Propagating Imprecision: Combining Confidence Intervals from Independent Sources

The Propagating Imprecision (PropImp) approach is a general, easily implemented method for calculating confidence intervals for a function of two or more parameters which are estimated separately. It extends the single-parameter substitution method of Daly (1998 Daly , L. E. ( 1998 ). Confidence limits made easy: interval estimation using a substitution method . Amer. J. Epidemiol. 147 : 783 – 790 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) and is very flexible and widely applicable. It does not assume linearity, but normally presupposes monotonicity over the working range of the parameters being estimated. We show several examples, and obtain some coverage, location, and width results for intervals derived by this approach. In many two-parameter applications, the MOVER approach yields a simpler solution, but PropImp is sometimes applicable when MOVER cannot be used.