COVID19: Incidence, Prevalence, Attack Rate,Test-Positive Rate… What Does It All Mean?

by Raywat Deonandan, PhD
Epidemiologist & Associate Professor
University of Ottawa
(I add my credentials to these COVID-19 blog posts in case they get shared. I want readers to know that my opinion is supposedly an educated and informed one)

Today I’m going to continue answering some of the more common epidemiological questions I get from both the media and general public. Specifically, we’re going to look at a couple of the numbers we should be tracking as this wave of the epidemic begins to wane.

But First…

As always, though, I want to make note of my recent media engagements (just so I have written them down somewhere…. this stuff is valuable to professors for our annual reports):

  • April 23, 2020 — interviewed by Kerry Campbell of CBC Charlottetown
  • April 23, 2020 — gave some comments to Jacques Poitras of CBC News
  • April 22, 2020 — interviewed on CJOB radio
  • April 22, 2020 — interviewed by Laurianne Croteau of French CBC
  • April 22, 2020 — gave some comments to Lisa Xing of CBC
  • April 21, 2020 — interviewed on CFRA radio
  • April 20, 2020 — interviewed by Alan Neal on CBC Radio’s “All In A Day”
  • April 18, 2020 — interviewed on CTV news
  • April 17, 2020 — interviewed by Mary Ormsby of the Toronto Star
  • April 17, 2020 — gave comments to Natasha MacDonald-Dupuis for CBC News
  • April 17, 2020 — gave comments to Michael Gorman of CBC News
  • April 16, 2020 — interviewed by Raffy Boudjikanian of CBC Edmonton


Incidence vs Prevalence

My students are sick of me preaching about the difference between incidence and prevalence. But in this sudden new era of epidemiologic awareness, I think it’s something most people should be aware of, even though many laypeople use the terms interchangeably.

It’s really quite simple. “Prevalence” refers to the proportion of the population who currently have the disease. Whereas “incidence” describes the proportion of susceptible people who newly acquired the disease in the time frame we’re looking at.

Prevalence = # people with disease / all the people in the population

Incidence = # new cases of the the disease in a given time / all the people who don’t yet have it

As you can probably guess, in the current pandemic, we really don’t know either of these. For prevalence, we don’t know how many people truly have it. It’s tempting to look at the number of positive tests (in Canada, as of today, that’s 43,888 cases) and to divide that number by the total population of Canada (37.6 million) to get a prevalence of 0.12%. But we’re clearly missing a lot of cases, so this number would be a great underestimate.

If you’re following the news, though, you might be aware that some tantalizing new studies that have randomly sampled various populations have attempted to estimate the true prevalence of COVID-19; and it’s a larger number than you might think. One study estimates it to be 2.5-4.1% in California; New York City reports 21.2% in its study; and in one German town, it’s about 14%.


Those studies actually did not measure prevalence, but something called “seroprevalence”. The difference is that true “prevalence” refers to people who have the disease, full stop. “Seroprevalence” refers to people who have blood markers for the disease, in this case antibodies indicating present or past infection. So seroprevalence doesn’t tell us how many people currently have COVID19, but rather how many people have had it.

Seroprevalence is useful if we’re trying to gauge how close we are to herd immunity. You will recall from an earlier post, herd immunity for COVID-19 probably kicks in when 40-70% of the population have acquired immunity. But simply having antibodies does not immediately mean that the people tested are immune. So all of this is still very much up in the air.

The way to get real seroprevalence and prevalence estimates is to conduct scientific studies that employ random sampling of the population. And the way to keep abreast of incident cases is to invest in what we call a surveillance system, which is a scary word that just means public health infrastructure for detecting cases as they arise. I will describe surveillance systems in a future post.

Attack Rate

With infectious disease outbreaks like COVID-19, we care a lot about a certain kind of incidence rate called the “attack rate”. This is a niggling detail, but the distinction is this: for an attack rate, the denominator is the number of at-risk people at the start of the outbreak. For a regular old incidence rate, the denominator is a weird combination of people at risk, controlled for how long each person was at risk. Confused? Don’t worry about it.

We usually talk about attack rates when investigating infectious disease outbreaks. But here’s the thing: as time goes on and more people become infected (and either die, recover, or stay sick), the number of at-risk people goes down. So the attack rate can sometimes naturally increase over time, as the denominator gets smaller. It makes this all very confusing sometimes.

Test-Positive Rate

But none of that really matters for the lay person reading the numbers. I only bring it up because you might hear experts talking about these terms casually on the news. One number you should get comfortable with, though, is the “test-positive rate”. Simply put, it’s the proportion of COVID-19 tests that come back positive.

Canada has performed 620,101 tests and has 40,888 cases. Dividing those two numbers gives us the test-positive rate, which is 6.6%. Is that low? Is it high? What does that mean?

As of today, New York State has performed 730,656 tests of which 277,445 came back positive, giving a test-positive rate of 38%. What do we do with that number?

Well, the WHO has outright said that if a lot of your tests are coming back positive, then you’re not testing enough. Because there’s no way that the true prevalence (not seroprevalence) of the disease is 38%.

This is an artifact of the testing policies, which say that you should only test the people showing the most severe symptoms. If you do that, of course you’re going to find more cases. It’s the old adage of looking for your keys where the light happens to be. The more you lessen your criteria for who gets tested, the more negative results you will find, and the test-postitivity rate goes down.

Imagine grabbing a bunch of people and testing them and getting a percentage of positive results. Now imagine grabbing a bigger bunch of people and testing them. Now, and even bigger bunch. And so forth. If the epidemic is spreading really fast, then the test-positivity rate in all those scenarios should remain the same. But if it continues to fall the bigger sample you choose, then it means the outbreak is more contained than not.

