In medicine, a diagnostic test examines whether a disease or a characteristic is present or not. Examples are tests for metabolic diseases during a new-born screening, HIV testing, or even a simple pregnancy test. Broadly speaking, there is a distinction between a screening test and a confirmatory test.
Screening tests are designed to detect early disease or the presence of risk factors in a large population of healthy individuals. Screening tests are usually simple and non-invasive thus individuals easily consent to the procedures. Their design is one of high sensitivity to make sure that potential disease is not missed. This bias towards sensitivity comes with an increase in false positives.
The confirmatory test is designed to establish the absence or presence of a disease and form the basis of diagnosis in symptomatic patients or patients who are positive of a screening test. They may be invasive and require some form of informed consent before undertaking them. These tests have a bias towards specificity rather than sensitivity thus, they have high accuracy rates in the identification of true negatives.
Statistical Quality Criteria of Diagnostic Tests
Sensitivity and specificity
The sensitivity of a diagnostic procedure gives us information as to what percentage of sufferers is actually recognized as sick by the test method. The sensitivity thus describes the “true positive results.” For example, the Ebola rapid test (ReEBOV test) by the company Corgenix (USA) has a sensitivity of almost 100%. In this sense, a patient suffering from Ebola is properly diagnosed in all cases with this test.
Image: A test should distinguish between sick and healthy people. Every person is represented by a dot which lies either to the left (ill) or to the right (healthy) of the black line. The dots in the oval are those people that have been classified as sick by the test.
Specificity indicates the probability at which a medical test method for a given disease will recognize that a healthy person is also actually healthy. With a specificity of 92%, our Ebola rapid test of 100 healthy patients detects, on average, 92 people as healthy (“true negative rate“). 8 healthy individuals are therefore erroneously diagnosed as having Ebola, even though they are healthy, and may have to endure quarantine measures as a result.
Positive predictive value
The positive predictive value is the probability of how many people, who had a positive medical test, are actually ill (right = positive). The positive predictive value is also dependent on the prevalence of the disease in the population. With a more common disease, the likelihood of actually being affected is a lot higher than with very rare diseases and a positive value.
Negative predictive value
The negative predictive value indicates how many people, whose medical test result turned out negative, are actually healthy. It also depends on the prevalence of the disease in the population.
It represents the number of times that you are more likely to have the disease. It is given by sensitivity/ (1- specificity).
Prevalence is an epidemiological measure for disease frequency. It indicates how many people are suffering from a disease during a particular period in time (period prevalence) or at a particular date in time (point prevalence). The value refers to a sample that is generalized extrapolated to the population or to actual numbers.
While relatively accurate data is available for notifiable diseases, others can only be representatively “extrapolated” through sampling. The prevalence thus describes a current state: how many people in 2015, for example, suffer from AIDS, regardless of when they came down with the disease.
Incidence refers to the rate of new cases of the disease which is usually reported as number of new cases of the disease occurring within a period of time (per month or per year).
It is also reported as the fraction of the population that is at risk of developing the disease i.e. per 100,000 or per 1,000,000 of the population.
The Fourfold Contingency Table
The fourfold contingency table combines the just mentioned test quality criteria in one model, and you will encounter it often as a medical student. In general and social medicine, you may find yourself in the situation of having to calculate the positive predictive value or sensitivity.
If the meaning of the parameters is clear, the calculation is actually quite simple. If you have given values for the quality criteria of certain tests, you can illustrate the ratios of the parameters based on numerical examples.
|Positive Test||Negative Test||Total Test Results||Calculation|
|Sick||a (true positive)||b (false negative)||a + b (all sufferers)||Sensitivity = a / (a + b)|
|Healthy||c (false positive)||d (true negative)||c + d (all healthy)||Specificity = d / (c + d)|
|Total Persons||a + c (all positive tests)||b + d (all negative tests)|
|Calculation||Positive predictive value = a / (a + c)||Negative predictive value = d / (b + d)|
Example: Suppose that 7% of the population in an affected area (this is freely chosen, as there are no reliable numbers regarding this) is suffering from Ebola and we are testing all the people in our small clinic. Altogether, 1,000 people are examined with the Ebola-rapid test in order to detect outbreaks early and be able to isolate the affected persons.
