Reference range determination: the problem of small sample sizes.

The process of developing and validating a quantitative test includes determination of a reference range. Traditionally this has been taken as the mean +/- 2 standard deviations for a random sampling from a reference population. However, this method fails to recognize the substantial variability in the sample mean and standard deviation for the small sample sizes frequently encountered in nuclear medicine. A new approach, which involves calculating confidence intervals for the upper and lower bounds of the traditionally defined range, recognizes three ranges of values: normal, indeterminate, and abnormal. The principles of this approach are illustrated using differential renal function in twelve renal transplant donors. The 99mTc-DTPA differential uptake between 1 and 2 min gave a traditionally-defined single-kidney range of 50% +/- 8%, whereas with our method the normal range would be 50% +/- 6% with indeterminate ranges of 37%-44% and 56%-63%. These values are consistent with the wide variation in reference ranges reported in the literature, and suggest that much of this variability may be a statistical artifact resulting from inadequate sample sizes. A nomogram has been derived that permits the power of the reference range determination to be easily calculated from the sample size. Analysis of the effect of sample size on the accuracy of the upper and lower bounds of the reference range is advocated whenever small reference populations are used.