Geometric mean estimation from pooled samples

Biomonitoring for environmental chemicals presents various challenges due to the expense of measuring some compounds and the fact that in some samples the levels of many compounds may be below the limit of detection (LOD) of the measuring instrument. Even though various statistical methods have been developed to address issues associated with data being censored because results were below the LOD, the expense of measuring many compounds in large numbers of subjects remains a challenge. One solution to these challenges is to use pooled samples. There are many problems associated with the use of pooled samples as compared with individual samples, but using pooled samples can sometimes reduce the number of analytical measurements needed. Also, because pooled samples often have larger sample volumes, using pooled samples can result in lower LODs and thereby decrease the likelihood that results will be censored. However, many data sets obtained from environmental measurements have been shown to have a log-normal distribution, so using pooled samples presents a new problem: The measured value for a pooled sample is comparable to an arithmetic average of log-normal results and thus represents a biased estimate of the central tendency of the samples making up the pool. In this paper, we present a method for correcting the bias associated with using data from pooled samples with a log-normal distribution. We use simulation experiments to demonstrate how well the bias-correction method performs. We also present estimates for levels of PCB 153 and p,p'-DDE using data from pooled samples from the 2001 to 2002 National Health and Nutrition Examination Surveys.