title: What can be learnt from nothing? - A statistical perspective.
abstract: BACKGROUND
  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).
  
  
  OBJECTIVE
  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%.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Department of Medical Informatics, Biometry and Epidemiology, University of Erlangen-Nürnberg, 91054, Erlangen, Germany.
authors.forename: Olaf
authors.initials: O
authors.lastname: Gefeller
authors.forename: Annette B
authors.initials: AB
authors.lastname: Pfahlberg
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Uter
mesh_terms: D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D017449:Dermatitis, Allergic Contact / Q000175:diagnosis / Q000453:epidemiology*; D015340:Epidemiologic Research Design; D006801:Humans; D010328:Patch Tests / Q000706:statistics & numerical data*; D015995:Prevalence
keywords: biostatistics; interval estimation; prevalence