ratesci (version 1.0.0)

clusterpci: Score confidence intervals for a single binomial rate from clustered data.

Description

Asymptotic Score confidence intervals for a proportion estimated from a clustered sample, as decribed by Saha et al. 2016. With optional skewness correction to improve interval location (to be evaluated).

Usage

clusterpci(x, n, level = 0.95, skew = TRUE, cc = FALSE, theta0 = 0.5)

Value

A list containing the following components:

estimates

the estimate and confidence interval for p and the specified confidence level, along with estimates of the ICC and the variance inflation factor, xihat.

pval

one-sided significance tests against the null hypothesis that theta >= or <= theta0 as specified.

call

details of the function call.

Arguments

x

Numeric vector of number of events per cluster.

n

Numeric vector of sample sizes per cluster.

level

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

skew

Logical (default TRUE) indicating whether to apply skewness correction or not. (To be evaluated)

cc

Number or logical (default FALSE) specifying (amount of) continuity adjustment. Numeric value is taken as the gamma parameter in Laud 2017, Appendix S2 (default 0.5 for 'conventional' adjustment if cc = TRUE).

theta0

Number to be used in a one-sided significance test (e.g. non-inferiority margin). 1-sided p-value will be <0.025 iff 2-sided 95\ excludes theta0.

Author

Pete Laud,

References

Saha K, Miller D and Wang S. A comparison of some approximate confidence intervals for a single proportion for clustered binary outcome data. Int J Biostat 2016; 12:1–18

Short MI et al. A novel confidence interval for a single proportion in the presence of clustered binary outcome data. Stat Meth Med Res 2020; 29(1):111–121

Examples

  # Data example from Liang 1992, used in Saha 2016 and Short 2020:
  # Note Saha states the ICC estimate is 0.1871 and Short makes it 0.1855.
  # I agree with Short - CI limits differ from Saha to the 4th dp.
  x <- c(rep(c(0, 1), c(36, 12)),
         rep(c(0, 1, 2), c(15, 7, 1)),
         rep(c(0, 1, 2, 3), c(5, 7, 3, 2)),
         rep(c(0, 1, 2), c(3, 3, 1)),
         c(0, 2, 3, 4, 6))
  n <- c(rep(1, 48),
         rep(2, 23),
         rep(3, 17),
         rep(4, 7),
         rep(6, 5))
  # Wilson-based interval
  clusterpci(x, n, skew = FALSE)
  # Skewness-corrected version
  clusterpci(x, n, skew = TRUE)
  # With continuity adjustment
  clusterpci(x, n, skew = FALSE, cc = TRUE)