Confidence intervals and sample size calculations to compare variant frequencies

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Abstract
Direct mutagenicity tests offer the opportunity of monitoring human populations to detect evidence of genetic damage that occurs in vivo. As such these tests offer the potential of linking earlier exposures to mutagenic agents to subsequent health effects. One such test detects mutant T-lymphocytes that arise in vivo in human peripheral blood. Statistical analysis of the value observed, the variant frequency (Vf), is the subject of this paper. We present and illustrate procedures for finding confidence intervals for a single variant frequency and for the ratio of two independent variant frequencies. We also derive formulae for required sample size to ensure adequate power to detect a specified change in a single variant frequency or a specified difference between two variant frequencies. Our approach is to exploit the approximate normality of the natural logarithm of a Poisson distributed variable. The procedures developed appear to be quite accurate even for the small (5–15) values often observed in the variant frequency assay. Moreover, the procedures are very easy to use and should prove valuable to investigators involved in direct mutagenicity testing.