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Live Long--And Have Confidence in Your Results

confidence intervals can tell you more about statistical results than odds ratios

Ever feel frustrated with the flip-floppy results reported in the medical news? Today a cup of coffee will lead you to an early grave. Tomorrow it will ensure that you’ll be dancing a jig on your 99th birthday. Every day, it seems there’s a new study that contradicts a previous finding.

 

In response, some people throw up their hands in helplessness. Others shrug—then chug another double-shot of espresso. Some even blame statistics, saying “you can use them to prove anything.”

The irony is, statistics itself isn’t the problem. In fact, statistics may be the critical tool to make sense of these seemingly contradictory results.

Does an apple a day really keep the oncologist away?

A few years back, researchers compared the odds of developing various cancers in 2 groups of people—those who ate at least one apple a day and those who didn't. They found that the daily apple-eaters had, on average, 0.79 times less chance of oral cancer, 0.75 less times chance of esophageal cancer, 0.82 less times chance of breast cancer, as well as lower odds of other cancers. As a result, the researchers reported a “consistent inverse association between apples and risk of various cancers.”

You can imagine what the headlines in the media might have blared the next day:

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newspaper header
 Grandma really did know best!  
 Eating an apple a day can prevent cancer.


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But what’s missing from this picture? Statistically, quite a lot. The confidence interval, for starters.

The confidence interval helps you evaluate the certainty of an estimate. It gives you a bigger picture of reality than just an “average” that might be reported in the news.

Take a look at the 95% confidence intervals for the odds of three types of cancers for the apple-a-day group compared to the apple-avoiders:

odds table

What do these CIs tell us? We can be 95% confident the true odds ratio of developing each cancer falls within the interval shown. So, for esophageal cancer, the confidence interval is fairly wide and goes from about half as likely (0.54) to slightly greater odds (1.03). These values, remember, refer to the relative odds of developing cancer for the apple-a-day group compared to the other group.

Notice that all the intervals include a value 1, which indicates “even” odds of developing each cancer for both groups.

So, looking at the CIs, we can’t rule out the possibility that the two groups may have the same odds of developing these cancers. Now suppose another study comes along and reports average odd ratios very close to 1 for these cancers for these two groups. That finding wouldn't blatantly contradict the results of this study. But if you  only looked at the odds ratios, and not the CIs, you might think they did.

If you use Minitab Statistical Software, you’ll see confidence intervals automatically included in your output for many analyses, including hypothesis tests, ANOVA, regression, and many others. These intervals give you a powerful way to gain deeper insight into your results.

So here’s my advice, which I promise not to contradict tomorrow...
If you like apples, go ahead and eat one every day. But in between bites, don’t forget to look at the confidence intervals in your output. 

Reference: Does an apple a day keep the oncologist away? Ann Oncol 2005;16(11):1841-4.

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