# *Geek Box: Confidence Intervals

#### *Geek Box: Confidence Intervals

You may want to read the ‘Results’ section again having read this, but let’s break down how to use confidence intervals to your advantage when interpreting research, especially epidemiological research.

Results are expressed according to the risk estimator that the investigators have used; relative risk [‘RR’, hazard ratios ‘HR’], or odds ratios [‘OR’], which depends on the type of analysis undertaken.

Because all of these calculations are against a reference group, the reference is 1.0; anything above 1.0 is a positive association, or increased risk/odds, while anything below 1.0 is an inverse association, or reduced risk/odds.

For example, HR 1.23 means the hazard ratio is a 23% [i.e., 23, after the decimal] increase in risk. Conversely, HR 0.82 means an 18% reduction in risk [i.e., 100-82 = 18].

Now, this is generally the part of the result that people hone in on, but a more refined approach is to look at the certainty, or confidence, that the result would fall within a certain range 95% of the time. Enter ‘confidence intervals’, which have also been described as the ‘coverage probability’. This is the probability that the interval expressed includes or covers the true effect size.

For example, let’s say the HR is 1.23 [a 23% increase], and the confidence interval for that result is 1.17-1.39; this shows that the entire interval is in a positive association range, and is significant. This indicates that the minimum increase in risk is 17% [1.17], and the maximum increase is 39% [1.39]. The HR may indicate a 23% increase in risk, but the true effect could be anywhere from 17% to 39%. This type of result warrants attention, because the true effect would still be positive.

The inverse is true for reduced risk; if you read [HR 0.82, 95% CI 0.76-0.93], you can see that while there was an 18% reduction in risk, the maximum reduction was 24% [0.76] and the minimum reduction was 7% [0.93]. This is also significant, as the true effect would be within an internal of reduced risk.

However, where a CI straddles 1.0, and is very wide, this result is practically meaningless, as we cannot deduce where the true effect would lie; such results are statistically insignificant. For example, HR 1.04, 95% CI 0.89-1.15 tells us nothing of meaning in inferring the risk associated with the exposure of interest.

Start to focus more on confidence intervals in interpreting findings, they provide a more refined assessment of the result than the risk ratio alone.