 Software
 Open access
 Published:
tPRiors : a tool for prior elicitation and obtaining posterior distributions of true disease prevalence
BMC Medical Research Methodology volume 22, Article number: 91 (2022)
Abstract
Background
Tests have false positive or false negative results, which, if not properly accounted for, may provide misleading apparent prevalence estimates based on the observed rate of positive tests and not the true disease prevalence estimates. Methods to estimate the true prevalence of disease, adjusting for the sensitivity and the specificity of the diagnostic tests are available and can be applied, though, such procedures can be cumbersome to researchers with or without a solid statistical background. This manuscript introduces a webbased application that integrates statistical methods for Bayesian inference of true disease prevalence based on prior elicitation for the accuracy of the diagnostic tests. This tool allows practitioners to simultaneously analyse and visualize results while using interactive sliders and output prior/posterior plots.
Methods  implementation
Three methods for prevalence prior elicitation and four core families of Bayesian methods have been combined and incorporated in this web tool. tPRiors user interface has been developed with R and Shiny and may be freely accessed online.
Results
tPRiors allows researchers to use preloaded data or upload their own datasets and perform analysis on either single or multiple population groups clusters, allowing, if needed, for excess zero prevalence. The final report is exported in raw parts either as.rdata or.png files and can be further analysed. We utilize a real multiplepopulation and a toy singlepopulation dataset to demonstrate the robustness and capabilities of tPRiors.
Conclusions
We expect tPRiors to be helpful for researchers interested in true disease prevalence estimation and who are keen on accounting for prior information. tPRiors acts both as a statistical tool and a simplified stepbystep statistical framework that facilitates the use of complex Bayesian methods. The application of tPRiors is expected to aid standardization of practices in the field of Bayesian modelling on subject and multiple groupbased true prevalence estimation.
Background
Apparent prevalence represents the observed rate of positive test results. Tests can give false positive and false negative results, thus apparent prevalence estimates are biased estimates of the true disease prevalence, while the extend of this bias depends on the overall misclassification rate of testing. Methods are available and can be applied to estimate the true prevalence of disease and, thus, adjust for the imperfect sensitivity and specificity of the diagnostic tests, either within a frequentist or a Bayesian framework [1, 2]. The primary advantage of the latter framework lies in its ability to incorporate in the estimation process existing and relevant knowledge for the parameters of interest in the form of priors [3]. Nonetheless, the application of such approaches can be cumbersome for researchers with or without a statistical background, which results in limited application of existing Bayesian methods for calculation of true prevalence by nonexperts. A statistical program that encompasses most of these prevalence models would boost the application of such methods and aid practitioners to perform basic and advanced Bayesian prevalence estimation.
In this manuscript we present Bayesian models for the estimation of apparent and true disease prevalence for a single and multiple populations (“Implementation section). Then, we introduce a new free webbased application, tPRiors, that facilitates the use of Bayesian prevalence methods by nonexperts (“The tPRiors webbased application” section), which has been developed with R and Shiny [4]. Finally, in “Results” section, we illustrate the use of tPRiors using a single toy population example [5], and a real multiple population example that is based on a systematic review and metaanalysis on the prevalence of Dementia in Europe [6]. The manuscript ends with a Discussion.
Implementation
Methods for prevalence estimation
Apparent prevalence estimation
Let us assume that in a single population of size N (i.e. nation, group of patients, animal herd or any cluster) y subjects test positive out of the n randomly sampled population subjects. Then y follows, approximately, a binomial distribution:
where π_{a} is the apparent disease prevalence and \(\alpha _{\pi _{a}},\beta _{\pi _{a}}\) are the parameters of the Beta prior distribution for π_{a}. The posterior distribution of the above model can be analytically calculated from \(Beta(\alpha _{\pi _{a}}+y,\beta _{\pi _{a}}y+n)\) or through the use of Bayesian statistical programs (WinBugs, Jags, Stan) [7–9]. In the absence of historical information, parameters \(\alpha _{\pi _{a}},\beta _{\pi _{a}}\) can be set close or equal to 1, which is similar to assuming a Uniform(0,1) prior on π_{a}. Relevant existing knowledge for π_{a} can be incorporated by specifying values for \(\alpha _{\pi _{a}},\ \beta _{\pi _{a}}\) that leads to a prior Beta distribution that captures such knowledge. tPriors can be used to specify these values (see “The tPRiors webbased application” section).
