CONFIDENCE-LIMITS MADE EASY - INTERVAL ESTIMATION USING A SUBSTITUTION METHOD

The use of confidence intervals has become standard in the presentatio n of statistical results in medical journals. Calculation of confidenc e limits can be straightforward using the normal approximation with an estimate of the standard error, and in particular cases exact solutio ns can be obtained from published tables. However, for a number of com monly used measures in epidemiology and clinical research, formulae ei ther are not available or are so complex that calculation is tedious. The author describes how an approach to confidence interval estimation which has been used in certain specific instances can be generalized to obtain a simple and easily understood method that has wide applicab ility. The technique is applicable as long as the measure for which a confidence interval is required can be expressed as a monotonic functi on of a single parameter for which the confidence limits are available . These known confidence limits are substituted into the expression fo r the measure-giving the required interval. This approach makes fewer distributional assumptions than the use of the normal approximation an d can be more accurate. The author illustrates his technique by calcul ating confidence intervals for Levin's attributable risk, some measure s in population genetics, and the ''number needed to be treated'' in a clinical trial. Hitherto the calculation of confidence intervals for these measures was quite problematic. The substitution method can prov ide a practical alternative to the use of complex formulae when perfor ming interval estimation, and even in simpler situations it has major advantages.