Diagnostic Testing in this COVID-19 Pandemic Explained with Bayes’ Rule
The COVID-19 pandemic stirred worldwide unrest because of the rapid spread of an unknown and deadly virus. Every day, we would see the news regarding the accelerated increase in infected individuals and the accompanying death rate.
To fight off such a novel respiratory disease, authorities and health workers test potentially infected individuals to know which needs to be quarantined and treated. Unfortunately, the diagnostic testing we currently use is not sufficiently accurate in identifying infection by coronavirus.
Testing errors resulting from diagnostic testing, such as false negatives, significantly hinder containment measures. As a result, health authorities inadvertently release infectious people, leading to a broader spread of the disease.
So, the diagnostic testing in COVID-19 features more than the mere positive or negative that we receive after getting tested. Hence, public health and authorities must understand the probability of individuals being infected or uninfected. And one model that we can rely on is Bayes Rule.
Defining the Problem
The Sars-Cov-2 pandemic is characterized by the rapid spread of a respiratory infection often manifested by shortness of breath, high fever, weakness, and other respiratory symptoms. Additionally, healthcare professionals employ different diagnostic testing methods to identify COVID-19 patients.
However, since the outbreak started, the containment methods enforced by authorities proved to be ineffective as we still see a steep increase in the number of daily infected patients and death rates.
From the authorities’ perspective, containment of the virus is the priority. Therefore, seeing a doctor for a COVID-19 positive patient, will not be as straightforward as getting treated immediately. According to authorities, containment of the virus takes precedence.
Containment is possible by asking infected individuals to be quarantined for the benefit of the general public. However, if health authorities wrongly ask someone uninfected to quarantine due to false-positive results, this will be an inefficient use of funds and resources.
A counterproductive act of authorities releasing infected undiagnosed individuals will cause further spread of the virus and put more public at risk. This policy is problematic because wide-scale outbreaks are likely if most authorities commit this mistake. Moreover, contact tracing and severe infections are more challenging to manage.
COVID-19 Diagnosis
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Given the need to prevent outbreaks and minimize errors in subjecting individuals to quarantine, accurate disease diagnosis becomes the top priority. Unfortunately, numerous studies illustrate how difficult it is to confirm the disease accurately. And we will attempt to clarify this below.
Diagnosis of the COVID-19 disease begins with asking for the patient’s travel history and initial assessment based on existing symptoms. Individuals working on the frontlines or traveling from high-risk areas are the most susceptible to being infected because of their contact.
Laboratory testing is then employed. Currently, we employ different methods using various samples from the patients. Some use saliva samples, blood samples, or nasal and oral swabs. The RT-PCR test, chest CT imaging scan, and numerical laboratory tests are three different diagnosis methodologies.
The currently accepted gold standard for identifying those infected with the disease is the reverse-transcription polymerase chain reaction method or RT-PCR test. However, the accuracy of the results received by the tested individuals is not absolute. The existing data from studies revealed that more than a third of the infected individuals might have a negative result. Hence, they would continue with their regular lives without undergoing quarantine. After a few days from obtaining their negative test result, these individuals may develop symptoms. The false sense of security from their false negative result will lead to behavior that promotes the spreading of the COVID-19 virus.
Both antigen and RT-PCR tests produce a false negative result when a swab sample does not have enough viral load to elicit the chemical reaction in the laboratory. It can either be due to the manner of swabbing or some biological influences from the individual. It may also be due to an error committed by the medical practitioner while processing the sample in the laboratory.
On the other hand, false positives may also occur. For example, a healthy individual may wrongly get a positive result after their RT-PCR tests. Such false positives can be due to contamination of swab samples or errors in processing in the laboratory.
Although the above examples show how currently available COVID-19 diagnostic tests are imperfect, it is essential to stress the importance of the diagnostic test to identify the disease.
Application of the Diagnostic Test Results In Medical Intervention
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Doctors ask for diagnostic test results to help decide if treatment or quarantine is necessary.