True prevalence estimation
The relationship between apparent (π_{a}) and true disease prevalence (π_{t}) is known and given by π_{a}=π_{t}S_{e}+(1−π_{t})(1−S_{p}) [10], where S_{e},S_{p} denote the sensitivity and specificity of the diagnostic test. Hence, replacing π_{a} with the above in Eq. 1,
where \(\alpha _{\pi _{t}},\beta _{\pi _{t}},\alpha _{S_{e}},\beta _{S_{e}},\alpha _{S_{p}},\beta _{S_{p}}\) are the parameters of the Beta prior distributions for p_{t},S_{e} and S_{p}, respectively [2].
Multiple populations
Let us suppose that n_{i}, i=1,2,...,k subjects are sampled randomly from multiple clusters (k). When multiple clusters are available, commonly a twostage clusterdesign is implemented. In the first stage k clusters are selected randomly within a region and then n_{i} subjects are sampled randomly from each cluster (i). In the end, y_{i} positive tests will be collected from each cluster. As in the single cluster case above, the number of tests, are assumed to follow a binomial distribution [1],
S_{e} and S_{p} are modelled through beta prior distributions and are assumed invariant between clusters. The sampled group prevalences are considered exchangeable as π_{ti}μ,ψ∼Beta(μψ,ψ(1−μ)), where μ denotes the average population prevalence and ψ is associated with the heterogeneity (betweengroup variance) of cluster prevalences around their mean. μ,ψ are modelled through a Beta and Gamma prior distributions respectively. Large values of ψ correspond to lower betweenstudy variability (heterogeneity). On all hyperparameters (i.e. α_{μ},β_{μ},α_{ψ},β_{ψ}) a hyperprior distribution can be assumed, also, all hyper parameters can be elicited based on expert opinion. A logical strategy, though, would be to reduce the number of unknown parameters, given that the data collection procedure relies solely on a basic binomial count [2].
Allowing for zero true prevalence
All models above assume a flexible beta prior distribution on π_{t}. This implies that π_{t}≠0, an assumption that may not be realistic on low prevalence populations or on populations with specific free from disease clusters. To account for the probability of zero disease prevalence, a mixture distribution can be applied such that \(\phantom {\dot {i}\!}\pi _{t}\sim Beta(\alpha _{\pi _{t}},\beta _{\pi _{t}})\) for a single population or π_{ti}μ,ψ∼Beta(μψ,ψ(1−μ)) for multiple populations with probability w, and π=0 with probability 1−w, where w is the probability that the group is actually infected [2].
In a similar sense, a beta prior distribution can be placed on w, with α_{π},β_{π}=1 denoting prior ignorance. It should be noted that omitting to place a mixture distribution on π_{a} may result in biases and possibly narrower credible intervals. Following the multiple population modelling, w can be further modelled similarly to π_{ti} to allow for zero prevalence in the whole region [11].
The multinomial model allows for estimation of (a) the grouplevel prevalence, (b) the prevalence distribution for groups, (c) the mean of the prevalence distribution, (d) the probability that the whole (sub) population is free of disease (at a prespecified level) and finally (e) the predicted probability that a group is free of disease (again at a prespecified level).
The tPRiors webbased application
tPRiors is an openaccess webbased application with a graphical, userfriendly interface which aids the estimation of true disease prevalence from single and multiple population data using the models presented in “Implementation” section. Nonexpert users on Bayesian analysis and relevant software, such as R/JAGS, can easily elicit priors, perform Bayesian statistical analysis, visualize results and download the corresponding reports.
One of the mechanisms of the tPRiors application is the ”PriorGen” R package (Kostoulas, 2018), which powers the prior elicitation by translating prior beliefs into usable prior information in the form of hyperparameters for the Beta (and Gamma) distributions. This package can be utilized for the generation of priors on the true prevalence of disease, the sensitivity and the specificity of diagnostic tests and the probability of zero true prevalence.
tPRiors is powered by Shiny, thus, it has be deployed on shinyapps.io that allows for easy user access without the need for installation of R or JAGS. The web application can be accessed from any device that has internet connection and a web browser, even though more optimal use is warranted via a computer or a laptop. tPRiors is currently freely accessible to download and use in R/Rstudio via https://github.com/kpatera/tPRiors or it can be directly accessed via https://publicandonehealth.shinyapps.io/tPRiors/. The application can be accessed through different operating systems and internet browsers, though, we recommend the use of an updated Google Chrome or Firefox browser.
tPRiors step by step walkthrough
The initial ”Start” page and the other menus of tPRiors are presented in Fig. 1. tPRiors consists of six individual pages/tabs: 1. Start, 2. Setup, 3. Prior(s), 4. I nput & O utput, 5. Report and 6. Acks. Three of these pages, “Set up”, “Prior(s)” and " I nput & O utput “, contain the core mechanisms. On each page the user has to press the ”Fix/Set" button, after choosing the preferred options and before clicking on the next tPRiors page. Frequently asked questions (FAQ) can be found in the ’Acks’ page. A description for each page follows.
