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p-value

Some things in life are certain. We are 100% sure that every human being will die at some point in their lifetime. Other things are close to 100% certain, but there is a small chance of an alternative outcome. When a person has a coronary angiogram to look at the arteries in their heart, we are 99.9% certain that they will have an uneventful procedure, but 0.1% of the time there will be a major complication such as bleeding, stroke, or a heart attack. If the person has had previous heart attacks or other illnesses, this chance increases and might reach as much as 2%. In still other situations, the chance of an outcome is much less certain. For example, the chance of surviving for 5 years after a diagnosis of bowel cancer may vary from less than 10% to near 100%, depending on the severity of the cancer.

There is a lot of uncertainty in medicine and in medical research, and yet media reports of health and science often give the impression of “black-and-white”, exact figures. The yoghurt in my fridge says “Best before 15/11/09”. Does that mean that all the yoghurts go off at the same time on the 15th of November? Of course not. The reality is that this date is an estimate and the date when my yoghurt goes off is within a range. Some yoghurts will go off earlier than the best before date, and others will go off after the best before date. This range is called a “confidence interval”. Confidence intervals can be set so that most of the possible results will be within that range. It might be that 99.9% of yoghurts are fine if eaten before 15/11/09, but this means that 0.1% of yoghurts will go off before or after that date.

In yesterday’s example, immobilisation for 15 minutes immediately after artificial insemination increased the relative risk of a successful pregnancy by 50%. However, the increase in relative risk actually lies between 10% and 120%. Moreover, the increase in risk is only in this range 95% of the time, and 5% of the time, it is outside of this range. A recent study of the UK’s GP database looked at the effect of statin therapy on future risk of gallstones and gallbladder surgery . The researchers showed that the odds of getting gallstones if you were on long-term statin therapy were 66% of the odds of gallstones if you were not taking statin therapy. However, the 95% confidence interval for the odds ratio was 59% to 70%. Therefore, long-term statin therapy seems to convincingly reduce the risk of gallstones and gallbladder surgery by a third. By convention, we accept 95% confidence intervals, and the narrower the range, the more certain we are of the finding.

In the New England Journal this week, American researchers were interested in whether or not the use of the heart-lung machine (“cardiopulmonary bypass”). during coronary-artery bypass graft (CABG) surgery affected death rates. Scientists test their results using hypotheses. The “null hypothesis” in this case was that use of the heart-lung machine during CABG surgery would make no difference to the death rate after 1 year. The “alternative hypothesis” was that use of the heart-lung machine during CABG surgery would make a difference to the death rate after 1 year. The alternative hypothesis was proved: (a) use if the heart-lung machine led to lower death rate and (b) less blockage in the grafted arteries at 1 year. By testing these results against the null hypothesis, we get a “p-value”. The p-value is simply the chance of the result occurring due to chance alone. Again, the cut-off is a p-value of 0.05 or 5%. For the death rate, the p value was 0.04 or 4%, whereas the p-value for the difference in graft blockage at 1 year was 0.01 or 1%. So the combination of confidence intervals and p-values tells us about how reliable a result is and with the rule of 5%, anybody can spot a chance finding and assess statistical significance.

Lesson 3

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