When is 8% not 8%

When you think it is 8 percentage points.

Let me pre-empt opinions that I’m a bastard by saying that I’m not. Much. I’m just a statistician.

The story is the increase in female teen suicide rates. You’ll notice I don’t use the popular adjectives, like dramatic, shocking, huge, etc. Just “increase”.

From the CDC:

Significant upward departures from modeled trends in 2004 were identified in total suicide rates for three of the six sex-age groups: females aged 10-14 years and 15-19 years and males aged 15-19 years. The largest percentage increase in rates from 2003 to 2004 was among females aged 10-14 years (75.9%), followed by females aged 15–19 years (32.3%) and males aged 15-19 years (9.0%). In absolute numbers, from 2003 to 2004, suicides increased from 56 to 94 among females aged 10-14 years, from 265 to 355 among females aged 15-19 years, and from 1,222 to 1,345 among males aged 15-19 years.

These massive increases are relative, and specific. For example, with respect to females aged 10-14 years, poisoning and hanging (I should probably have warned of the weird morbidity of this post):

CDC Figure 1

Similarly with regard to females aged 15-19:

CDC Figure 2

Risks: relative versus actual

First: I am not suggesting that an increase like this, bucking a trend of steady declination in suicides, is nothing about which to be concerned. However.

Notice the vertical axes on these graphs. This is the difference between percentage increases and percentage point increases. So suicide risks among young people have increased 8%, not by 8 percentage points. In fact they have increased by 22% for young women, specifically. This means increasing from 6.59 per 100,000 to 8.06 per 100,000; alternatively from .00659% to .00806%.

Second, while I’m not suggesting that a 22% increase in suicides for young women vs. 4.9% for males is nothing about which to be concerned, consider this table:

CDC Table

Click on it for the big version.

The number of young males committing suicide has increased from 33.55 per 100,000 to 35.2 per 100,000; alternatively from .03355% to 0.0352%. The rate of suicide per 100,000 is 436% greater for males than females.

Finally, these are 2003 to 2004 changes, as per the data the CDC has used. So before panicking, of first importance is making sure the numbers are okay (without offense intended to the researchers), finding out what in hell is the deal with the poisoning and suffocation, and finding out what the numbers are like for the last three years. Was that spike merely a spike, or has a new trend begun? Suicide rates could be back on the declining trend, today, or far, far higher.

Just something to mull. I have a big prejudice against reporting with relative risks. The endless parade of things that increase the risk of cancer are what did it. If I increase your risk of death from 0.01% to 0.02%, I’ve doubled it. It’s still only 2 in 10,000, though. Perspective, necessary in responsible statistical inference and appropriate policy response, goes missing a lot when dealing with relative risks.


2 comments so far

  1. PalMD on

    I like Number Needed to Harm, when trying to understand relative risks in medical studies. It really cuts to a number that is more “intuitive”.

  2. zooeygoethe on

    Quite so. Non-health-economists/epidemiologists:


    It turns risk on its head, basically, and turns these numbers into the number of people that need to be exposed to a risk factor (poisons? Firearms? The endless world of unattainable physical ideals for young girls?) for one person to ‘be harmed’ as a result (assuming they would not have, without that risk factor) – i.e. catch the disease.

    It is a great perspective to take on the panoply of stories about Things That Increase The Risk Of Cancer, and goes a long way towards correcting the overblown reactions we’re clearly expected to have when newspapers report relative risks as though they’re somehow actual risks.

    Thanks for the post. PalMD (for the rest of you) contributes to something called the Rational Wiki:


    Give it a few minutes, when you have them. It’s quite interesting over there.

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