Medical professionals must be confident in the result of the RT-PCR test to have an accurate diagnosis and treatment plan. Unfortunately, they may still commit errors, such as prescribing treatment to non-infected individuals or not giving treatment to infected individuals.
The Feature Correlated Naïve Bayes (FCNB) Classification Strategy
Naïve Bayes is a well-used classifier in weather forecasting, bioinformatics, and even medical diagnosis. When looking at this strategy along with understanding the rapid growth of the COVID-19 outbreaks, detecting the virus remains the priority. Aside from being accurate, punctual detection using diagnostic tests is essential. The Feature Correlated Naïve Bayes strategy, or FCNB, improves the traditional Naïve Bayes system by grouping the important features we need to look at to help medical practitioners arrive at accurate assessments. The primary job of the FCNB is to tell us the diagnosis of whether someone is COVID-19 positive or not.
COVID-19 Outbreak and Unreliable Tests
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Many researchers believe that the diagnostic tests commonly used to identify COVID-19 cases are unreliable because they have very low sensitivity to the virus. Researchers even noted that patients with the disease are only positive for around 30% to 50% of the testing attempts. Low sensitivity diagnostic tests become unreliable because the chances of getting a positive result for an infected individual are too low.
Researchers also confirmed that subjecting the suspected infected individuals to multiple tests gives more confidence to the healthcare personnel in terms of the reliability of the results obtained. Unfortunately, not all facilities have the luxury of providing such options due to a lack of quarantine areas or financial resources.
Unreliable diagnostic tests hinder the containment of COVID-19 cases. So, authorities have initially enforced a large-scale containment plan assuming that every suspected individual is infected.
Initial Assessment of a Patient
Before proceeding to diagnostic testing, patients are assessed based on several hints in their history that would make us suspect they have the COVID-19 infection. The difference in patients’ locations is one thing to consider. The infection rate is higher in certain epicenters where COVID-19 infections oversaturate the area. Hence, people from those areas are more likely to be infected. In addition, social contacts from those infected are also more likely to contract the disease.
The COVID-19 disease has a generic set of symptoms associated with other common respiratory illnesses. Currently,the characteristic symptoms to look out for are fever, cough, and shortness of breath. Lastly, doctors also ask for radiographic imaging done because the virus manifests in the lungs of infected patients.
Unfortunately, not every clue is assessed in suspected individuals. For example, airports only record the traveler’s temperature and travel history. Doctors can also fail to link the different hints in patient assessment and not request further diagnostic testing. More complex cases are asymptomatic patients where no clues are present at all.
Diagnostic Testing: Probability and Statistics
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After the initial patient assessment, medical professionals should have gathered enough information to suspect the patient’s COVID-19 disease. A diagnostic test result will then confirm the suspicion.
As we talked about earlier, different diagnostic methodologies are available. These look for the presence of the virus from body samples like saliva, nasal swabs, and the like. However, because we usually learn that science is a reliable field, people often fall into a misleading trap.
Even healthcare personnel may commit these incorrect interpretations. Hence, the below-perfect-reliability diagnostic testing and misinformed interpretation of the results lead to poor responses in managing the virus containment. Thus, there needs to be a deeper understanding of the probability of diagnostic testing. One way to solve this is to look into the problem with Bayesian probability.
Bayes’ Rule Applied in Unreliable Testing and Inefficient Containment of COVID-19
Being confident in claiming that an individual does not have the coronavirus disease can be seen through the perspective of Bayes’ theorem. Other statistical tests rely on the negative predictive value. This value refers to the chances of an individual being utterly free from the disease even after testing negative for it. However, the negative predictive value is unreliable because it is calculated based on the prevalence of COVID-19. Because of the rapid infection rates, the prevalence of COVID-19 remains high and alters the values obtained from testings.
In contrast, the negative likelihood ratio used in Bayes’ rule interprets a test result without considering the prevalence of the disease, unlike the other statistical tests, which use negative predictive value. In other words, to apply Bayes’ rule, we categorize results in terms of post-test probabilities instead of strictly classifying them as positives and negatives. For example, suppose you got a negative result and have not considered the post-test probability. The doctors’ response to the scenario is severely affected as there is a higher chance of committing an error. The correct containment process and treatment rendered will not always be appropriate for the case. Because the Bayes’ rule reveals the danger in false negatives and false positives — a negative result is never 100% conclusively negative, and a positive result is never 100% conclusively positive.