Start
The first page provides a general overview of tPriors and a brief description on how the user should proceed.
Set up
In this page the users select the modelling framework that best captures the structure of their data/population. The users first specify whether they will analyse data from one or multiple populations/clusters. Then, they define whether they wish to estimate true or apparent prevalence. Subsequently, they need to decide whether they wish to allow for the possibility of zero prevalence for some of the populations/clusters. Finally, they indicate whether there is a priori information for the prevalence (apparent or true) that they wish to use and then they decide which measure of central tendency (mean, median or mode) or dispersion (percentiles) they will employ for this prior specification on prevalence. The multiple population models option currently supports one prior specification measure (the mean).
Prior(s)
In this page the users should specify the available information that will be used for generation of the prior distribution for apparent or true prevalence. If, in the previous page, they have declared that the they are estimating true prevalence then two additional subpages become available for the sensitivity and specificity of the diagnostic test. Clicking on the ‘Help’ button will provide an example on how to elicit a prior based on the available questions. We urge users of tPRiors to first answer all questions, input values on all available parameters, and only then press the ’Set priors’ button, in this way small subjectivity would be inserted in the elicitation proccess. Prior specification is a guidedthrough process, though, further guidance can be found when the ’Help’ button is clicked or in the FAQ section of the ’Acks’ page. Furthermore, additional information can be found at the PriorGen manual [12].
I & O (Input & Output)
Based on their selection in the “Prior(s)” page, in this page users should input and model either single or multiple population data. For single population data, users should specify via a number of sliders, the sample size, number of events and Markov Chain Monte Carlo (MCMC)  related options. For multiplepopulation data, users should upload a dataset (.csv/.xls). Each row of the data table should correspond to a different site/study and the dataset should contain at least 2 columns. One column named “positive” that contains the observed number of events per site/population and one column named “n” that contains the sample sizes per site/population. When all parameters are set the user should then press the ’Fix model’ button and only then click on the “Report” page. Caution! Both Step 1. Data and Step 2. Output tabs have to be clicked to fully run the multiplepopulation models.
Report
After navigating through the above pages, users find a dynamic report in the fifth page. This report contains all previous selected options, information on the selected prior distributions as well as posterior prevalence inferences and MCMC diagnostics to check convergence. All figures can be directly downloaded. In the case of multiple populations, box plots are provided for each study in a dynamic graph (Fig. 2), together with information that aims to aid researchers in planning an upcoming prevalence study.
Near the end of the report a series of diagnostic plots are presented. More specifically, barplots and density plots of the main parameters are available at the top of the section, alongside traceplots and running mean plots, followed by complete versus partial chain plots and autocorrelation plots of the main parameters. When the MCMC analysis runs into issues users will identify noncommon patterns in these graphs. Mostly diagnostic plots point towards convergence issues. The simple density plots can show abnormalities in the posterior densities, if any density look different than expected the user should check the data and prior inputs. The multiple chain or partial chain density plots should contain densities of different chains that mostly coincide, otherwise posterior Bayesian convergence is impacted by each MCMC run and the results may not be trusted. MCMC traceplots should depict multiple chains that often cross in order to validate convergence while, the ergodic mean plots and the correlation plots should move very quickly towards the mean and zero respectively, otherwise the user should increase the thinning interval and/or the number of MCMC samples. We refer interested readers and practitioners to the CODA and GSS R packages and we suggest that, when in doubt, they should always consult with a statistician.
Finally, tPRiors provides further access to the analysis by making available three files at the bottom of the ”Report” page and analytical details on how to reanalyse them. These files are available under the 1) Input, 2) Model and 3) Output tabs. Interested users have the option to utilize Rstudio or R to work with the specific rData file of interest. By utilizing these files, i.e. studylevel plots can be reproduced to identify and diagnose further methodological issues or change the appearance and labels of the figures. Detailed steps on how to reproduce diagnostic plots can be found at the end of the “report” page, right before the download data tabs. Briefly, the MCMC samples can be downloaded from the “Report” page via the ’Output’ tab. Within the downloaded object, multiple MCMC chains are stored for each parameter of interest. Following the detailed steps on the “Report” page, practitioners can repetition (mentioned right above) attempt further analyses.
