Statistician to the Stars!
Here is a question I added to my chapter on logic today.
New York City “Health Czar” Thomas Frieden (D), who successfully banned smoking and trans fat in restaurants and who now wants to add salt to the list, said in an issue of Circulation: Cardiovascular Quality and Outcomes that “cardiovascular disease is the leading cause of death in the United States.” Describe why no government or no person, no matter the purity of their hearts, can ever eliminate the leading cause of death.
I’ll answer that in a moment. First, Frieden is engaged in yet another attempt by the government to increase control over your life. Their reasoning goes “You are not smart enough to avoid foods which we claim—without error—are bad for you. Therefore, we shall regulate or ban such foods and save you from making decisions for yourself. There are some choices you should not be allowed to make.”
The New York Sun reports on this in today’s paper (better click on that link fast, because today could be the last day of that paper).
“We’ve done some health education on salt, but the fact is that it’s in food and it’s almost impossible for someone to get it out,” Dr. Frieden said. “Really, this is something that requires an industry-wide response and preferably a national response.”…”Processed and restaurant foods account for 77% of salt consumption, so it is nearly impossible for consumers to greatly reduce their own salt intake,” they wrote. Similarly, regarding sugar, they wrote: “Reversing the increasing intake of sugar is central to limiting calories, but governments have not done enough to address this threat.”
Get that? It’s nearly impossible for “consumers” (they mean people) to regulate their own salt intake. “Consumers” are being duped and controlled by powers greater than themselves, they are being forced to eat more salt than they want. But, lo! There is salvation in building a larger government! If that isn’t a fair interpretation of the authors’ views, then I’ll (again) eat my hat.
The impetus for Frieden’s latest passion is noticing that salt (sodium) is correlated—but not perfectly predictive of, it should be emphasized—with cardiovascular disease, namely high blood pressure (HBP). This correlation makes physical sense, at least. However, because sodium is only correlated with HBP, it means that for some people average salt intake is harmless or even helpful (Samuel Mann, a physician at Cornell, even states this).
What is strange is that, even by Frieden’s own estimate (from the Circulation paper), the rate of hypertension in NYC is four percentage points lower than the rest of the nation! NYC is about 26%, the rest of you are at about 30% If these estimates are accurate, it means New York City residents are doing better than non residents. This would argue that we should mandate non-city companies should emulate the practices of restaurants and food processors that serve the city. It in no way follows that we should burden city businesses with more regulation.
Sanity check:
[E]xecutive vice president of the New York State Restaurant Association, Charles Hunt…said any efforts to limit salt consumption should take place at home, as only about 25% of meals are consumed outside the home.
“I’m concerned in that they have a tendency to try to blame all these health problems on restaurants…This nanny state that has been hinted about, or even partially created, where the government agencies start telling people what they should and shouldn’t eat, when they start telling restaurants they need to take on that role, we think its beyond the purview of government,” Mr. Hunt said.
Amen, Mr Hunt. It just goes to show you why creators and users of statistics have such a bad reputation. Even when the results are dead against you, it is still possible to claim what you want to claim. It’s even worse here, because it isn’t even clear what the results are. By that I mean, the statements made by Frieden and other physicians are much more certain than they should be given the results of his paper. Readers of this blog will not find that unusual.
What follows is a brief but technical description of the Circulation paper (and homework answer). Interested readers can click on.
This is just a rough prototype meant to be easy to play with inside a post. READ the help and guidebook! Suggestions for new canned examples welcome—the hard part is deriving historical performance data.
This article provides you with an introduction and a step-by-step guide of how to make good decisions in particular situations. These techniques are invaluable whether you are an individual or a business.
These results hold for all manner of examples—from deciding whether to have a PSA test or mammography, to get a vaccine, to finding a good stock broker or movie reviewer, to situations that require intense statistical modeling, to financial forecasts, to lie detector usefulness. Any situation that has a dichotomous outcome can use these techniques.
Many people opt for precautionary medical tests—frequently because a television commercial or magazine article scares them into it. What people don’t realize is that these tests have hidden costs. These costs are there because tests are never 100% accurate. So how can you tell when you should take a test?
When is worth it?
Under what circumstances is it best for you to receive a medical test? When you “Just want to be safe”? When you feel, “Why not? What’s the harm?”
In fact, these are not good reasons to undergo a medical test. You should only take a test if you know that it’s going to give you useful information. You want to know the test performs well and that it makes few mistakes, mistakes which could end up costing you emotionally, financially, and even physically.
Let’s illustrate this by taking the example of a healthy woman deciding whether or not to have a mammogram to screen for breast cancer. She read that all women over 40 should have this test “Just to be sure.” She has heard lots of horror stories about breast cancer. Testing almost seems like a duty. She doesn’t have any symptoms of breast cancer and is in good health. What should she do?
What can happen when she takes this (or any) medical test? One of four things:
This table shows all the possibilities in a test for the presence of absence of a thing (like breast cancer, prostate cancer, a lie, AIDS, and so on). For mammograms, “Present” means that cancer is actually there, and “Absent” means that no cancer is there. For a PSA test, “Present” means a prostate cancer is actually there, and “Absent” means that it is not. For a Movie Reviewer, “Present” means you liked a movie, and “Absent” means you did not.
| Present | Absent | |
| Test + | Good: True Positive | Bad: False Positive |
| Test – | Bad: False Negative | Good: True Negative |
“Test +” says that the test indicates the test said the thing (cancer) is present. “Test -” says that the test indicates the absence of the thing. For the Movie Reviewer example, “Test +” means the reviewer recommended a film.
There are two cells in this graph that are labeled “Good,” meaning the test has performed correctly. The other two cells are labeled “Bad,” meaning the test has erred. Study this table to be sure you understand how to read it because it will be used throughout this article.
Error everywhere
The main point is this: all tests and all measurements have some error. There is no such thing as a perfect test or perfect measurement! Mistakes always happen. This is an immutable law of the universe. Some tests are better than others, and tables like this are necessary to understand how to rate how well a particular test performs.