Misconceptions about Diagnostic Test Results
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First, we are informed that a positive diagnostic test result always means that you have the virus, while a negative means you are free from it. However, this is not 100% true because test reliability is not perfect.
Misleading results can be due to having minimally detectable viral load during the early stages of the illness, having the virus at deep locations in the body which was not swabbed, or sample contamination.
Testing kit manufacturers are aware of the shortcomings of their products. So, they specify the reliability of their tests on their product labels. Let us suppose that a company has a 90% accurate test kit. A common mistake from this is wrongly interpreting the probability. A common incorrect interpretation is that a 90% accurate test refers to having a 90% chance of having the virus if you have a positive result. Similarly, you have a 90% chance of not being infected if you have a negative result. These misconceptions about diagnostic test results bring more errors on treatment planning from the healthcare workers’ end.
Diagnostic Test Results According to Bayesian Probability
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We have noted several misconceptions about diagnostic testing and highlighted the need to evaluate them better. The Bayesian probability is an applicable theorem for a better understanding of the COVID-19 diagnostic test results.
This probability, is best explained in a mathematical formula to see the relationship between the factors involved. Essentially, the Bayes’ rule looks into the existing probability of a test and incorporates new ideas for an updated interpretation. For example, considering Bayes’ rule, the doctor will encounter two new unknown instances: the probability of a positive result from an infected patient and a positive result from a non-infected patient.
The sensitivity of a diagnostic test refers to the probability of getting a positive result after being infected. We can look at this so that the test is sensitive to the virus in the sample and would hence detect it. On the other hand, specificity is the other end of the discussion where it is the chance of having a negative test result in non-infected individuals.
To apply this rule, let us use it in a situation where eight people tested for coronavirus turned out negative and six other people came out positive with the disease. According to Bayes’ rule, since diagnostic testing is not 100% sensitive and specific, only four out of the six truly have COVID.
The nature of the tests makes it impossible to efficiently contain the disease because doctors fail to pinpoint who is infected accurately. Hence, quarantine and treatment to supposed infected individuals are often extended to those who do not need it.
Decisions Must Minimize Uncertainty and Must Take Acceptable Risks
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The COVID-19 outbreaks will continue to be a pressing problem because numerous factors remain unable to provide the most accurate means of determining who must quarantine, who needs to undergo treatment, and who may resume their regular lives.
We have emphasized that tests for COVID-19, even the RT-PCR, which is the gold standard, remain unreliable because of the prevalence of false negatives and false positives. Hopefully, we could achieve a more reliable means of testing potential coronavirus patients to cut down the unreliable factor to as little as 5%.
Given what we have now, unreliable and imperfect tests help doctors and practitioners decide what to do. However, decisions will still be fraught with uncertainty because an unreliable diagnosis inevitably leads to the wrong management.
There is only a certain level of acceptable risk that practitioners must be willing to take. Therefore, before taking further action on a patient, the doctor must know the risks and calculate which decisions yield the least risky treatment plan.
Acceptable risks include mild conditions and those which are not life-threatening. Similarly, healthcare providers must consider if the threat permanently affects the patient. If long-term health issues are absent, the risk is acceptable.
Also, the risk is acceptable if the benefit of getting treatment is more important. For example, if the harm of not having any treatment is more threatening than having any treatment, then the risk of undergoing treatment is acceptable.
On the other hand, we must avoid unacceptable risks. Namely, we must reconsider extreme treatment with expected harmful and irreversible side effects.
What Happens When Decisions are Made Without Reliable Diagnostic Tests
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Ideally, our medical world would have 100% reliable tests. But given that it does not exist yet to identify the coronavirus disease, we need to work on the uncertainty of diagnostic tests. Doctors can base their decisions on existing realistic values to work with unreliable diagnostic test results.
