So, What’s the Chance?

What are my chances of dying from prostate cancer? What are my chances of getting mugged tonight? Just what are my chances? Well, it depends on whom you’re asking.

Statistics can be a very helpful tool for figuring out the likelihood that something may happen. Should I pack an umbrella for tomorrow; should I double down on this hand; do I need flood insurance? These are all important questions and our society depends on having some kind of numeric measure on which to rely. Fortunately, we have statistics. There is a 40% chance of showers tomorrow; you should never double down on a 16; no, you live significantly outside the 100 year flood plane. But when it comes to our health, should we rely on the numbers that represent our chances of dying or recovery? The short answer: Unless you’re sure you are looking at the absolute risk and not the relative risk, no, you shouldn’t.

Let me explain. Here is an example from Scientific American Mind:

In October 1995 the U.K. Committee on Safety of Medicines warned that third-generation oral contraceptive pills increased the likelihood of potentially life-threatening blood clots in the legs or lungs twofold—that is, by 100 percent. This information was passed on in “Dear Doctor” letters to 190,000 general practitioners, pharmacists and directors of public health and in an emergency announcement to the media. The news caused great anxiety, and women stopped taking the pill, which led to an estimated 13,000 additional abortions in the following year in England and Wales. For every additional abortion, there was also one extra birth, including some 800 more conceptions among girls younger than 16. (Ironically, abortions and pregnancies are associated with an increased risk of thrombosis that exceeds that of the third-generation pill.)

Such panic could have been avoided had the data been reported in a more straightforward manner. The evidence showed that about one in every 7,000 women who took the second-generation pill had a blood clot; this number increased to two in 7,000 among women who took third-generation pills. That is, the absolute risk increase was only one in 7,000 even though the relative risk increase was indeed 100 percent. Absolute risks are typically small numbers, whereas the corresponding relative changes tend to look big—particularly when the base rate is low.

This passage should help illuminate the difference between the two risks, and how the use of relative risk is completely unreliable. One cannot truly infer the risk when risks are stated as “two-fold” or “fifty percent increase” because you have no clue what the baseline they are comparing to is. Unfortunately, this makes for great advertisements, campaigning rhetoric for politicians or fear tactics for control.

Statistical Abuse

Let’s use one of the most successful medical marketing campaigns in the US — breast cancer awareness. Millions and millions of dollars have been spent on advertising campaigns that are meant to inform and to “wake you up” to the risks of breast cancer. Now that everyone has been “informed,” is such heightened awareness a good thing? Well, that is a tough but important question.

If you have paid attention to the current headlines in medicine, you may have seen these headlines: Study: 1 in 3 breast cancer patients overtreated, Five Myths About Breast Cancer and Breast Cancer Treated Too Often. It sounds as if the doctors and patients aren’t understanding the actual risks of breast cancer. Let’s take a look at two different ways of making use of statistics.

Here are some marketing stats for breast cancer (snipped from BreastCancer.org): “Breast cancer incidence in women in the United States is 1 in 8 (about 13%).” As well as, “A woman’s risk of breast cancer approximately doubles if she has a first-degree relative (mother, sister, daughter) who has been diagnosed with breast cancer.”

Okay, so let’s dig a little deeper. The BreastCancer.org website used the 1 in 8 statistic (or 13%) without the disclaimer that this stat is a lifetime risk (what I call a projected risk), not a yearly risk like most other statistics (what I would call a present risk). If we look at the absolute yearly risk, it is one in every 750 women, or 0.1%, will be diagnosed with breast cancer. One can obviously see the massive difference between these two percentages. A 25 year old getting out of college does not have a 1 in 8 chance of developing breast cancer any time soon since this stat is a lifetime risk. For that year, the 25 year old has a 0.1% chance of being diagnosed.

Now I am not trying to minimize the risk or dangers of breast cancer, but fear can make us overreact to benign blips on the mammography radar. Leading to unnecessary procedures and dangerously toxic therapies.

The second marketing statistic refers to a genetic predisposition for breast cancer. Your chance “approximately doubles” if you have a relative that is diagnosed with breast cancer? Hmm, let’s look at this closely. The only known genetic cause of breast cancer is the gene BRCA1 and the gene BRCA2. Having these genes increases your risk by 60 to 80%, but considering “only 5 to 10 percent of those diagnosed with breast cancers have a family history.” Your mother or sister that was diagnosed with breast cancer is only 5 to 10% likely to have had breast cancer because of BRCA1 and BRCA2. That means your absolute risks are not 60 to 80% (which I might add is not double) unless your mother or sister was in the 5 to 10% bracket. Even then, you may have lucked out and not received that particular gene.

As you can see, none of this is nearly as black and white as they make it out to be. But then again, people make a large amount of money from keeping everything black and white.

Giuliani’s Relative Abuses

With relative risks being all the rage, you can bet that politicians won’t hesitate to abuse statistical data for their own political gain. Rudy Giuliani is one that has been caught with his statistical pants down. During the presidential primaries in 2008, it seems that he used some statistical data to “prove” how “dangerous” socialized medicine is for older men.

[Giuliani] apparently used data from the year 2000, when 49 British men in every 100,000 were diagnosed with prostate cancer, of whom 28 died within five years—about 44 percent. Using a similar approach, he cited a corresponding 82 percent five-year survival rate in the U.S., suggesting that Americans with prostate cancer were twice as likely to survive as their British counterparts were. That implication, however, is false because these survival statistics largely reflect diagnostic differences between the two countries rather than better treatment and prolonged survival in the U.S.

To understand why, imagine a group of prostate cancer patients diagnosed (by their symptoms) at age 67 in the U.K., all of whom die at 70. Each survived only three years, so the five-year survival of this group is 0 percent. Now imagine that the same group is diagnosed in the U.S., where doctors detect most prostate cancer by screening for prostate-specific antigens (PSA). (The PSA test is not routinely used in Britain.) These U.S. patients are diagnosed earlier, at age 60, but they all still die at age 70. All have now survived 10 years, and thus their five-year survival rate is 100 percent. Even though the survival rate has changed dramatically, nothing has changed about the time of death. This example shows how setting the time of diagnosis earlier can boost survival rates (lead-time bias), even if no life is prolonged or saved.

– Scientific American Mind

As you can see, one can never run out of ways to abuse the data to give a desired outcome. What these dangerous statisticians don’t take into consideration is the amount of unnecessary procedures that are related to premature diagnosis. Just like breast cancer, there are conditions of the prostate that can trigger a false positive, and the following procedures can very easily lead to incontinence and impotence.

Know Your Data

Hopefully, by now, you are wary of everything. Good, you should be. Even though it sounds scientific, it probably is not. What has to be accounted for is who is benefiting from this misinformation. Propaganda is everywhere, so the most important thing you can do is learn your basic statistics. Learn the difference between absolute data and relative data, pay attention to the measures that are used and/or find the raw data by digging past the surface.

Any ignorance one may have in how to interpret numbers is their power in manipulating your perception. Learn statistics and demand absolutism in your politics and medicine.