Counting rules for estimating concentrations of long asbestos fibers

Our plain-English summary of Counting rules for estimating concentrations of long asbestos fibers, by K.S. Crump, D.W. Berman (The Annals of Occupational Hygiene, 2011).

The study

• Authors: K.S. Crump, D.W. Berman
• Journal: The Annals of Occupational Hygiene
• Published: 2011;55(7):723-35
• Read it: PubMed · Publisher

Abstract

Mounting evidence that long asbestos fibers (e.g. >20 or even 40 μm) pose the greatest cancer risk underscores the need for accurate measurement of concentrations of such fibers. These fiber lengths are of the same order of magnitude as the size of openings in the grids (typically ≈90 μm per side) used to analyze asbestos samples by transmission electron microscopy. This means that a substantial proportion of long fibers will cross the edge of a grid opening (GO) and therefore not be completely visible. Counting rules generally deal with such fibers by assigning a length equal to twice the visible length. Using both theoretical and simulation methods, we show that this doubling rule introduces bias into estimates of fiber concentrations and the amount of bias increases with fiber length. We investigate an alternative counting rule that counts only fibers that lie completely within a GO and weights those fibers by the reciprocal of the probability that a fiber of that length lies totally within a GO. This approach does not have the bias inherent in the doubling rule and is essentially unbiased if the stopping rule specifies a fixed number of GOs to be scanned. However, a stopping rule based on successively scanning GOs until a fixed number of fibers have been counted will introduce bias into any counting method, although this bias may typically not be large enough to be of practical concern. We recommend use of the weighted approach as a supplement to use of the doubling rule when estimating concentrations of long fibers, irrespective of the stopping rule employed.

In plain English

This paper was a statistical methods study, not a study of people or disease. It looked at how asbestos fibers are counted under transmission electron microscopy (TEM). In TEM, filters are viewed through grid openings that are typically about 90 micrometers on a side. Long fibers often cross the edge of an opening, and common counting rules assign such fibers twice their visible length (the "doubling rule"). Using mathematical derivations and computer simulations, the authors found that the doubling rule overstated how many long fibers there were, and the error grew with fiber length. In the simulations, doubling-rule estimates of fibers 30 micrometers or longer were 20 to 100% too large. The authors proposed a weighted method instead. It counts only fibers lying entirely within an opening and gives each one more weight the less likely a fiber of that length is to be fully visible. In the simulations its bias for those long fibers was about 2% or less, but it required scanning 35% more grid openings. Stopping the count after a set number of fibers also caused bias, which was under 10% in all simulated cases. The authors recommended the weighted method as a supplement to the doubling rule.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Methodological study using mathematical (theoretical) derivation and computer simulation of TEM fiber counting rules, with the two counting methods also compared on an existing data set of archived textile factory dust samples
• Who was studied: No human subjects. Simulated fiber counts on TEM grid openings assumed to be 90 micrometers on a side, with 1000 simulated data sets per case and three scans modeled on Dement et al. (2008). Also archived samples of textile factory dust analyzed by Dement et al. (2008).
• Exposure: Airborne asbestos fibers as counted by TEM. Fiber lengths were modeled with log-normal and gamma distributions. The study compared the doubling rule (edge-crossing fibers assigned twice their visible length) with a weighted estimator that uses only fully visible fibers, under two stopping rules (a fixed number of fibers counted, or a fixed number of grid openings scanned).
• Main results:
  • For a grid opening 90 micrometers on a side, a fiber 45 micrometers long had a probability of 0.56 of crossing an edge of the opening.
  • In the theoretical comparison, the doubling rule assigned slightly too few short fibers and increasingly too many long fibers. For the proportion of fibers 40 micrometers or longer (mean 4.1, SD 4.6), the doubling-rule-to-true ratio was 1.3 for the log-normal and 3.9 for the gamma distribution. For gamma-distributed lengths, the doubling rule's expected proportion of fibers 60 micrometers or longer was 26 times the true number.
  • Of fibers assigned lengths of 40 micrometers or longer under the doubling rule, the fraction coming from edge-crossing fibers (whose true lengths cannot be seen) ranged from 0.69 to 0.72 for the three log-normal distributions and from 0.69 to 0.89 for the three gamma distributions.
  • In simulations with a stopping rule based on a fixed number of fibers, the two estimators performed roughly the same for fibers 10 micrometers or longer. For fibers 30 micrometers or longer with gamma-distributed lengths, the bias was 100% for the doubling estimator and 2% for the weighted estimator. Table 1 shows 24% versus 2.0% for log-normal lengths.
  • Across the simulated cases, doubling-rule estimates of the concentration of fibers 30 micrometers or longer were 20 to 100% too large.
  • To count the same numbers of fibers, the weighted estimator required scanning 35% more grid openings than the doubling estimator.
  • Bias from stopping rules based on a fixed number of fibers counted was less than 10% of the true value in all simulated cases.
  • In the archived textile factory dust data, the ratio of doubling-rule to weighted estimates for primary structures rose with length, from 1.02 (5 micrometers or longer) to 1.45 (60 micrometers or longer). For component structures the trend went the other way, from 0.88 to 0.56.
• The authors' conclusion: The authors concluded that the doubling rule biases concentration estimates, increasingly so for longer fibers. They considered it premature to recommend using only the weighted procedure, but recommended applying it as a supplement to the doubling rule when estimating concentrations of long fibers.
• Limitations the authors state:
  • The fiber length distributions and parameter values were chosen to illustrate points, not necessarily to represent distributions found in practice.
  • The authors stated it is difficult to determine the extent of the doubling rule's bias from standard statistical analyses of existing data sets.
  • The weighted estimator cannot count fibers longer than the diagonal of a grid opening, so it estimates a truncated distribution. The authors regarded this as mainly of theoretical interest because such fibers are extremely rare.
  • The authors could not explain the opposite trend for component structures in the textile dust data. They hypothesized it relates to difficulty enumerating and sizing components of complex structures.
  • A stopping rule based on counting a fixed number of fibers introduces bias into any counting method, including the weighted estimator.

Topics

Medical terms in this study, explained in our Lexicon: Fiber Length, Transmission Electron Microscopy (TEM).

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