We aim to utilize values that are as realistic as possible. For instance, the specificity of many flu tests is about 90–95%. The sensitivity of these tests is roughly around 40%. This comes close to the sensitivity reported for COVID-19 coronavirus testing.
Assume a patient resides in a region where a coronavirus epidemic recently occurred and is now coming to a medical clinic with coronavirus symptoms. If it is determined that the patient has a 50% chance of contracting COVID-19 and is believed to likely contract the virus, several scenarios can happen.
First, the positive result from the diagnostic test can lead to an 80% chance of having a coronavirus infection. If a negative result is obtained, the probability of having the disease drops to 40%. Unfortunately, having a 40% chance of having the illness despite being negative is still relatively high. In this case, errors made in deciding what to do may be harmful to both the patient and the disease management in the community.
Regardless of a positive or negative result, a patient’s risk of infection cannot be decreased to an acceptable level by a single inaccurate test.
Avoid Deciding for Epidemic Management Without Reliable Diagnostic Tests
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The coronavirus pandemic has been going on for quite a long time already. The pandemic has not reached its endemic stage yet despite authorities’ efforts. Given the modern technology and medicine that we have now, it is still not over as researchers are still identifying more virus variants.
Furthermore, we can also associate the problem with the poor decision-making done by practitioners and the authorities. Decision-making based on unreliable tests which cannot rule out infected from uninfected will yield inadequate pandemic responses.
Consider a situation where people are isolated until authorities are confident they are free from the coronavirus. If the test is not accurate, it will fail to verify the presence or absence of the infection. In other words, the test has no bearing on decision-making because the patient will remain in quarantine anyway.
The healthcare field can easily fall into the trap of committing mistakes one after the other. There are still confusion and misconceptions about the results of the tests — a disappointing reality faced by the healthcare field every day.
COVID-19 is very infectious and fatal. Therefore, doctors can only tolerate a small amount of risk to ensure that the patients get the best treatment they need. For example, practitioners got confused with an unreliable test for a trustworthy one. Because they thought the test was reliable, their initial perception of 50% likelihood would decrease to an actual 40% probability of infection, but it would be 2% in their minds. If they proceeded to discharge the patient, the repercussions might be severe. Some unwanted consequences would be the further spread of the infection into the community, failure to get punctual treatment, or even cause severe illness and death.
The limitations highlighted above underline the importance of authorities and the medical world to base their protocols on scientific evidence. Doctors need to be confident about what their technology can and cannot do. Current literature now emphasizes the need to do multiple tests to boost the reliability of diagnostic testing results for COVID-19.
A prudent doctor knows the unreliability of existing COVID-19 tests. Hence, they would know that a single negative result from one test is insufficient in convincing them that it is not a false-negative result. The doctor would then offer multiple tests or consideration of post-test probability as noted in Bayes’ rule.
There is a limit to how many negative test results from multiple diagnostic tests can convince the prudent doctor of an accurate non-infected individual. Assume that if the chance of infection decreases to less than 5%, the doctor will be confident that there is no infection.
A doctor estimates that a patient has a 50% chance of having COVID-19 after a clinical assessment. However, he recognizes that the diagnostic test is unreliable, with a sensitivity of 40% and a specificity of 90%, so he orders a battery of tests.
In Conclusion
The current medical world commits the mistake of falling into the Bayesian trap where they face the probability of something that may or may not occur. And it is not easy to point it out immediately because the means that we have to help us diagnose the disease remains unreliable.
We can best manage the COVID-19 outbreaks with a deeper understanding of the meaning of diagnostic test results and their unreliable initial results. For healthcare practitioners, it is best to be updated on the best diagnostic testing procedures and what protocols to follow to assure top-notch decision-making. You can get in touch with Hyfe, explore our Hyfe app. This piece of software allows your patients to own their conditions and help you track your patient’s cough efficiently and effectively. The Hyfe App can nicely complement current testing and better help you to characterize the post-test probabilities that would help you and your institution get out of the Bayesian trap. Accurate diagnosis is the key to helping you and your patients recover from the virus, contain the disease, and move closer to concluding the pandemic.
