Estimating Common Parameters of Lognormally Distributed Environmental and Biomonitoring Data: Harmonizing Disparate Statistics from Publications

Abstract

The progression of science is driven by the accumulation of knowledge and builds upon published work of others. Another important feature is to place current results into the context of previous observations. The published literature, however, often does not provide sufficient direct information for the reader to interpret the results beyond the scope of that particular article. Authors tend to provide only summary statistics in various forms, such as means and standard deviations, median and range, quartiles, 95% confidence intervals, and so on, rather than providing measurement data. Second, essentially all environmental and biomonitoring measurements have an underlying lognormal distribution, so certain published statistical characterizations may be inappropriate for comparisons. The aim of this study was to review and develop direct conversions of different descriptions of data into a standard format comprised of the geometric mean (GM) and the geometric standard deviation (GSD) and then demonstrate how, under the assumption of lognormal distribution, these parameters are used to answer questions of confidence intervals, exceedance levels, and statistical differences among distributions. A wide variety of real-world measurement data sets was reviewed, and it was demonstrated that these data sets are indeed of lognormal character, thus making them amenable to these methods. Potential errors incurred from making retrospective estimates from disparate summary statistics are described. In addition to providing tools to interpret "other people's data," this review should also be seen as a cautionary tale for publishing one's own data to make it as useful as possible for other researchers.

Identification of fipronil metabolites by time-of-flight mass spectrometry for application in a human exposure study

“…The median from the occupational exposure study was calculated from the mean (μ) and standard deviation (σ) provided via a method by Pleil et al (2014) where the geometric mean is used to estimate the median which is equal to μ/[1 + 0.5 × (σ/μ) 2 ]. Interestingly, the maximum concentration observed in this study (3.9 ng/mL) was only slightly less than the calculated median of 5.2 (GSD = 2.4) ng/mL for the occupationally exposed workers (Herin et al, 2011) (see Fig.…”

“…The dotted line represents the median calculated from an occupational exposure study (Herin et al, 2011; Pleil et al, 2014). * n = 96, four samples were excluded due to insufficient volume.…”

Use of Dried Blood Spots for Estimating Children?s Exposures to Heavy Metals in Epidemiological Research

“…The geometric mean (GM) and geometric standard deviation (GSD) are calculated under the assumption of lognormal distribution [32]; the remaining statistics are strictly observational; that is, no particular underlying distributions are assumed. Entries of "<LoD" indicate that the value is below the level of detection, entries with "-" occurring for the blank corrected (subtracted) DBS were negative.…”

Comparing biomarker measurements to a normal range: when to use standard error of the mean (SEM) or standard deviation (SD) confidence intervals tests

“…The details for making these assertions will be discussed in a future editorial; for now, we will take it for granted. The general issues of dealing with distributions and assumptions have been discussed previously by the author (Pleil & Sobus, 2013;Pleil et al, 2014).…”