jeffreysci: Jeffreys and other approximate Bayesian confidence intervals...

In PeteLaud/ratesci: Confidence Intervals for Comparisons of Binomial or Poisson Rates

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 correction" parameter.

Usage

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

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 correction". 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(s)

Pete Laud, [e-mail]

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

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

PeteLaud/ratesci documentation built on July 22, 2023, 1:12 p.m.