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Selected confidence intervals for the single binomial or Poisson rate.

Source: R/rateci.R
rateci.Rd

Confidence intervals for the single binomial or Poisson rate. Including SCAS and Jeffreys intervals, with or without continuity adjustment, and 'exact' Clopper-Pearson/Garwood or mid-p intervals, and another version of the exact or mid-p interval derived from Beta distributions (from p.115 of Brown et al.), with an equivalent using Gamma distributions for a Poisson rate. Note that these closed-form calculations exactly match the iterative calculations for the exact interval (when cc = TRUE), but not for the mid-p interval (cc = FALSE) This function is vectorised in x, n.

Usage

rateci(
  x,
  n,
  distrib = "bin",
  level = 0.95,
  std_est = TRUE,
  cc = FALSE,
  precis = 8
)

Arguments

x

Numeric vector of number of events.

n

Numeric vector of sample size (for binomial rate) or exposure times (for Poisson rate).

distrib

Character string indicating distribution assumed for the input data: "bin" = binomial (default), "poi" = Poisson.

level

Number specifying confidence level (between 0 and 1, default 0.95).

std_est

logical, specifying if the crude point estimate for the proportion value x/n should be returned (TRUE, default) or the method-specific alternative point estimate consistent with a 0% confidence interval (FALSE).

cc

Number or logical (default FALSE) specifying continuity adjustment.

precis

Number (default 8) specifying precision (i.e. number of decimal places) to be used in root-finding subroutine for the exact confidence interval. (Note all other methods use closed-form calculations so are not affected.)

Value

A list containing, for each method, a matrix containing lower and upper confidence limits and point estimate of p for each value of x and n. Methods shown depend on the cc parameter, which specifies whether the continuity adjustment is applied to the SCAS and Jeffreys methods. The corresponding 'exact' method is Clopper-Pearson/Garwood if cc = TRUE and mid-p if cc = FALSE. The last list item contains details of the function call.

References

Laud PJ. Equal-tailed confidence intervals for comparison of rates. Pharmaceutical Statistics 2017; 16:334-348. (Appendix A.4)

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

Garwood F. Fiducial limits for the Poisson distribution. Biometrika 1936; 28(3-4):437, doi:10.1093/biomet/28.3-4.437.

Author

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