jeffreysci: Jeffreys and other approximate Bayesian confidence intervals for a single binomial or Poisson rate.

Description

Generalised approximate Bayesian confidence intervals based on a Beta (for binomial rates) or Gamma (for Poisson rates) conjugate priors. Encompassing the Jeffreys method (with Beta(0.5, 0.5) or Gamma(0.5) respectively), as well as any user-specified prior distribution. Clopper-Pearson method (as quantiles of a Beta distribution as described in Brown et al. 2001) also included by way of a "continuity adjustment" parameter.

Usage

jeffreysci(
  x,
  n,
  ai = 0.5,
  bi = 0.5,
  cc = 0,
  level = 0.95,
  distrib = "bin",
  adj = TRUE,
  ...
)

Value

A list containing the following components:

estimates: a matrix containing estimated rate(s), and corresponding approximate Bayesian confidence interval, and the input values x and n.
call: details of the function call.

Arguments

x: Numeric vector of number of events.
n: Numeric vector of sample sizes (for binomial rates) or exposure times (for Poisson rates).
ai, bi: Numbers defining the Beta prior distribution (default `ai = bi = 0.5`` for Jeffreys interval). Gamma prior for Poisson rates requires only ai.
cc: Number or logical specifying (amount of) "continuity adjustment". cc = 0 (default) gives Jeffreys interval, cc = 0.5 gives the Clopper-Pearson interval (or Garwood for Poisson). A value between 0 and 0.5 allows a compromise between proximate and conservative coverage.
level: Number specifying confidence level (between 0 and 1, default 0.95).
distrib: Character string indicating distribution assumed for the input data:
"bin" = binomial (default);
"poi" = Poisson.
adj: Logical (default TRUE) indicating whether to apply the boundary adjustment recommended on p108 of Brown et al. (set to FALSE if informative priors are used).
...: Other arguments.

Author

Pete Laud, p.j.laud@sheffield.ac.uk

References

Laud PJ. Equal-tailed confidence intervals for comparison of rates. Pharmaceutical Statistics 2017; 16:334-348.

Brown LD, Cai TT, DasGupta A. Interval estimation for a binomial proportion. Statistical Science 2001; 16(2):101-133

Examples

Run this code

# Jeffreys method:
jeffreysci(x = 5, n = 56)

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