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

Source: R/moverci.R
jeffreysci.Rd

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,
  ...
)

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.

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.

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

Author

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

Examples

# Jeffreys method:
jeffreysci(x = 5, n = 56)
#> $estimates
#>           lower        est     upper x  n
#> [1,] 0.03489147 0.09177968 0.1846509 5 56
#> 
#> $call
#> distrib   level      cc     adj      ai      bi 
#>   "bin"  "0.95"     "0"  "TRUE"   "0.5"   "0.5" 
#>