Estimation of reference intervals from small samples: an example using canine plasma creatinine

According to international recommendations, reference intervals should be determined from at least 120 reference individuals, which often are impossible to achieve in veterinary clinical pathology, especially for wild animals. When only a small number of reference subjects is available, the possible bias cannot be known and the normality of the distribution cannot be evaluated. A comparison of reference intervals estimated by different methods could be helpful.

The purpose of this study was to compare reference limits determined from a large set of canine plasma creatinine reference values, and large subsets of this data, with estimates obtained from small samples selected randomly.

Twenty sets each of 120 and 27 samples were randomly selected from a set of 1439 plasma creatinine results obtained from healthy dogs in another study. Reference intervals for the whole sample and for the large samples were determined by a nonparametric method. The estimated reference limits for the small samples were minimum and maximum, mean +/- 2 SD of native and Box-Cox-transformed values, 2.5th and 97.5th percentiles by a robust method on native and Box-Cox-transformed values, and estimates from diagrams of cumulative distribution functions.

The whole sample had a heavily skewed distribution, which approached Gaussian after Box-Cox transformation. The reference limits estimated from small samples were highly variable. The closest estimates to the 1439-result reference interval for 27-result subsamples were obtained by both parametric and robust methods after Box-Cox transformation but were grossly erroneous in some cases.

For small samples, it is recommended that all values be reported graphically in a dot plot or histogram and that estimates of the reference limits be compared using different methods.