Incidence and Prevalence, Part One

I was telling my wife the other day that I was really angry at a man on the radio who criticized investment in overseas HIV/AIDS relief because, according to him, "the prevalence of AIDS continues to increase." My wife answered, "Of course it is. People are still getting infected." Now, unless you completely understand the meaning of "incidence" and "prevalence," you might have (maybe) agreed with the man, like my wife did. (She agreed prevalence was increasing because of new cases, not on the de-funding part.) And that's the thing, folks. People who know better (and some who don't) are using whatever epidemiological statistics fit their agendas. So let's clear up the confusion after the jump...

I'm confused. Is he catching the cat?

A THOUGHT EXPERIMENT
I need you to draw up a mental image in your... uh... mind. Yeah, I need you to think of a bucket of water under the faucet. The bucket in mind also has an opening to drain out water. Got that image? Great. Here's some help in case you really can't visualize it:

Like this, but under a faucet

So we open the faucet and water starts to fill the bucket. Then we open the spigot on the bucket and water comes out. Keep that in mind as we talk about the difference between incidence and prevalence.

INCIDENCE
In epidemiological terms, incidence is defined as the number of new cases of a disease or condition in a population, divided by the total number of people at risk of contracting the diease in the population per unit of time. It is usually given as "4.9 new cases of disease X per 100,000 people per year," for example.

In our thought experiment, incidence is the water that we are pouring into the bucket per unit of time. So let's say we're pouring water in there at a liter an hour and there were five liters in there to begin with. Our incidence of water would be 0.2 liters of water per liter of water per hour... Or 20% to make it clearer. So, remember, incidence are new cases (or new water) per unit of time. (It's the unit of time that makes things "rates". Had it been just the fraction, it would have been only a proportion.)

PREVALENCE
In epidemiological terms, prevalence is defined as the number of existing cases of a disease or condition in a population, divided by the total number of people at risk of contracting the disease in that population per unit of time. Like with prevalence, it is usually given as "5.9 cases of disease X per 100,000 per year," for example.

In our thought experiment, prevalence is the water that exists in the bucket plus the water that is coming into the bucket in a unit of time. So we're pouring in one liter per hour, right? Our prevalence would be 5.0 L at time zero, 6.0 L at one hour, and so on... We would describe it as 1.0 liters of water per liter of water per hour at time zero. At one hour, we would have 6.0 liters of water per liter of water... And so on.

YES, IT'S COMPLICATED
So let's just talk in percentages or absolute numbers... Or, better yet, graphs. But we also need to discuss the "population at risk" part of the definitions of incidence and prevalence, because that affects the numbers.

AT RISK
If you're dealing with an infection that renders you immune after you've had it, then you're out of the "at risk" pool. As a result, you can have a lot of new cases, but the "at risk" pool is constantly being reduced. It's like you're opening the spigot and letting water out. This is also the case when you can die from the disease (like HIV). When you're letting the water out, you'll be affecting the denominator, which will have an effect on incidence and prevalence. Why? Because incidence is new cases divided by the population at risk. The population at risk is reduced. Get it?

On the other hand, if the disease is one that you can catch over and over again, like the flu, then your population at risk is always being replenished once the person recovers from the flu. (Yes, it can still be diminished from people dying, but just stay with me on this.) In those cases, when the spigot is open and closed, both incidence and prevalence will go up and down with the outbreaks of the disease.

THAT'S IT FOR NOW
Alright, folks. That's all for now. I've decided to make this a 2-part "lesson" because the concepts are a little intricate. Next time, we'll look at several examples of incidence and prevalence under different conditions:

• Incidence and prevalence when everyone recovers right away from the disease.
• Incidence and prevalence when there is an equal number of cases each year (100), when no one recovers, but they never die of the disease.
• Incidence and prevalence in HIV/AIDS.

In all cases, we'll look at the total number of incident and prevalent cases, and then we'll look at the proportions per time (or rates).

As always, I'm open for questions, and I thank you for your time.