Reference interval estimation of small sample sizes: A methodologic comparison using a computer-simulation study

According to the ASVCP and other guidelines, samples should comprise at least 120 individuals for reference interval (RI) estimation. Unfortunately, this minimum sample size is difficult to achieve in veterinary medicine. Several statistical methods are described to determine RIs from small sample sizes, but it is unclear which method provides the best accuracy.

This study aimed to compare statistical strategies for estimating RIs and determine which strategy best enhances accuracy when the sample size is between 20 and 120.

Different sample size groups (n = 120, 100, 80, 60, 40, and 20) were randomly selected 50 times from simulated Gaussian, log-normal, and left-skewed populations of 5000 total values. RIs were calculated using seven different statistical strategies comprising robust, parametric, nonparametric, and bootstrap methods, alone or in combination. RI accuracy was compared among these strategies at each sample size. The strategy that was significantly more accurate than others in the largest number of comparisons was considered as the one that best-enhanced RI accuracy.

The strategies that best-enhanced RI accuracy included using the parametric method when the Shapiro-Wilk P > 0.2 and, otherwise, using the nonparametric method to determine the upper and lower RI limits when there were between 60 and 100 reference individuals, and finding the lower RI limit when there were 40 reference individuals. The Box-Cox transformation parametric method best-enhanced RI accuracy of the upper RI limit when there were 40 reference individuals, and the nonparametric method best-enhanced RI accuracy of both RI limits when there were 20 reference individuals.

Using the parametric method when the Shapiro-Wilk P > 0.2, and the nonparametric method in other instances, will likely enhance RI accuracy when there are between 40 and 100 reference individuals. For smaller samples, the nonparametric method might be preferred.