# Sensitivity And Specificity Example Questions Pdf

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*Peter J.*

- Disease Screening - Statistics Teaching Tools
- Estimating Prevalence Using an Imperfect Test
- Understanding and using sensitivity, specificity and predictive values
- Remembering the meanings of sensitivity, specificity, and predictive values

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## Disease Screening - Statistics Teaching Tools

Peter J. The standard estimate of prevalence is the proportion of positive results obtained from the application of a diagnostic test to a random sample of individuals drawn from the population of interest.

When the diagnostic test is imperfect, this estimate is biased. We give simple formulae, previously described by Greenland for correcting the bias and for calculating confidence intervals for the prevalence when the sensitivity and specificity of the test are known. We suggest a Bayesian method for constructing credible intervals for the prevalence when sensitivity and specificity are unknown. We provide R code to implement the method.

The prevalence , , of a disease is the proportion of subjects in the population of interest who have the disease in question [ 1 , page 46]. A standard way to estimate prevalence is to apply a diagnostic test to a random sample of individuals and use the estimator where is the number of individuals who test positive.

An imperfect test is one for which at least one of and is less than one. An imperfect test may give either or both of a false positive or a false negative result, with respective probabilities and. A similar issue arises in individual diagnostic testing.

In that context, prevalence is assumed to be known and the objective is to make a diagnosis for each subject tested. Important quantities are then the positive and negative predictive values , defined as the conditional probabilities that a subject does or does not have the disease in question, given that they show a positive or negative test result, respectively. Even when both and are close to one, the positive and negative predictive values of a diagnostic test depend critically on the true prevalence of the disease in the population being tested.

In particular, for a rare disease, the positive predictive value can be much smaller than either or. Suppose that an imperfect test is applied to a random sample of subjects, of whom give a positive result. The standard estimator given by 1 is now biased for. Let denote the expectation of. Then, the relationship between and is linear, and given by [ 2 ]. Under the reasonable assumption that , that is, that the test is superior to the toss of a coin and is an increasing function of.

It follows that if the values of and are known a confidence interval, say, for can be converted straightforwardly to a confidence interval for by applying the pair of transformations See Figure 1 for an illustration.

Typically, when the true prevalence is low, and the effect of the bias correction is to shift the interval estimate of prevalence towards lower values. For example, if and , then. As the true prevalence increases, the relative difference between and decreases; for example, if as before but now , then. If and are unknown, can still be estimated, albeit with reduced precision, using a Bayesian approach. This requires us to specify a prior distribution for and informative prior distributions for and informative, because the data give essentially no information about or.

Assume temporarily that and are both known. The sampling distribution of , the number of positive test results out of individuals tested, given is binomial, with number of trials and probability of a positive outcome , where and.

A convenient, uninformative prior for is the uniform distribution on. The marginal distribution of is then obtained as where is the incomplete beta function. The posterior distribution for given and follows as where is given by 4. Finally, to allow for the uncertainty in and , we substitute and on the right-hand-side of 6 and integrate with respect to the joint prior, say, for and , to give the posterior distribution for as. Suppose that we sample individuals, of whom give positive results.

The uncorrected estimate of prevalence 1 is 0. We now assume that and are unknown and specify independent beta prior distributions, each with parameters but scaled to lie in the interval ; hence, the prior for each of and is unimodal wit prior expectation 0. This is much closer to the classical confidence interval, which is as expected since we have specified an uninformative prior for.

Figure 2 shows the posterior distributions for assuming known or unknown and. The greater spread of the latter represents the loss of precision that results from not knowing the sensitivity and specificity of the test.

When both and are close to one, the absolute bias of the uncorrected estimator defined in 1 is small but the relative bias may still be substantial. An example is the use by the African Programme for Onchocerciasis Control of a questionnaire-based assessment of community-level prevalence of Loa loa in place of the more accurate, but also more expensive and invasive, finger-prick blood-sampling and microscopic detection of microfilariae [ 3 ].

Exactly the same argument would apply to the estimation of prevalence in more complex settings. For example, where prevalence is modelled as a function of explanatory variables, say , an interval estimate for can be calculated at each value of by applying 3 to the corresponding interval estimate of. R function for Bayesian estimation of prevalence using an imperfect test. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Special Issues. Academic Editor: Leo J. Received 18 Jun Accepted 02 Aug Published 23 Oct Abstract The standard estimate of prevalence is the proportion of positive results obtained from the application of a diagnostic test to a random sample of individuals drawn from the population of interest. Introduction The prevalence , , of a disease is the proportion of subjects in the population of interest who have the disease in question [ 1 , page 46].

