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CONFIDENCE INTERVALS




You will often see the results of a study reported in a format of  45%(CI: 40% - 50%).   The first number is the mean of the results.  The numbers in parenthesis represent the confidence interval.  A confidence interval tells us the range that includes the true relative risk reduction 95% of the time.  The mean result we can expect is, for example, a 45% reduction in risk of mortality.  If we were to conduct the same study an infinte number of times, we can expect that 95% of the time the mean reduction in mortality will fall somewhere between 40% and 50%.  


There are two qualities that a confidence interval may have that could bring the results into question.  One type of confidence interval is one that is particularly wide.  If the mean, again, is a 45% reduction in the risk of mortality but the confidence interval runs from 1% to 99%, this tells us that the researchers had a very small sample size and thus the results had a much wider spread.  A fairly large sample produces much narrower results.

In daily conversation, we say that a penny, when flipped, has a 50% chance of landing heads-side up.  However, when asked to bet on whether a single penny would in fact land heads-side up 5 times out of ten, you'd be a little more hesitant to back up that statistic.  10 times simply isn't enough to produce the "true" 50% likelihood.  However, if the penny were flipped 1,000 times you might come closer to that 50% probability, although there is a 95% chance that it will in fact fall within the 45-55% probability.  The larger the number of chances, the closer to real likelihood the probability becomes.

When there is a wide confidence interval, you will need to take into consideration the characteristics of your specific patient and determine if  your patient is more likely to fall closer to the lower end of the interval or the higher end.

It may occur that the confidence interval crosses 0.  With a 45% mean reduction in mortality, you may experience a confidence interval that runs between -2 and 53.  In addition to being a fairly wide confidence interval (and this a small sample), the crossing of 0 tells us that the results are not statistically significant.  While this is interesting to biostatisticians, medical practitioners are more interested in results that are clinically significant.  Results can be clinically significant without being statistically significant.  A negative confidence interval tells us that the results were opposite the expected outcome.  While there is a mean probability of 45% reduction in mortality and no greater than a 53% chance, it is also true that for some subset of the population studied, there is a 2% chance of an increase in mortality.  

Again, it falls to your own clinical judgment to determine whether your specific patient's characteristics lean more towards the increased mortality or decreased mortality as described in the study.

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