Acks
In the final page/tab an overview of the dependencies on R packages can be found. tPRiors web application was built using a number of R packages such as: shiny, shinydashboard, rmarkdown. R2jags, rootSolve, reshape, ggplot2, dplyr, DT and plotly among others. The different colours represent the four main categories of use., i.e. the orange colour denotes main packages, the green colour denotes shinybased packages, blue and variations denote packages that aid plotting/reporting and the red colour denotes packages for data manipulation.
Results
The following section presents two, a multiple and a single population, examples of true prevalence estimation while taking into account the sensitivity and specificity of the applied (imperfect) diagnostic test.
Multiple population illustrative example
The multinomial approach estimates true prevalences that can directly be compared among the multiple study sites (i.e. studies, regions, cities, groups) as they are adjusted for imperfect diagnostic testing.
We present the systematic review on prevalence from Bacigalupo et al. [6]. The authors conducted a systematic review and metaanalysis on dementia and Alzheimer’s disease. They selected studies that diagnosed patients according to the DSM (Diagnostic and Statistical Manual of Mental Disorders) IV criteria but also studies that had a high quality score according to Alzheimer’s Disease International study quality score criteria [13]. The metaanalysis included 9 studies conducted in Europe between 1993 and 2018 with patients aged >65 years. The total number of participants were 18263, out of which 2137 were diagnosed with dementia based on DSM IV criteria. The metaanalysed pooled prevalence rate estimate was reported as equal to 12.4% (95% CI 7.6%–17.2%). The raw data are summarized in Table 1.
A number of subjects have been tested (n_{i}) per study/country, out of which (y_{i}) subjects showed positive test results. The test procedure was based on DSM IV criteria for all participants. In comparison with previously used diagnostic procedures, the DSM IV criteria result in higher specificity. On average, based on historical data and previous studies, sensitivity may be set equal to 95% and specificity can be set equal to 88% [14–16], though if comorbidities or mild dementia are present, specificity may drop even further [17].
On tPRiors, the user selects to model 1) true prevalence, 2) multiple populations, 3) nonzero true prevalence, 4) informative priors^{Footnote 1} and then clicks fix. Consequently, in the “Prior(s)” page and given the above information, the researcher specify priors on the disease prevalence and the test specificity and sensitivity. Via the use of simple sliders in the tab “Priors”, a lowinformative prior is elicited for the true prevalence, as a π_{t}∼Beta(0.14,0.55). The tPRiors shiny application input for this prevalence prior would be: π_{t}(0.2, 0.99, 0.3, 0.986). This prior has a median equal to 1.6% and IQR (Interquartile range) equal to (0.06%, 39.03%) denoting our limited knowledge on the true prevalence for dementia in Europe. Similarly, for the specificity parameter S_{p} ∼Beta(25,3.5) is elicited, while for the sensitivity parameter S_{e} ∼Beta(25.6,1.4) is elicited based on the user inputs on the tPRiors “Prior(s)” page. The tPRiors shiny application input for the sensitivity and specificity priors would be: S_{e}(0.88, 0.80, 0.90)  S_{p}(0.95, 0.85, 0.97)]. The sensitivity prior implies a prior median value of 0.88 (IQR: 0.85, 0.92)and the specificity prior implies a prior median value of 0.95 (IQR: 0.93, 0.98).
Analysis and report
Regarding our multiplepopulation motivating example, after running the analysis with the defined priors, settings and uploaded datasets, the following statistics are reported by the tPRiors application. The reported probability that the posterior true prevalence would be higher than 0.05 was equal to 1. The prevalence posterior mean equals to 18.5% which is larger than the original pooled estimate of the Bacigalupo et al. review and may imply less modelled heterogeneity and thus larger weights on Mathillas et al (6) and Lucca et al (9) studies. In comparison with the simple apparent prevalence estimates, the lower studies’ prevalence shrunk towards zero, while study 6 and 9 showed an increase in prevalence when accounting for imperfect testing, a behaviour that is partially explained by the test’s low specificity. In this example, we did not model the probability of zero prevalence as we assumed that the dementia prevalence would not be zero in the age groups studied.
