# Economists Do It With Models

## An Economist Reads An STD Warning Poster…

When I posted before with the title “An Economist Reads The Newspaper”, I had no idea that it would be a theme…nor did I envision the theme taking a turn for the creepy this soon. Regardless, I was walking in the Harvard Science Center the other day and saw a poster that said the following:

“50-75% of people who have chlamydia have no symptoms.”

This poster clearly achieved it marketing goal, at least in the short term, since it immediately made me think two things. First, it made me think that *obviously* I must have chlamydia, since I am exhibiting no symptoms (at least not to my knowledge). Second, as a corollary, it made me think that maybe I’ve been doing it with too many models. *rim shot*

Luckily, as a skeptical economist, I quickly saw the error in my initial train of thought. The fallacy in my thought process was a misapplication of Bayes’ Rule. (I suggest scrolling down to the examples on that link, since your brain might explode otherwise.) I don’t want to get too technical on you here, so suffice it to say that I was mistaken to make an inference before stopping to say to myself “wait a minute, this all depends on how likely it is for someone to have chlamydia in the first place.” (Sidenote: I can only imagine what I’m going to see now for search terms that people use to get to my site.) Like any true geek, I looked up statistics on the prevalence of chlamydia, and I determined that a reasonable infection rate to use is about 1 percent. I also figured that I would make the middle of the road approach regarding the data from the poster and assume that 62.5 percent of people who have chlamydia don’t have any symptoms…even though that clearly doesn’t have the same ring to it.

To do the math, we need to consider the following:

• The conditional probability of one thing happening (let’s call it A) given that another thing happened (let’s call it B) is given by “the probability that both A and B happened divided by the probability that B happened.”
• The probablity that one has chlamydia and no symptoms is 1% times 62.5%, or 0.625%.
• The probability that one has chlamydia and does have symptoms is 1% times (1-62.5%), or 0.375%.
• The probability that one doesn’t have chlamydia yet exhibits symptoms…well, let’s just assume that this is zero. (This should logically be zero unless chlamydia shares exact symptoms with another disease.)
• The probability that one doesn’t have chlamydia and doesn’t exhibit symptoms is then 1-1%, or 99%.

Why this is information is helpful is summarized by the following:

Lesson learned: in a lot of cases, no news is most likely good news. Note, however, that if chlamydia were more prevalent in the population overall, this number would be higher. Revised lesson learned: no news is most likely good news when the news is that you don’t have burn marks from getting struck by lightning. (Hint: you probably didn’t get struck by lightning, but you already knew that.)

### 14 responses so far ↓

• 1 econgirl // Jun 15, 2009 at 8:22 am

“You forgot to factor in how many models you’ve done. As you do more models, your statistical probability of falling into the category of having it without exhibiting symptoms rises exponentially due to your high-risk behavior.”

If you scroll down about 1/6 of the way in the Bayes’ Rule link you will see the following: “Objective Bayesians emphasise that these probabilities are fixed by a body of well-specified background knowledge (K), so their version of the theorem expresses this.”

You then see a formula that takes the background knowledge into account, so you would get something like “the probability of having chlamydia given that you exhibit no symptoms and are a slut is equal to…” So technically the reader is correct in that my fear, or subsequent lack thereof, was not conditioned on what I know about my own behavior.

• 2 J Frank // Jun 15, 2009 at 10:36 am

If you get chlamydia in a forest, and no symptoms follow to hear, are you better off not knowing? (I say yes, unless you care about your partners welfare more than you care about having partners)

• 3 Dan L // Jun 15, 2009 at 10:42 am

Maybe I’m too much of an “economist” but the message of the poster seems both clear and effective: Don’t think you’re safe from STDs just because you and your partners don’t have have any symptoms. The effect that the poster had on you (and others) was not only desirable but also statistically justified, really: If you didn’t already know the 50-75% statistic, then however concerned you were about chlamydia (presumably based on your sexual behavior, etc.), you should be a lot *more* concerned after reading the poster. (Unless your concern was exactly zero to start with.)

Also, I noticed that the link you gave suggests that as much as 1.25% of the population has undiagnosed chlamydia. That might sound small, but that’s actually a huge percentage. The CDC also estimates that 1 in 20 women of reproductive age have chlamydia, as well as 1 in 10 adolescent girls. Yikes! Now here would likely be a good scare statistic if they could estimate it: Incidence of undiagnosed chlamydia for those who’ve had 2 or more sexual partners in the last year (or something like that).

Aside: People call that Bayes’ Rule? Really? I guess people like to name things to make sure students know that they’re Important.

• 4 centrist58 // Jun 15, 2009 at 11:33 am

Following up on Dan L’s observations, the incidence is increasing over time and is concentrated in certain populations. The high rate of missed diagnosis (75%) and multiple partners means that the 1 in 20 estimate germane to econgirl is likely higher in 2009 than in 2006 when the estimate was made. We need some Network Theory math to figure out how to update the probability – that’s an aspiration for me (Matthew Jackson’s “Social and Economic Networks” is a recent, unread addition to my library).

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