So what’s the magic number that tells you that you’re testing enough? The WHO recommends 10% as a benchmark. If 10% or fewer of your COVID-19 tests come back positive, you’re probably deploying your testing in a somewhat efficient manner. (Though that doesn’t include the strategic necessities of testing all long term care facilities, all health care workers, all personal support workers, etc.)

But 10% seems rather high, no? I personally feel that when the test-positivity rate drops to 1% or less, your community probably has a good grasp of its outbreak. In other words, you’re probably capturing almost all the cases.

This is an important benchmark as we move forward to the next phase of this thing: re-opening the economy. Despite what Rudy Giuliani thinks, testing and contact tracing are going to be the key tools that allow us to re-enter society. Keeping an eye on the test-positivity rate, especially as we transition to a true prevalence/surveillance system, will be an important way or us to know if the disease is returning in force.

In Canada, here are the testing statistics as of today:

BC 1795 58848 3.1
AB 3401 108521 3.1
SK 326 24504 1.3
MB 257 20651 1.2
ON 12879 178467 7.2
QC 20965 180833 11.6
NL 256 6862 3.7
NB 118 11464 1.0
NS 772 24884 3.1
PE 26 2344 1.1
YK 11 878 1.3
NT 5 1512 0.3
NU 0 333 0.0
TOTAL 40824 620101 6.6

You will note that Saskatchewan, Manitoba, PEI and New Brunswick all have test-positive rates scratching unity. It’s not a surprise that these provinces are the most vocal about opening up their economies really soon.

It’s why I’ve been fielding a fair number of media questions about that prospect today.

My Responses to Media

For the rest of today’s post, then, I thought I would share with some of my text responses to journalists (and a couple of members of the general public) on this and other issues.


(1) New Brunswick plans to open its economy. CBC asked for my comments. I have appended them below:

The NB plan for re-opening the economy


“New Brunswick has 118 cases, 88% recovered, with a test-positivity rate of 1%

I think NB has a good handle on the extent of their epidemic and is in a good position to CAREFULLY re-open.

The outdoor activities seem safe. I’m unclear about how the post-secondary education situation will look, but I’m assuming distancing will be in place, as well as proper hygiene controls. I don’t know if they have thought about how to manage public bathrooms in such institutions.

I don’t think mass religious services are a good idea, given that most churches and temples have close seating for a prolonged time.

Of the Maritime provinces, NB and PEI are best positioned to re-open somewhat, given their low caseload.

However, I would like to know that both provinces have in place a plan for heavy disease surveillance, intense random testing, contact tracing, and closed borders. Absent those features, I hope the NB government has a plan to quickly pull the plug if things go awry.”

(2) Question from a friend: I ask this question in seriousness, not jest, and as an uninformed observer. If we are destined to be randomly exposed to COVID-19 to achieve some “herd immunity”, why not develop a process for controlled exposure? Thereby making the flow of ICU cases into the health system more predictable. Or is that basically the intent of a vaccine, albeit in a safer manner?

“You have described the original UK and Swedish approaches. The assumption is that everyone is going to get it anyway, and that a number of people (60% of population multiplied by case fatality rate) are going to die anyway, so why not process them through the system at an optimal rate, accept the deaths, and achieve herd immnunity?

Problems: (1) no guarantee that recovery grants immunity; a vaccine has a higher chance of being calibrated to confer a large enough antibody response to confer immunity; (2) infection comes with brutal symptoms and often long term disability, including lung fibrosis and cardiovascular disease, whereas a vaccine would not; (3) we learn everyday more about how to avoid death, so people that would have died through this approach would not have died if we had waited a year from now, or if we had waited for the vaccine.”

(3) PEI is considering re-opening their economy. I was asked for comments from a CBC reporter.

“I advise another 2 weeks of lockdown to let outstanding cases resolve. But if I were the federal government, I would spend the money to test each of their 156,000 residents to do a proper prevalence study. Then they can seal their borders and run wild on the island. But then there’s that pesky tourism thing. Another revenue source will have to be found.”

(4) I’m told that as a policy, the CBC does not cite non-peer reviewed studies. This is a great policy. But there is an important pre-reviewed paper by Fisman et al about the COVID outbreaks in Ontario long term care facilities. I was asked to give a quick peer review to enable them to cite the paper. Here are my comments:

“This is a very solid paper written by the leaders of the field in this country. I see no glaring errors or weaknesses other than those acknowledged by the authors themselves (specifically, the possibility of misclassification bias, which is a small risk since those who died in LTCs were presumably well investigated post-mortem to ensure a proper determination of cause of death.)

Furthermore, by comparing the LTC rates to the general public, in a variety of age brackets, they minimize the risk of further bias. Therefore, the finding that LTC residents aged 70 and above had a 13X greater risk of dying of COVID19, as compared to those aged 70 and above NOT living in LTCs, is chilling.

It would be tempting to assume that institutionalized people are by definition more vulnerable, therefore we expect them to die at a higher rate. But a 13-fold increase in risk is well beyond the pale.

I would think that this paper would get published as-is in most peer-reviewed journals.

The key takeaways are:

  1. LTC residents in Ontario have a MUCH HIGHER risk of dying than age-matched people living in the community
  2. Those deaths were most likely driven by infected staff members more than by infected residents
  3. The infected staff who infected the residents were able to do so because of ‘infection lag”, meaning that they were spreading the disease before symptoms arose and before their infection was acknowledged

It’s an important study that really underlines how badly we failed the LTC population in this province. We can probably take some of these lessons to other restricted communities, like prisons, group homes and work camps.”

Friends, that’s all I have for you today. As always, thanks for reading, stay home, stay safe, and stay hopeful. We’re doing all the right things to get us through this.