What can be learnt from nothing? – A statistical perspective

Abstract

No observed event is a special, but not uncommon, result in patch test studies. The interpretation of such findings depends critically on the sample size (n) of the investigation, and is statistically addressed by the use of confidence intervals (CIs). To define the statistically correct method of calculating a CI with a confidence level of 1 - α, where α denotes the tolerated statistical error probability, for an observed prevalence of 0%. A literature survey and evaluation of the statistical methods was conducted. The popular statistical software packages SPSS™ and SAS™ were examined with regard to the methods implemented, and the results obtained, for estimating such CIs in this special case. The evaluation identified [0; 1 - α(1/n) ], which is well approximated by [0; 3/n] for α = 0.05, as an appropriate method to compute a CI with a confidence level of 1 - α. The resulting CI is an exact one, and more efficient than standard solutions. Popular statistical software such as SPSS™ and SAS™ offers only various inefficient or even invalid procedures, but does not include this method. It is easy to calculate a CI for an observed prevalence of 0% obtained in some studies. Such a CI facilitates the interpretation of such a finding, as it puts the observed zero result into adequate statistical perspective.