Calculating Covid-19 Positivity Rates

On August 12, 2020, the Commonwealth of Massachusetts changed the way that it calculated the positivity rate from covid-19 testing. This reduced the headline positivity rate from covid-19 testing in Massachusetts. It is also misleading, and counter to the way in which most aggregators calculate positivity rates. This post serves to explain the differences between this calculation and the two other more widely used methods.

In all cases, the positivity rate is a simple ratio between two numbers. The numerator uses some definition of cases or positive tests results. The denominator uses some definition of tests or tested people. The positivity rate is just (Cases or Test Results) / (Tests or Tested People) (multiplied by 100 to convert to percent, if desired). In Massachusetts, and generally elsewhere, the results are restricted to tests obtained through molecular (PCR) tests, not antibody or antigen tests.

Focus on Tests (Massachusetts Method)

The Massachusetts method changes the focus of positivity rates from individuals to tests. It simply uses the ratio of the number of positive tests to the ratio of tests performed. The upshot of this is that repeat testers can have a significant impact on the positivity rate. For example, if a professional athlete gets tested every day, all of those tests increase the denominator in the calculation (regardless of whether the athlete tests positive or negative on any given test).

If someone is retested frequently, and never get a positive test result, this reduces the positivity rate compared to a calculation in which each person is counted only once. The flip-side of this is that if an individual tests positive, and comes back to be tested again a week later, and tests positive a second time, this will again count as a positive test. Hence, there is no guarantee that this method will result in a lower positivity rate, but it generally does. Most of the people being retested are presumably doing so for health and safety reasons, and not because they suspect they have Covid or have tested positive in the past.

In Massachusetts, the number of people being retested is quite significant. For example, as of this writing, about 30-35% of the tests being conducted in Massachusetts over the past several weeks are for people being retested. These people have a much lower positivity rate than people being tested for the first time – the trailing 7-day positivity rate for the re-testers is 0.4% (as of August 27) compared to 1.5% for those who have only been tested once.

Focus on Individuals Tested (Standard Method)

A more common approach to calculating positivity is to focus on individuals, not tests. Until August 12th, this is the way that Massachusetts calculated positivity rates. Each person is only counted once both for determining the numerator (with this method the number of cases) and denominator (with this method the number of individuals tested) in the positivity rate calculation.

To focus on the professional athlete or safety professional again, this means that each retest does not change the denominator of the calculation, regardless of the test results. Each person is only counted once, regardless of how many times they are tested. If an individual does test positive, this will count as a positive case, even if they are tested two weeks later and then get a negative test result. This retest with a negative result does not increase either the numerator or denominator in the calculation.

However, if a person has a negative test result, but comes back later and tests positive, the numerator will increase by one person, but the denominator doesn’t change. (This all presupposes nobody is reinfected with Covid. Although there have been recent validated reports of reinfection, this remains exceedingly rare as of now).

Include Suspected Cases (Enhanced Method)

The final method to calculate positivity rates is to include suspected cases in the calculation. Essentially, this method (used by Johns Hopkins, among others, in its calculations) assumes that all individuals suspected of having Covid, if tested, would test positive. By definition, this increases the positivity rate compared to the standard method. Specifically, the calculation is:

(Individuals with Positive Covid Tests + Probable Cases) / (Individuals Tested for Covid + Probable Cases).

In other words, the number of probable or suspected cases is added to both the numerator and denominator in the calculation. In Massachusetts, the number of probable cases is not insignificant. Over the life of the pandemic, almost 8% of all confirmed and probable cases have been probable, and over the past several weeks, this figure has ranged between 15% and 20% of probable and suspected cases. Hence, the positivity rate calculated this way has been noticeably higher than calculated the standard way.


(1) Testing Based Calculation (Massachusetts)

All Positive Molecular Tests / All Molecular Tests Performed.

(2) Individual Based Calculation (Standard)

All Individuals with Positive Molecular Test / All Individuals with Molecular Test.

(3) Enhanced Calculation (Include Probable)

(All Individuals with Positive Molecular Test + Individuals Probably Infected) / All Individuals with Molecular Test + Individuals Probably Infected).

5 replies on “Calculating Covid-19 Positivity Rates”

This is fantastic information. Thank you, Snoyd. We are grateful for your honest, intelligent analysis. As a younger person with underlying conditions which leave me vulnerable to severe infection if I were to contract COVID-19, and with children to care for, this information is incredibly valuable to my family.

Thanks so much for posting here without the noise from the Globe comments. If you have the time and inclination to continue, I’m positive many of us would follow along. Thanks again for taking the time.

Thanks Rob. Please subscribe if you’re interested, and if you have other data nerd friends, let them know about this.

Thanks Snoyd, I have been unable to follow your blog unless you post the link in the Globe but I love your way with numbers

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