Test Test Test ? A glimpse into the screening and diagnostic tests' world

Today I will like to discuss about the most popular phrase in the current COVID 19 situation “Test Test Test!” and academically deliberate is this with an intent to expand our perspective. There are more variables that have to be taken into consideration before taking decisions at a city/state/national level.

Will testing more people help us and will it optimally support our healthcare system without adding too much burden? This is the question we will be exploring, I shall present my point of view and let you decide. This article will not delve on the process to identify a gold standard test for any disease, but more on the methodology &math, which will help decision makers (and common folks like us to evaluate and critically discuss the decisions thus made).  

Before we get into the details let us get a few basic definitions listed sourced from NCBI (National Center of Biotechnology Information) link is at the end of the article:

Patient: Positive for disease (has the disease)

Healthy: Negative for disease (does not have the disease)

Outcomes of the tests can be categorized in the following buckets:

True positive (TP) = the number of cases correctly identified as patient

False positive (FP) = the number of cases incorrectly identified as patient

True negative (TN) = the number of cases correctly identified as healthy

False negative (FN) = the number of cases incorrectly identified as healthy

Accuracy: The accuracy of a test is its ability to differentiate the patient and healthy cases correctly. To estimate the accuracy of a test, we should calculate the proportion of true positive and true negative in all evaluated cases. Mathematically, this can be stated as:

Accuracy=(TP+TN)/(TP+TN+FP+FN)

Sensitivity: The sensitivity of a test is its ability to determine the patient cases correctly. To estimate it, we should calculate the proportion of true positive in the patient cases.

Sensitivity=TP/(TP+FN)

Specificity: The specificity of a test is its ability to determine the healthy cases correctly. To estimate it, we should calculate the proportion of true negative in the healthy cases.

Specificity=TN/(TN+FP)

Now we all have a common understanding of the terms. Let’s try to get more comfortable with a simplistic example.

Assume there is a city with 1,00,000 people. Of which there are 50% of them are affected by a disease. We also 1,00,000 testing kits for the disease so we are in a condition to test everybody and immediately treat the people who have the disease. Also assume the accuracy of the test is 95%, which we should feel is close to accurate. For the sake of simplicity let us keep both the sensitivity and specificity at the same 95% (this will vary based on tests, more on it later).

This means the following:

50,000 people with disease

50,000 people are healthy

The test kit will accurately identify 95% of the infected people correctly, i.e. 47,500 people out of 50,000 infected people will be identified (by the test as true).

Also, the test will identify 95% of the healthy people correctly too, i.e. 47,500 people out of the 50,000 healthy people.

Let us summarize this in a small table form

	True	False	Total
Positive	47,500	2,500	50,000
Negative	47,500	2,500	50,000

The total positive cases will tell us how many people will be treated by the healthcare system because the test was positive.

Now let us see what happens if the infection rate is 20% instead of 50% with the same number of test kits.

	True	False	Total
Positive	19,000	4,000	23,000
Negative	76,000	1,000	77,000

Now we will be treating the 23,000 people who were tested positive, which is about 3,000 (15%) more than the actual count.

Let’s try a higher infection rate, say 80% for the same situation

	True	False	Total
Positive	76,000	1,000	77,000
Negative	19,000	4,000	23,000

Here we will be treating 77,000 people who tested positive, which is 3,000 (3.75%) less than the actual count.

Now let us try to work with a few more variations focusing on the test’s accuracy, infection rate and total positive cases, for the same 1,00,000 people (assuming all of them are tested).