Estimation of Prevalence Suppose that an imperfect test is applied to a random sample of subjects, of whom give a positive result. Figure 1. Converting an interval estimate of , the probability of a positive test result, into an interval estimate of , the true prevalence, for a test with sensitivity 0.

The vertical and horizontal arrows denote the interval estimates of and , respectively. Figure 2. Posterior distributions of prevalence for a sample of individuals of whom 20 tested positive, using a test with a known sensitivity and specificity each equal to 0. Algorithm 1. References K. Rothman, S. Greenland, and T. View at: Google Scholar I. Takougang, M. Meremikwu, S. Wandji et al. View at: Google Scholar P. Smith and R. More related articles.

Download other formats More. Related articles. R function for Bayesian estimation of prevalence using an. Prior for prevalence is uniform on 0,1. Priors for sensitivity and specificity are independent scaled. Function uses a simple quadrature algorithm with number of. T: number of positive test results.

## Estimating Prevalence Using an Imperfect Test

The table below shows the results from looking at the diagnostic accuracy of a new rapid test for HIV in , subjects, compared to the Reference standard ELISA test. The rows of the table represent the test result and the columns the true disease status as confirmed by ELISA. Please remember to click the Submit button for each separate question, and read the feedback comments! What is the Sensitivity of the new rapid test for HIV? Report the answer to 3 decimal places. The answer is 0.

Statistics for Bioengineering Sciences pp Cite as. This chapter introduces several notions fundamental for disease or device testing. Unable to display preview. Download preview PDF. Skip to main content.

Margaret, Pittsburgh, Pa. The 2 x 2 tables from which these terms are derived are familiar to some physicians Table. Sensitivity and specificity are fixed for a particular type of test. For example, though current screening tests for HIV have high sensitivity and specificity, the low prevalence of HIV in the general population cannot justify universal screening since the majority of positive tests would be falsely positive ie, low PPV. Begin by assuming that you have 4 patients.

## Understanding and using sensitivity, specificity and predictive values

Example: Cascell's Problem. We want to know how likely it is that the individual with a positive test result will actually suffer from the disease. In other words, we want to know the positive predictive value of the test:. It is important to be able to quantify how a test result increases the diagnostic ability of a test i.

Screening refers to the application of a medical procedure or test to people who as yet have no symptoms of a particular disease, for the purpose of determining their likelihood of having the disease. The screening procedure itself does not diagnose the illness. Those who have a positive result from the screening test will need further evaluation with subsequent diagnostic tests or procedures.

RIS file. Properties of diagnostic tests have traditionally been described using sensitivity, specificity, and positive and negative predictive values. These measures, however, reflect population characteristics and do not easily translate to individual patients.

### Remembering the meanings of sensitivity, specificity, and predictive values

In this article, we have discussed the basic knowledge to calculate sensitivity, specificity, positive predictive value and negative predictive value. We have discussed the advantage and limitations of these measures and have provided how we should use these measures in our day-to-day clinical practice. We also have illustrated how to calculate sensitivity and specificity while combining two tests and how to use these results for our patients in day-to-day practice. Modern ophthalmology has experienced a dramatic increase in knowledge and an exponential increase in technology. Regrettably, there is sometimes a tendency to use tests just because they are available; or because they are hi-tech. The basic idea of performing a diagnostic test is to increase or decrease our suspicion that a patient has a particular disease, to the extent that we can make management decisions. This includes assessing symptoms and signs, as well as what we conventionally refer to as tests: such as laboratory investigations, gonioscopy, Optical Coherence Tomography OCT , etc.

Within the context of screening tests, it is important to avoid misconceptions about sensitivity, specificity, and predictive values. In this article, therefore, foundations are first established concerning these metrics along with the first of several aspects of pliability that should be recognized in relation to those metrics. Clarification is then provided about the definitions of sensitivity, specificity, and predictive values and why researchers and clinicians can misunderstand and misrepresent them.

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## 1 Comments

Erica G.Assessment of test effectiveness. Is the test valid? • Sensitivity. • Specificity HST AOCOPM. Example. Screening. Test. Diastolic Hypertension. Yes.