Repeatability of paired counts.

The Bland and Altman technique is widely used to assess the variation between replicates of a method of clinical measurement. It yields the repeatability, i.e. the value within which 95 per cent of repeat measurements lie. The valid use of the technique requires that the variance is constant over the data range. This is not usually the case for counts of items such as CD4 cells or parasites, nor is the log transformation applicable to zero counts. We investigate the properties of generalized differences based on Box-Cox transformations. For an example, in a data set of hookworm eggs counted by the Kato-Katz method, the square root transformation is found to stabilize the variance. We show how to back-transform the repeatability on the square root scale to the repeatability of the counts themselves, as an increasing function of the square mean root egg count, i.e. the square of the average of square roots. As well as being more easily interpretable, the back-transformed results highlight the dependence of the repeatability on the sample volume used.