No of people tested	100,000
Test Accuracy	Infection Rate	No of Infected people	No of People whose test was positive (TP +FP)	% deviation from actual infected people	No of healthy people identified as sick (FP) by test
95%	5%	5,000	9,500	90%	4,750
95%	10%	10,000	14,000	40%	4,500
95%	20%	20,000	23,000	15%	4,000
95%	30%	30,000	32,000	7%	3,500
95%	40%	40,000	41,000	3%	3,000
95%	50%	50,000	50,000	0%	2,500
95%	60%	60,000	59,000	-2%	2,000
95%	70%	70,000	68,000	-3%	1,500
95%	80%	80,000	77,000	-4%	1,000
95%	90%	90,000	86,000	-4%	500
90%	5%	5,000	14,000	180%	9,500
90%	10%	10,000	18,000	80%	9,000
90%	30%	30,000	34,000	13%	7,000
90%	50%	50,000	50,000	0%	5,000
90%	80%	80,000	74,000	-8%	2,000
80%	5%	5,000	23,000	360%	19,000
80%	10%	10,000	26,000	160%	18,000
80%	30%	30,000	38,000	27%	14,000
80%	50%	50,000	50,000	0%	10,000
80%	80%	80,000	68,000	-15%	4,000

If we follow the patterns, we will notice that as the infection rate increases the deviation from actual no of infected people. That implies that as the infection level increases in a population, we will be treating a very small % of healthy people identified as sick. This will not be big strain on resources compared to treating the people identified as sick in a low infection % city.

So, is there no reason to test the population or will we have to wait till majority of the population gets the disease? The answer to both the questions is no.

There are different tests for these two scenarios. This is where the distinction between a screening test and a diagnostic test is needed.

A screening test is administered to a large group of people to make sure nobody who is infected is left out. These tests are designed for easy execution and to get the results quickly. to be It has a high sensitivity less focus on its specificity (there by affecting its accuracy). Those cases identified by the test will be taken for further investigation/tests. We can see these kinds of tests outside of the medical world in many places. One good example is the airport security. The objective is to not let any dangerous item to be taken on the flight and we are ready to err on the over detection side.

A diagnostic test is generally a confirmatory test. This can either be the first test or the follow up test after a screening test. This is generally costlier, difficult to administer and may take some time to get the results compared to the screening test. This has very a high level of accuracy (gold standard) than the screening test for the same disease (high sensitivity and specificity).

General differences	Screening Test	Diagnostic test
Objective of the test	Not to miss any infected person	To be sure that only the” true” person has the disease
Start of treatment	Generally followed by investigation or diagnostic test	Usually treatment starts after the test
Ease of administering	Very easy, can be used to test a large group of people in a short time	Not as easy as the screening test. It may sometimes need the patient’s cooperation to be conducted
Duration to get the results	Very quick, sometimes instantaneously	May take sometime
Cost	Very cheap	Costlier than the screening tests

Taking all this information into account, we can come to a conclusion that in an epidemic or pandemic we should take a decision to test the population keeping few other constrains in mind. These are hospitals’ capacity to admit and treat the positive tested cases, cost of medication, panic & mental agony of a person who is wrongly diagnosis etc. Can our doctors treat nearly all of our population assuming they have the disease? No. This is exactly the situation that will happen if we start treating everyone who is tested positive by test with low specificity.

Hence, I prefer a targeted population testing where the probability of an infected person is high compared to a whole population testing. The questions like what is the target population, what are its characteristics etc are best left to the doctors and administrators (the experts in this context). Please share your thoughts with me about this in the comments section. I hope to learn more during the interaction.

The article is too simple to give a view into the complexities of the decision making process. For example the silent (asymptomatic) carriers problem in COVID 19. This is where the community quarantine helps the administrators. We can test the people with symptoms first, next the high risk group which has come into contact with the people with infections followed by anyone who comes into contact with the infected population. Another aspect is who (and how) to treat ? What about the social and economic aspects ?  Just too many things to be considered for taking a decision and also evaluating its effectiveness.

Let me end with a quote, not sure to whom to attribute it, which aptly sums up our power of contribution. 

"This is the time where we can save the world by sitting at home and doing nothing !"

Happy "Saving the world". Stay safe and healthy.  

Referred sources:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4614595/

Thank you for suggesting the Edits C (Aravind)