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- Abstract
- 1. Introduction
- 2. Inter-Animal Variability
- 3. Sensitivity to Increases above the Spontaneous Frequency
- 4. Number of Reticulocytes Required to be Scored to Reduce Counting Error to Less than Inter-Animal Variability
- References

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Mutat Res. Author manuscript; available in PMC 2007 December 12.

Published in final edited form as:

Published online 2007 August 6. doi: 10.1016/j.mrgentox.2007.07.010

PMCID: PMC2133347

NIHMSID: NIHMS34563

* Corresponding author: Dr. Grace E. Kissling, (919) 541-1756 (phone), (919) 541-4311(FAX), Email: kissling/at/niehs.nih.gov

Until recently, the *in vivo* erythrocyte micronucleus assay has been scored using microscopy. Because the frequency of micronucleated cells is typically low, cell counts are subject to substantial binomial counting error. Counting error, along with inter-animal variability, limit the sensitivity of this assay. Recently, flow cytometric methods have been developed for scoring micronucleated erythrocytes and these methods enable many more cells to be evaluated than is possible with microscopic scoring. Using typical spontaneous micronucleus frequencies reported in mice, rats and dogs, we calculate the counting error associated with the frequency of micronucleated reticulocytes as a function of the number reticulocytes scored. We compare this counting error with the inter-animal variability determined by flow cytometric scoring of sufficient numbers of cells to assure that the counting error is less than the inter-animal variability, and calculate the minimum increases in micronucleus frequency that can be detected as a function of the number of cells scored. The data show that current regulatory guidelines allow low power of the test when spontaneous frequencies are low (e.g., ≤ 0.1%). Tables and formulas are presented that provide the necessary numbers of cells that must be scored to meet the recommendation of the International Working Group on Genotoxicity Testing that sufficient cells be scored to reduce counting error to less than the inter-animal variability, thereby maintaining a more uniform power of detection of increased micronucleus frequencies within each species across the range of spontaneous frequencies observed in these three species.

The ability of the *in vivo* erythrocyte micronucleus assay to detect small increases in the spontaneous background frequency of micronucleated cells in a group of animals (or study subjects) is limited by either the binomial counting error, when the number of cells scored gives small numbers of scored events (micronucleated cells) [1–4], or by inter-animal variation, when that variation is so large that it obscures a small, but real, increase. Furthermore, the sensitivity to detect small increases in the micronucleus frequency in an individual animal is limited at small micronucleus counts by the binomial counting error and at higher counts by the spontaneous variability in that individual animal over the time span in which measurements are made. Recognizing these facts, the working group on the *in vivo* micronucleus assay organized by the International Workshops on Genotoxicity Testing (IWGT) has recommended that, whenever possible, sufficient cells should be scored to reduce the counting error to less than the variability in MN frequency between individual animals (for comparison of values in different treated groups) [5].

Prior to the development of flow cytometric scoring methods, the number of cells scored was generally limited by the practical consideration of the number of cells that could be scored in a reasonable period of time by a microscopist, and therefore the minimum number of cells recommended to be scored in current regulatory guidelines is generally less than that required to discern differences between individual animals. Flow cytometric methodologies now make it practical to reduce the counting error to very small values [6–8], allowing, for the first time, reliable determination of the inter- and intra-animal variation in the spontaneous micronucleus frequency.

We summarize below experimentally determined mean and variability among animals in the spontaneous frequency of micronucleated reticulocytes (MN-RETs) in peripheral blood reticulocytes in the Sprague-Dawley rat, CD-1 mouse, and beagle dog, and in bone marrow reticulocytes in the Sprague-Dawley rat, and compare this inter-animal variability with the microscopic counting error associated with the current regulatory recommendations for scoring bone marrow or peripheral blood reticulocytes in these species. From these values, we determine the minimum increase in group mean frequencies of MN-RETs that can be detected in these species, tabulate the minimum increases that can be detected as a function of the number of RETs scored, and identify the numbers of cells that need to be scored to meet the IWGT recommendation that sufficient cells should be scored such that the error in individual animal MN-RET frequencies is less than the inter-animal variability.

The inter-animal variability of the percentage of MN-RETs among RETs (#MN-RET/#RETs scored × 100) in the peripheral blood of Sprague-Dawley rats, CD-1 mice, and purpose-bred beagle dogs, and also in the bone marrow of Sprague-Dawley rats after removal of nucleated cells on a cellulose mini-column as described by Romagna [9] and Weiner et al. [10], was estimated by scoring 20,000 reticulocytes using the flow cytometric method described by Dertinger et al. [11–13]. These data are summarized in Table 1. The data are taken from previously reported studies in these species [14,15]. Details of the experimental methodology are reported in the previous publications. As is discussed below, scoring 20,000 RETs results in a sufficient number of events (MN-RETs) that the error associated with individual animals does not exceed approximately 50% of the inter-animal variability of spontaneous MN-RET frequencies in the respective species. The inter-animal % coefficient of variation (%CV = Standard Deviation ÷ Mean × 100%) of the MN-RET frequencies was 41% for the rat, 35% for the mouse, and 30% for the dog.

Mean and Inter-Animal Variation of the Micronucleated Reticulocyte Frequency in the Peripheral Blood (PB) and Bone Marrow (BM) of Sprague-Dawley Rats, Swiss Mice, and Beagle Dogs.