|Positive test||Negative test||Total Test Results||Calculation|
|Sick||70||0||70 (7% prevalence)||Sensitivity = 100%|
|Healthy||65||865||930 (100 – 7 = 93% Healthy)||Specificity = 92%|
|Total Persons||135||865||1.000 (tested persons)|
|Calculation||Positive predictive value = 0,52||Negative predictive value = 1|
Out of 1,000 tested persons, 70 people (7%) are actually infected by the virus and their test is positive. Because of the lower specificity of the rapid test, 65 of the healthy 930 people also get a positive Ebola test result. Out of a total of 135 Ebola tests with a positive result, almost half, 65 people in our hospital, will have been diagnosed with a false positive and had to be treated for safety reasons and put in isolation. Despite the apparently high values, the chance to be truly suffering from Ebola with a positive test result, in our example, is only 52%!
Such considerations become important in the medical profession in the case of well-known screening tests, such as mammography for breast cancer or the PSA level determination for prostate cancer prevention. A false positive test may result in uncertainty and invasive diagnosis for the patient, therefore, it is useful to be able to deal with test results and probabilities in order to optimally inform patients and to plan further diagnosis and treatment steps.
Other Statistical Values
Incidence is the number of new cases in a defined period of time. This is usually specified as the number of new cases/100,000 inhabitants and is called the incidence rate.
The pretest probability indicates how likely a test will yield a positive result; therefore, it is dependent on the prevalence. For example, the pretest probability for our Ebola rapid test is much lower in East Africa than Sierra Leone due to a much lower prevalence.
A true “descriptive study” is an example of “descriptive epidemiology”.
- Your neighborhood
- Right now
Right now, 23 % of students in your neighborhood are left handed.
Historic Triumphs: Smallpox
The global eradication of smallpox was certified, based on intense verification activities in countries, by a commission of eminent scientists on 9 December 1979 and subsequently endorsed by the World Health Assembly on 8 May 1980 – “Resolution WHA 33.3”
In 1975, two-year-old Rahima Banu contracted last known case of naturally-occurring variola major Smallpox. (Source: Wikipedia)
Global eradication was possible because of herd immunity.
- 400,000 people died each year
- 1/3 of the survivors became blind
- Survivors also developed immunity to smallpox
- Edward Jenner took interest in cowpox to find solutions in the prevention of smallpox
- Effort to prevent smallpox
- WHO began the eradication program
- 15 million people developed smallpox annually
- 2 million people died
- WHO and eradication of smallpox
At a Glance: Statistical Principles
- Sensitivity: How many sufferers are “true positive” and considered truly ill?
- Specificity: How many healthy people are considered “true negative” (healthy) by the test?
- Positive predictive value: Positive test result and truly ill.
- Negative predictive value: Negative test result and truly healthy.
- Prevalence: How many people are suffering from a particular disease in the XY time period?
- Incidence: How many people fall ill from a particular disease during the XY period?
- Pretest probability: How likely is the test to be positive? Prevalence – influence!
Popular Exam Questions on Statistical Principles in Epidemiology and General Medicine
The answers are listed below the references.
1. Out of 100,000 inhabitants, 346 people are suffering from a particular disease in 2014 in Germany. This number statistically corresponds to…
- …the positive predictive value.
- …the incidence rate.
- …the negative predictive value.
- …the sensitivity.
2. Which statistical parameter corresponds to the number of true positive test results?
- Positive predictive value.
- Negative predictive value.
- None of the above.
3. Prevalence is a parameter for…
- …incidence rate.
- …mortality rate.
- …birth rate.
- …disease frequency.
- …probability of a positive test result.