Using the confidence interval confidently

Abstract

Biomedical research is seldom done with entire populations but rather with samples drawn from a population. Although we work with samples, our goal is to describe and draw inferences regarding the underlying population. It is possible to use a sample statistic and estimates of error in the sample to get a fair idea of the population parameter, not as a single value, but as a range of values. This range is the confidence interval (CI) which is estimated on the basis of a desired confidence level. Calculation of the CI of a sample statistic takes the general form: CI = Point estimate ± Margin of error, where the margin of error is given by the product of a critical value (z) derived from the standard normal curve and the standard error of point estimate. Calculation of the standard error varies depending on whether the sample statistic of interest is a mean, proportion, odds ratio (OR), and so on. The factors affecting the width of the CI include the desired confidence level, the sample size and the variability in the sample. Although the 95% CI is most often used in biomedical research, a CI can be calculated for any level of confidence. A 99% CI will be wider than 95% CI for the same sample. Conflict between clinical importance and statistical significance is an important issue in biomedical research. Clinical importance is best inferred by looking at the effect size, that is how much is the actual change or difference. However, statistical significance in terms of P only suggests whether there is any difference in probability terms. Use of the CI supplements the P value by providing an estimate of actual clinical effect. Of late, clinical trials are being designed specifically as superiority, non-inferiority or equivalence studies. The conclusions from these alternative trial designs are based on CI values rather than the P value from intergroup comparison.

Keywords: Confidence interval (CI); P value; clinical significance; confidence level; statistical inference.

Figure 1

The positioning of 95% confidence limits around the point estimate in the test intervention group to establish non-inferiority, equivalence or superiority in clinical trials. The line of no difference is indicated by zero; negative delta indicates the non-inferiority margin or the lower bound of the equivalence margin, while positive delta indicates upper bound of the equivalence margin or the superiority margin.