Table 2 presents the binomial error in the count of MN cells in an individual animal obtained by scoring 2000, 4000, 8000, or 20,000 RETs as a function of the spontaneous frequency of MN-RETs. It should be noted that the spontaneous frequency in rodent bone marrow or peripheral blood reported by different experienced laboratories has ranged from 0.05% in rat (see individual laboratory values in [14]) to a mean value of 0.2% in the mouse [15,16] and 0.31% in the beagle dog. Since the counting error depends on the background rate and the number of cells scored, we have tabulated values over the range of spontaneous frequencies commonly reported in rodents and recently observed in the beagle dog (manuscript in preparation). As can be seen in Table 2, when 2000 cells are scored (the recommended number in the current OECD, FDA, and EPA regulatory guidelines [17–19] the error in the counts observed in individual animals is substantially greater than the variation between animals (Table 1). When the spontaneous frequency is 0.1%, approximately 6000 cells would need to be scored to reduce the error in the individual animal count to less than the inter-animal variability observed in the rat.

Table 3 summarizes the minimum increases above the spontaneous frequency that can be detected in groups of five animals (the minimum currently recommended in OECD, FDA, and EPA guidelines [17–19] as a function of the number of target cells scored (in this case RETs) and observed spontaneous frequency (in this case %MN-RETs among RETs). Minimum detectable increases in MN-RET frequencies at p ≤ 0.05 or p ≤ 0.01, with 90% or 95% power were determined using Monte Carlo simulations. Specifically, to reflect inter-animal variability, five binomial probabilities were randomly selected from a normal distribution with the following mean, μ_{0}, and standard deviation, σ, combinations: (μ_{0}, σ) = (0.05%, 0.02%), (0.10%, 0.045%), (0.20%, 0.070%), or (0.30%, 0.092%). For a given fold-increase, *f*, a second set of five binomial probabilities were randomly selected from a normal distribution with mean, μ_{1} = μ_{0} × *f*, and the same σ given above. Using the 5 binomial probabilities from the spontaneous mean group, five MN-RETs frequencies were randomly generated from binomial distributions, with *n* = number of RETs scored, 2000, 4000, or 20,000. Such selection from a binomial distribution introduces the binomial counting error. Five MN-RET frequencies were similarly generated using the 5 binomial probabilities from the increased mean group. A one-tailed Mann-Whitney test was then performed on these 10 counts, comparing the spontaneous group to the increased group, and the p-value was noted as to whether it was 0.05 or less and/or 0.01 or less. This was repeated 3000 times and the percentages of the 3000 ‘samples’ for which the p-value was 0.05 or less and 0.01 or less were calculated. The process was repeated over a series of increases, *f*, at increments of 0.1, to determine the first point at which the power exceeded 90% or 95%. We obtained very similar results (not shown) by generating the 5 binomial probabilities from beta distributions having the above combinations of μ_{0}, μ_{1} and σ.

Minimum Detectable Increases in MN-RET Frequency in Groups of Five Animals as a Function of Spontaneous Frequency and Number of RETs Scored^{a}

For the line labeled “∞” in Table 3, there is no counting error; rather, the variability in frequencies is due to inter-animal variation alone. If we assume that inter-animal variation is normally distributed, the minimum difference between μ_{1} and μ_{0}, δ = μ_{1} − μ_{0}, detectable using 5 animals per group with significance level α and power 1 − β is

[20]. Here, *t*_{α} and *t*_{β} are the critical values from the 5 + 5 − 2 = 8 degree of freedom *t*-distribution having upper tail probabilities α and β, respectively. The minimum detectable fold-increase over the spontaneous group is then

While spontaneous MN-RET frequencies determined from counting 2000 RETs from different animals are not often normally distributed, it has been our experience that spontaneous frequencies determined from counting 20,000 RETs from different animals are approximately normally distributed. Therefore, the assumptions of normality that we made above are most likely reasonable.

It should be noted that even if the counting error of the MN-RET frequency in each individual animal could be eliminated, the sensitivity of detection of changes in the observed mean group frequency would still be limited by the inter-animal variability (represented in Table 3 by the line in which an infinite number of cells is scored). It is clear that the regulatory assay as currently conducted is relatively insensitive to changes in the spontaneous frequency, especially when the spontaneous frequency is low. For example, when the spontaneous frequency is 0.05% and only 2000 RETs are scored, even a 6.8-fold increase would fail to be detected at a confidence level of p ≤ 0.01 in 10% of experiments conducted. Even at the more commonly-reported spontaneous frequency of 0.1% a 4.8-fold increase would fail to be detected 10% of the time at this same confidence level. The use of flow cytometric scoring to achieve a sufficient cell count to allow individual animal frequencies with adequate certainty (*i.e.*, certainty of the individual value relative to the inter-animal variation) would increase the sensitivity such that a doubling of a spontaneous frequency of 0.1% among 20,000 RETs scored would be detected nearly 90% of the time at a confidence level of p ≤ 0.05. It should also be noted that, regardless of the spontaneous frequency, the sensitivity achieved by scoring 20,000 RETs is close to the optimal sensitivity that could be achieved if no counting error were present.

Table 4 summarizes the number of cells required to be scored to reduce the counting error of individual animal values (Table 2, %CV) to the observed inter-animal variation or less (Table 1, %CV). These numbers were calculated by setting a multiple (*m* = 1.0, 0.5, or 0.2) of the inter-animal %CV equal to the binomial counting error %CV and solving for the required sample size, *n*. Mathematically, if *p* is the percent of MN-RETs among all RETs within an animal, then

Number of Reticulocytes Required to be Scored to Reduce Counting Error to Less Than the Observed Inter-Animal Coefficient of Variation.

Solving for *n*, we get

The numbers of RETs required are prohibitively laborious to obtain by conventional microscopic scoring, but are easily achieved by automated procedures such as flow cytometry.

We thank Ronald Fiedler of Pfizer, Inc. for providing the data on spontaneous frequencies and inter-animal variability of the frequency of micronucleated reticulocytes in the bone marrow of Sprague-Dawley rats. This research was supported in part by the Intramural Research Program of the NIH, National Institute of Environmental Health Sciences.

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