ci2num function

Convert a proportion and credible interval to a numerator and denominator

Estimate the number of events and denominator that contain roughly equivalent information to an estimate and uncertainty interval for a proportion, by interpreting the estimate and interval as a Beta posterior arising from a vague Beta(0.5,0.5) prior updated with the data consisting of that number and denominator.

ci2num(est, lower, upper, epsilon = 0.5, denom0 = 1000)

Arguments

• est: Point estimate
• lower: Lower 95% credible limit
• upper: Upper 95% credible limit
• epsilon: If any of lower are zero, then they are replaced by the minimum of epsilon and est/2. Similarly values of 1 for upper are replaced by the maximum of 1-epsilon and (1+est)/2.
• denom0: Denominator to use as a default when the point estimate is exactly 0 or 1 (which is not compatible with the beta distribution). Should correspond to a guess of the population size used to produce the estimate, which should be no greater than the actual population of the area, and usually less. Should be either a scalar, or a vector of the same length as est (though note if it is a vector, then only the elements where est is 1 or 0 get used).

Returns

A data frame with elements num and denom corresponding to the supplied estimate and limits.

Details

Based on fitting a Beta distribution by least squares, using the method provided by the SHELF package.

Requires that the estimate and upper and lower limits are all distinct (except that est=0 is allowed and handled specially for convenience, see denom0). Vectors of estimates and limits may be supplied.

Examples

est <- 3.00 / 100 
upper <- 3.52 / 100 
lower <- 2.60 / 100 
ci2num(est, lower, upper)

References

Oakley (2020). SHELF: Tools to Support the Sheffield Elicitation Framework. R package version 1.7.0. https://CRAN.R-project.org/package=SHELF