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An incidence rate (whether an incidence density or an incidence proportion) measures the probability of an event (typically a new case of the relevant health condition in epidemiology) divided by time. Incidence rate: probability of becoming a new case over time.*

A prevalence (whether a period prevalence or a point prevalence**) is not a rate, as there is no probability of new cases over time, but just the probability of individuals being a case at some point in time (except the instantaneous measurement implied by "point" doesn't truly happen all that often, and so prevalences are situated with respect so some period of time like a day, or year). Prevalence: probability of being a case during some period.

Lots of respectable epidemiology textbooks make this distinction (i.e. between rates and prevalences, and being explicit that the latter are not rates), and yet, some epidemiologists are quite happy to publish "prevalence rates". For example, the CDC says:

Prevalence, sometimes referred to as prevalence rate, is the proportion of persons in a population who have a particular disease or attribute at a specified point in time or over a specified period of time.

Wherefore "prevalence rate"? (Really, it just makes me twitch when I encounter the term, but I wonder if there is a good story or history there, or a nuance I am missing?)



* A rate is a more general concept than incidence rate, specifically. Rates imply how much of one thing happen given another thing; for example, the rate we term speed measures how much distance happens over time.

** I suspect all prevalences are technically period prevalences, as instantaneously concurrent measurement of, for example, health conditions, makes less sense at shorter and shorter period intervals.

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    $\begingroup$ An oxymoron is contradictory. A tautology is repetitive. (I was revising some lecture slides just recently and thought to check. I'd been using it incorrectly each year for a few years.) Which do you mean? (As you happen to know, I am not an epidemiologist.) $\endgroup$
    – Nick Cox
    Commented Oct 26, 2020 at 23:37
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    $\begingroup$ Come on, Nick, I mean clickbait, mostly! ;) Seriously though, I mean oxymoron: If "prevalence is not a rate," then "prevalence rate" strikes me as oxymoronic. (BTW, in my experience epidemiologists do not mean $\Delta \text{prevalence} \div \text{time}$ when they say "prevalence rate," although rate of change in prevalence is an interesting outcome for population health in time series models that I wish was taught more.) $\endgroup$
    – Alexis
    Commented Oct 26, 2020 at 23:56
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    $\begingroup$ Dunno, but incidence & prevalence are often discussed together, especially in the classroom, and incidences are rates. Why do people think mediation & moderation are similar? They don't seem like very similar ideas to me, although they both start with "m". $\endgroup$
    – gung - Reinstate Monica
    Commented Mar 11 at 18:50
  • $\begingroup$ There seems to be an implied view here that a rate should measure things per time, but that need not be the case. A rate can be expressed with respect to any arbitrary quantity. The tax rate, for example, is a per-dollar rate that has nothing to do with time at all. A prevalence rate can be interpreted as a rate expressed with respect to the N of the population. I don't see the self-contradiction. $\endgroup$
    – Nuclear Hoagie
    Commented Mar 11 at 19:52

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"Prevalence rate" is not oxymoronic or self-contradictory. A rate most generally simply measures the amount of one quantity with respect to another - there is no requirement that a rate must be measured per time as the question seems to imply. Any measure of X per Y is a rate. A prevalence of 3 diseased individuals per 1000 is indeed a rate. The term "prevalence rate" is at worst redundant, since prevalence is naturally expressed with respect to the entire population, so is by its very nature a rate.

The tax rate is the amount of money you pay per dollar of income. The fertility rate is the number of children born per woman. The prevalence rate is the number of individuals exhibiting some condition per person in the population. None of these express anything with respect to time, yet they are all still rates.

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    $\begingroup$ Even if I run with the idea that a "rate" can be abstracted to a ratio of any two quantities, (my training was otherwise on this point), what then is a prevalence in and of itself? I think you'll find in the literature, that prevalence is usually a frequency of subjects with events (cases) over subjects at risk (denominator). Perhaps the OP's question should be "is prevalence rate redundant"? $\endgroup$
    – AdamO
    Commented Mar 13 at 22:52
  • $\begingroup$ I really appreciate this comment viz. 'redundant' @AdamO. Nuclear Hoagie, see also my comment to PeterFlom's answer. $\endgroup$
    – Alexis
    Commented Mar 18 at 16:02
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Any answer on this point can be, at best, speculative. It is unfortunately just as you say. There is no well-defined concept of "prevalence rate". If we had to give it a meaning, it would just be prevalence. This is perhaps useful because there are over a million indexed hits when I search this in Google, https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=%22prevalence+rate%22&btnG= and the top 6 seem to indicate exactly what CDC has defined in your link.

Although incidence and prevalence are distinct topics, they are metrics that can be assessed in the same outcome - such as lung cancer diagnoses or deaths, smoking, voter registration, etc. When people perform literature reviews, they often knowingly or unknowingly assimilate reports on incidence and prevalence for certain outcomes, and can make broad statement that are not altogether incorrect. For example, "The prevalence rate of vaping among teens correlates with an increased diagnoses of asthma." I think a pulmonologist would understand exactly what's meant here, and they would infer that prevalence and incidence are implied by it, especially since vaping has only existed for about a decade or so.

It is never wrong for a statistician to point out that such language is imprecise and can be improved. Qualitative statements can forgo such language altoghether, for instance, "Rises in vaping among teenagers has seen a spike is asthma diagnoses." Is, in my opinion, fine for an introduction or conclusion.

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  • $\begingroup$ +1 Thank you as always, AdamO. See my comment to @PeterFlom's answer also. :) $\endgroup$
    – Alexis
    Commented Mar 18 at 16:00
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I don't see anything oxymoronic or repetitive here.

Prevalence can be give per a number. Indeed, in a paper I recently reviewed, the authors said something like "the prevalence was 42" and I asked "42 per what?"

I think using the word "rate" might be a way to avoid this.

EDIT: Maybe it's a LITTLE repetitive, but language is like that.

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    $\begingroup$ Because "rate" is such an overloaded term, I try to avoid it in technical analysis. But then again it is quite difficult to avoid due to the 'prevalence' of its usage. 😜 $\endgroup$
    – Galen
    Commented Mar 13 at 15:07
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    $\begingroup$ +1 Peter Flom, my thinking was that because prevalences are so often communicated along side incidence rates, and because incidence rates are also divided by population, that the time in the denominator in incidence rates—whether calendar time as in incidence proportions, or person-time as in incidence densities—was the important distinction between 'is a rate' and 'is not a rate' in this context. The answers (including yours) and comments, particularly the recent ones, have me rolling my thinking back on the 'oxymoron' part. $\endgroup$
    – Alexis
    Commented Mar 18 at 15:59
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    $\begingroup$ @Alexis Just like in chemistry, where keeping a key account of the units is pivotal to deriving correct quantities, "persons" as a denominator and "person-time" as a denominator are distinct concepts. In fact, there are massive philosophical issues with correctly differentiating prevalence-case bias in measuring incidence. For instance, COVID19 pandemic led to a decrease in cancer diagnoses because people weren't attending scans. Once vaccinations begun, cancer increased because prevalent cases were detected by screening. $\endgroup$
    – AdamO
    Commented Mar 18 at 16:39
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    $\begingroup$ @Galen Amen, "rate" is almost synonymous with "data" as a meaningless thing that statisticians provide. Any regression parameter can be a rate if you squint hard enough. $\endgroup$
    – AdamO
    Commented Mar 18 at 16:41

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