Single population illustrative example
In this section we reanalyse a single population toy example to reproduce a previously published analysis from Spreybroek et al. [5]. In their example, for simplicity the authors have assumed a sample size of 500 with two assumed apparent prevalences, one equal to 24% that corresponds to a number of positives equal to 120 and one equal to 5% that corresponds to a number of positives equal to 25. Spreybroek et al. considered two Bayesian models. They have assumed either 1) a fixed value for the sensitivity (S_{e}=0.80) and specificity parameter S_{p}=0.90), or 2) a uniform distribution for the two parameters S_{e}∼Unif(0.7,0.9) and S_{p}∼Unif(0.85,0.95). We partially adopt their assumptions by setting Beta distributions on prior parameters with mean test sensitivity equal to 80% and mean test specificity equal to 90%, while avoiding the use of fixed values (Table 2). As prior probability for the true prevalence we elicit a a) π_{t}∼Beta(1,1), denoting Setup A and a b) π_{t}∼Beta(1.3,1.3), denoting Setup B. Both setups express our belief that, before observing the data all values are likely or almost equally likely possible for the true prevalence. In setup A we assume that the mean value of the true prevalence equals 0.5 and it is uniformly distributed around this value. The π_{t}∼Beta(1.3,1.3), prior distribution on the true prevalence of Setup B has a mean value of 0.5 (95% CrI 0.28,0.72). The tPRiors application shiny input for setup A would be: [ π_{t}(0.5, 0.05, 0.95)  S_{e}(0.8, 0.75, 0.97)  S_{p}(0.9, 0.85, 0.97)]. Setup B places slightly smaller weight in prior true prevalence values close to 0/1, a plausible assumption as we expect that the prevalence would neither be very small nor very large. The tPRiors application shiny input for setup B would be: [ π_{t}(0.5, 0.08, 0.95)  S_{e}(0.8, 0.75, 0.97)  S_{p}(0.9, 0.85, 0.97)]. For the sensitivity and specificity parameters in all scenarios we assume a mean value of 0.8 and 0.9 with a 97% probability that the mean values are higher than 0.75 and 0.85 respectively. Therefore, both Setup A and Setup B place the same prior on the sensitivity (0.8, CrI: 0.78, 0.82) and the same prior on the specificity (0.9, CrI: 0.88, 0.92). For both setup A and setup B, the user is able to impose a nonzero prevalence prior, if the prior probability of this prior is low, posterior inference would set additional density weight on zero. Let us assume that when nonzero true prevalence is selected, the tPRiors application shiny input for the nonzero true prevalence alternative could be: [ w(0.2, 0.1, 0.95)], meaning that based on the available literature the mean value for nonzero prevalence probability is expected to be equal to 0.2 and we can be 95% sure that it is higher than 0.1.
Analysis and report
As depicted in Fig. 3(AB), the posterior distribution of true prevalence points toward a lower prevalence than the apparent prevalence. Table 2 presents the toy example results of the original study [5] and the results produced by the tPRiors webbased application. The posterior mean of the original manuscript and the webbased application are very similar. Some discrepancies are observed on the width of the 95% credible intervals. More specifically, the tPRiors Setup A results in intervals (e.g. 24%: CrI (0.13, 0.27)) that lie between the two intervals produced by the original manuscript model 1 (24%: CrI (0.15, 0.25)) and model 2 (24%: CrI (0.11, 0.29)) Table 2]. This result is sensible as our prior assumptions are more relaxed than model 1 but more concentrated than the original model 2 prior distributions in Speybroeck et al. [5]. Finally, regarding the zeroprevalence prior alternative, Setup A, when assuming that the apparent prevalence equals to 5%, the analysis results in posterior mean true prevalence equal to 0.010 (95% CrI: 0.001, 0.032), while when assuming that the apparent prevalence equals to 24%, the analysis results in posterior mean true prevalence equal to 0.1988 (95% CrI: 0.1120, 0.2745). These values should be interpreted with caution, as the resulting posterior distribution is expected to have two peaks as expected and as it can be seen in the tPRiors ’Report’ page.
Discussion
In this manuscript, we introduced tPRiors, a newly implemented webbased application for the calculation of prevalence based on prior information. During recent years such webbased applications have gained considerate popularity, as they are able to streamline and replicate otherwise complex analyses. Several similar applications are available in different areas of medical research and epidemiology as online tools or as statistical packages such as: i) IWA, an application that implemented full hierarchical model for prevalence estimation [11], ii) IPDmada an application that performs individual patient data metaanalysis [18], iii) covid19tracker, an application that visualizes data from 20192020 covid pandemic [19] or iv) shinyCircos for visualizing genomic data [20]. To our knowledge, tPRiors is the first application that incorporates elicited prior knowledge, transform the latter into prior distributions and calculated posterior inferences for a variety of single and multiple population prevalence models. tPRiors makes the development and implementation of prevalence Bayesian inferences less cumbersome for researchers with or without strong statistical knowledge. Besides the basic Bayesian inference provided in tPRiors, an important function of such a webbased application is the interactive setting of the prior distributions on the relevant parameters, which can aid researchers towards prior elicitation in a natural and visual way.
