Confidence Ellipse

A graphical way of representing confidence intervals in cost-effectiveness analysis or cost-utility analysis. Confidence ellipses show where a specified percentage (such as 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 comparator, so that we are in the north east quadrant of the cost-effectiveness plane shown in the figure. The slope of rays such as a' and b' shows the incremental cost-effectiveness ratio (AC/AE) 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' and b' 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 AC and AE. The confidence ellipse is more circular when two variables are uncorrelated. Cf. Confidence Box.

Confidence Ellipsoid

Same (roughly speaking) as confidence ellipse.

64 Confidence Interval Confidence Interval

The range of values within which a population parameter such as the population mean or variance is expected to lie with a given degree of confidence. The convention is to set the 'confidence' level at 95 per cent, in the (frequentist) sense that, with repeated sampling, there is a 95 per cent chance that the true parameter value lies within that range.

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