where much of the data are below the limit of detection or where the data are highly skewed; with a geometric standard deviation of 3 or more. Another method, involving replacing the censored data with the limit of detection divided by the square root of 2, has been recommended when relatively few data are below the detection limit or where data are not highly skewed. A third method that was examined is Cohen's method. This involves mathematical extrapolation of the left-hand tail of the distribution, based on the distribution of the uncensored data, and calculation of the maximum likelihood estimate of the arithmetic mean. When these three methods were applied to the data in this study it was found that the first two simple methods give similar results in most cases. Cohen's method on the other hand, gave results that were generally, but not always, higher than simpler methods and in some cases gave extremely high and even implausible estimates of the mean. It appears that if the data deviate substantially from a simple log-normal distribution, particularly if high outliers are present, then Cohen's method produces erratic and unreliable estimates. After examining these results, and both the distributions and proportions of censored data, it was decided that the half limit of detection method was most suitable in this particular study.