Confidence limits for risk differences and risk ratios adjusted for estimated sensitivity and specificity

Abstract

In this paper, a procedure to construct approximate confidence intervals (CIs) of risk differences and risk ratios taking into account the sensitivity and specificity of a diagnostic test, and also taking into account the size of the samples from which sensitivity and specificity were estimated is proposed. The new method combines the originally proposed method of Rogan and Gladen, and the general method described by Zou and Donner for calculating the CI of difference between two effective measures based on their individual CI limits. The performance of the new method will be evaluated by calculating the exact coverage of the resulting CIs. More methods are known to account for sensitivity and specificity considered to be constant, however, when the sensitivity and specificity of a test were estimated within studies with small sample sizes then ignoring their variability may lead to biased estimates. This will be shown through real examples.

KEYWORDS:

• Risk ratio
• risk difference
• misclassification
• confidence interval

Acknowledgements

The authors would like to express special thanks to Prof. Dr Jenő Reiczigel and Dr Zsolt Lang (University of Veterinary Medicine Budapest) for their contribution and useful comments on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Péter Hársfalvi

Dr. Hársfalvi currently serves as Director of Clinical Operations at BiTrial CRO. He holds Doctor of Pharmacy degree from Semmelweis University of Budapest and a postgradual degree in Biostatistics. He is currently a PhD student at the University of Veterinary Medicine in Budapest with main research interests in adaptive clinical trial designs and sample size calculation.

Júlia Singer

Dr. Singer has more than 25 years of experience in most biostatistical areas of the Pharma industry, comprising both clinical and pre-clinical research. She is responsible for defining development strategies, study designs, ensuring that the Biostatistics team applies state-of-the-art, efficient methods for the statistical evaluation of clinical results at Accelsiors CRO.