Currently, four core models are incorporated in the webapplication and “infinite” variations of these basic models can be constructed given input from the user, though, more models may be applied in practice. tPRiors has been developed as a framework that could encompass more models in the near future, either through a further systematic search or through alternative approaches researched from within our group, in an updated version of this webapplication. No comparisons between approaches were performed, hence, interested readers are prompted to read the manuscripts that introduced or critically discussed these models [1,2,5]. To aid researchers, we provide templates/preloaded multiple population datasets, as multiple population data should be uploaded in a specific format. No specific analyses for missing outcome data is currently incorporated, Bayesian inference, however, lends itself to accounting for missing outcome data via proper assumptions. Such considerations were out of scope but can be readily incorporated in the current models. Finally, tPRiors implements modelling with and without assuming a mixture distributions that allow for zero true infection prevalences. We should note that, especially in populations with low or zero prevalence, even though simpler models may be more intuitive, if mixture models for prevalences are not applied, posterior inferences might be artificially inflated. In practice, we should note that the multiple population models perform more robustly when more than eight clusters are considered.
Conclusions
The application of tPRiors is expected to aid standardization of practices in the field of Bayesian modelling on subject and multiple groupbased true prevalence estimation. We further believe that tPRiors will help towards the increase of popularity of the aforementioned methods among practitioners and researchers in the public health sector. Although,  tPRiors  aims to aid researchers to perform Bayesian analysis with ease, we recommend at least one statistician to be part of the research team when such analyses are formally conducted.
Highlights

1. tPRiors is a new webbased tool for conducting Bayesian inference of crosssectional sampling via the use of single or multiple population diagnostic tests results.

2. tPRiors is a free tool, available for all researchers/practitioners and it does not require advanced knowledge or installation of any statistical software (i.e. R, SAS, SPSS).

3. tPRiors is designed to guide the user to the final analysis via the use of simple questions, leading to a printable final report.

4. Development of tPRiors will increase the quality of calculation and reporting of (true) prevalence studies.
Availability and requirements
Project name: tPRiors
Project home page:https://publicandonehealth.shinyapps.io/tPRiors/ and https://github.com/kpatera/tPRiors, publicly released [21]
Operating system(s): Platform independent
Programming language: R / Shiny
Other requirements: Firefox >v96 or another internet browser
License: GNU GPL v3.0
Any restrictions to use by nonacademics: License needed
Availability of data and materials
All datasets exploited in this manuscript can be found online in the corresponding tPRiors application specific single or multiple population pages [21].
Notes
Do you have single or multiple populations/clusters? Multiple, Do you want to model the true or the apparent prevalence? ? True prevalence, Do you want to account for zero true prevalence? No, Would you specify informative priors? Yes
Abbreviations
 DSM:

Diagnostic and statistical manual of mental disorders
 IQR:

Interquartile range
 CrI:

Credible interval
 FAQ:

Frequently asked questions
 MCMC:

Markov chain Monte Carlo
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Acknowledgments
The Shiny web application participated in the 3rd annual Shiny Contest 2021. The authors would like to thank two anonymous reviewers for considerably improving the manuscript/web application and Eleftherios Meletis for performing a thorough test of the tPRiors shiny application.
Funding
The authors would like to acknowledge financial support from the European Commission, H2020 Health Grant no 101016216, unCoVer  Unravelling data for rapid evidencebased response to COVID19. The funding body played no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.
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KP and PK contributed equally. PK contributed to the concept. KP designed and developed the Shiny web application. KP and PK generated data and tested the application. KP drafted the manuscript. PK critically, under the reviewed the manuscript. Both authors further revised the design of the tPriors application. The authors read and approved the final manuscript.
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Pateras, K., Kostoulas, P. tPRiors : a tool for prior elicitation and obtaining posterior distributions of true disease prevalence. BMC Med Res Methodol 22, 91 (2022). https://doi.org/10.1186/s12874022015571
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DOI: https://doi.org/10.1186/s12874022015571