This page contains supplementary material to the paper


Reiczigel J, Földi J, Ózsvári L (2010) Exact confidence limits for prevalence of a disease with an imperfect diagnostic test, Epidemiology and infection, 138: 1674-1678.


Abstract: Estimation of prevalence of disease, including construction of confidence intervals, is essential in surveys for screening as well as in monitoring disease status. In most analyses of survey data it is implicitly assumed that the diagnostic test has a sensitivity and specificity of 100%. However, this assumption is invalid in most cases. Furthermore, asymptotic methods using the normal distribution as an approximation of the true sampling distribution may not preserve the desired nominal confidence level. Here we proposed exact two-sided confidence intervals for the prevalence of disease, taking into account sensitivity and specificity of the diagnostic test. We illustrated the advantage of the methods with results of an extensive simulation study and real-life examples.


Simulation results (pdf)          Further examples (pdf)          R function (txt)


 The method is also included in the on-line software tool Epi Tools by AusVet. EpiTools offers a rich collection of useful epidemiological methods, it is worth trying. To reach directly the page with true prevalence calculations, click here.


On-line calculator


If you have two (or more) groups, you may be interested in comparing the prevalences. To do this, you can calculate the ratio prevgroup1 / prevgroup2, which is called risk ratio (RR), also called prevalence risk ratio (PRR) or prevalence ratio (PR). If you have several groups, the usual method is to select one as the reference group, and compare others to that one by means of RRs. RRs may also be affected by sensitivity and specificity of the diagnostic tests. To compute true RRs, adjusted for Se and Sp, find our R function and on-line calculator, together with some application examples here!



The following results are related to the paper


Lang Zs, Reiczigel J (2014) Confidence limits for prevalence of disease adjusted for estimated sensitivity and specificity, Preventive Veterinary Medicine, 113, 13-22.


addressing the problem of prevalence estimation when sensitivity and specificity of the diagnostic procedure is not known exactly but estimated from samples. In this case the uncertainty in sensitivity and specificity estimates increases the uncertainty of the prevalence estimate, making standard errors greater, and confidence intervals wider. We propose a new confidence interval for the true prevalence incorporating the uncertainty of sensitivity and specificity estimates. In order to improve poor coverage probabilities of the method by Rogan and Gladen (1978), we propose an adjustment similar to the “add two successes and two failures” by Agresti and Coull (1998). 


R function (txt)                   Excel sheet (xls)


According to the simulation results, the new procedure, although not exact, maintains the nominal level fairly well. For comparison, we present the simulation results for the Rogan and Gladen procedure without the proposed adjustment. In the simulation we varied the sample sizes for the prevalence, sensitivity, and specificity estimates (Nprev, Nsens, Nspec), also varied the true sensitivity and specificity (Sens, Spec), and for each combination of these determined the coverage for true prevalence 0.005, 0.01, 0.02, 0.03, 0.05, 0.1, 0.2, 0.3, and 0.5. Prevalences >0.5 are not included because coverage for any prev>0.5 is same as that for (1-prev) with (Sens, Nsens) and (Spec, Nspec) swapped.


Simulation results: 

New procedure, 90% (pdf)               New procedure, 95% (pdf)               New procedure, 99% (pdf)


Rogan and Gladen, 90% (pdf)          Rogan and Gladen, 95% (pdf)          Rogan and Gladen, 99% (pdf)


On-line calculator



Our conference poster presented at the 27th International Biometric Conference (Florence, Italy, 6-11 July 2014) related to this research project can be downloaded here.



 (last updated on 28 July 2018)