Farr's Law

00:01 Let's talk now about Farr's law.

00:03 This was put forth by Dr. Farr in the 19th century.

00:08 And he was instrumental in exploring how to use observations of death to better understand epidemics.

00:17 So, Farr's said some interesting things, one of which was, "The death rate is a fact; anything beyond this is an inference." What he meant by this was that when you're observing infections in a population, you only know the cases that you are detecting.

00:35 You don't know the ones who didn't present themselves for testing.

00:38 There is a detection bias at play here.

00:41 We are usually underestimating the true burden of infection in the population.

00:47 We also never know when infection curve has actually shifted in real time, because we can't really test that well.

00:56 And there are delays and lags.

00:58 But Dr. Farr argued, we always know pretty well about death.

01:04 He can argue about whether or not somebody is dead.

01:06 And death is such a serious endeavor that usually the healthcare system is aware of it.

01:12 So, we've made the observation that epidemic events rise and fall in roughly symmetrical patterns.

01:20 That means that the rate of decline of an epidemic, meaning its infection, incidence rate, is going to look a lot like its rate of increase before we got to the peak.

01:33 So, in other words, you can use a bell curve to approximate the shape of the rate of infection in a population.

01:44 Now, he sent a famous letter in 1840, to talk about his theories about smallpox.

01:48 I won't go through the details of the letter.

01:51 But the takeaway is that he noticed that the smallpox incident rate was increasing regularly until it's stopped, and then it decreased.

02:02 And he noticed that the rate of increase looked a lot like the rate of decrease almost step by step.

02:07 There was symmetry in the death rate and the incidence rate.

02:12 And he concluded from this that we can use this symmetry to predict when an epidemic is going to wane.

02:22 So, that brought up this thing called Farr's law, which is not really a law, it's just an observation.

02:27 Farr's law simply says that, once the peak infection has been reached, it will roughly follow the same symmetrical pattern on the downward slope.

02:37 So, this incident, cumulative incident curve, or rather the incidence rate curve will look like a bell shaped.

02:49 The thing is, deaths tend to lag infections.

02:53 Because it takes time.

02:55 You can be infected for several days, you become hospitalized, get sicker, and then you die.

03:02 So, if you were to look at the curve, describing deaths in a population versus the curves describing incident rate, they will be separated.

03:13 They will be a part because the deaths come later.

03:16 They are lagging, but both will be symmetrical.

03:20 So, Dr. Farr was suggesting that by observing the deaths, you can start to make some guesses about the incidence rate.

03:29 So, once the deaths start declining, and you can observe the deaths, you can be confident that the incidence rate in the community has also started declining.

03:39 And you can do some mathematical investigations to backfill the data, and therefore predict when the epidemic is likely to end.

03:51 Now, Farr's law isn't a law, as I mentioned.

03:54 It's just an interesting rule of thumb we could use to make models.

03:58 It's only really valid if all other things are equal.

04:03 Things like incubation time and other dynamics in the population.

04:08 When used to break AIDS deaths, for example, it really failed because the underlying infection processes the transmission dynamics of AIDS were very different.

04:19 So, on the left, there is a projection of HIV/AIDS done in 1990, of when we thought the epidemic would wane based upon Farr's law.

04:32 The actual curve looked a little more dire.

04:36 So, Farr's law did not serve us well here.

04:39 It showed that in the case of HIV/AIDS in the USA, symmetry was not observed.