# Confidence Ellipse

## Definition

### Health Economics

- Graphical way of representing confidence intervals in cost-effectiveness or cost-utility analyses. Confidence ellipses show where a specified percentage (e.g. 95 per cent) of the data in a scatter plot will lie. Consider a health care technology that is costlier but also more effective than its (single) comparator, so we are in the north-east quadrant of the cost-effectiveness plane shown in the figure. The slope of rays such as a 9 and b 9 show the incremental cost-effectiveness ratio (ΔC/ΔE) of the technology under investigation relative to an alternative (control). The steeper the ray, the greater the marginal cost per marginal gain in output compared with the comparator. The upper and lower confidence limits of incremental cost are plotted against the upper and lower confidence limits of the effectiveness measure in the form of an ellipse (inside the confidence box). Rays a 9 and b 9 are the outer limits of the confidence interval (usually 95 per cent) and will lie within the rays defined by the corners of the confidence box. Confidence ellipses are visual indicators of correlation: they are stretched out from south-west to north-east if there is a positive covariance between ΔC and ΔE. The confidence ellipse is more circular when two variables are uncorrelated.

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