prec_riskdiff {presize}

Sample size or precision for risk difference

Description

prec_riskdiff returns the risk difference and the sample size or the precision for the provided proportions.

Usage

prec_riskdiff(
  p1,
  p2,
  n1 = NULL,
  conf.width = NULL,
  r = 1,
  conf.level = 0.95,
  method = c("newcombe", "mn", "ac", "wald"),
  ...
)

Arguments

p1

risk among exposed.

p2

risk among unexposed.

n1

number of patients in exposed group.

conf.width

precision (the full width of the confidence interval).

r

allocation ratio (relative size of exposed and unexposed cohort (n1 / n2)).

conf.level

confidence level.

method

Exactly one of newcombe (default), mn (Miettinen-Nurminen), ac (Agresti-Caffo), wald. Methods can be abbreviated.

...

other options to uniroot (e.g. tol)

Details

Exactly one of the parameters n1 or conf.width must be passed as NULL, and that parameter is determined from the other.

Newcombe (newcombe) proposed a confidence interval based on the wilson score method for the single proportion (see prec_prop). The confidence interval without continuity correction is implemented from equation 10 in Newcombe (1998).

Miettinen-Nurminen (mn) provide a closed from equation for the restricted maximum likelihood estimate . The implementation is based on code provided by Yongyi Min on https://users.stat.ufl.edu/~aa/cda/R/two-sample/R2/index.html.

Agresti-Caffo (ac) confidence interval is based on the Wald confidence interval, adding 1 success to each cell of the 2 x 2 table (see Agresti and Caffo 2000).

uniroot is used to solve n for the newcombe, ac, and mn method.

References

Agresti A (2003) Categorical Data Analysis, Second Edition, Wiley Series in Probability and Statistics, doi:10.1002/0471249688.

Agresti A and Caffo B (2000) Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures, The American Statistician, 54(4):280-288.

Miettinen O and Nurminen M (1985) Comparative analysis of two rates, Statistics in Medicine, 4:213-226.

Newcombe RG (1998) Interval estimation for the difference between independent proportions: comparison of eleven methods, Statistics in Medicine, 17:873-890.

Fagerland MW, Lydersen S, and Laake P (2015). Recommended confidence intervals for two independent binomial proportions, Statistical methods in medical research 24(2):224-254.

Examples

# proportions of 40 and 30\%, 50 participants, how wide is the CI?
prec_riskdiff(p1 = .4, p2 = .3, n1 = 50)
# proportions of 40 and 30\%, 50 participants, how many participants for a CI 0.2 wide?
prec_riskdiff(p1 = .4, p2 = .3, conf.width = .2)

# Validate Newcombe (1998)
prec_riskdiff(p1 = 56/70, p2 = 48/80, n1 = 70, r = 70/80, met = "newcombe")  # Table IIa
prec_riskdiff(p1 = 10/10, p2 = 0/10, n1 = 10, met = "newcombe")  # Table IIh

# multiple scenarios
prec_riskdiff(p1 = c(56/70, 9/10, 6/7, 5/56),
              p2 = c(48/80, 3/10, 2/7, 0/29),
              n1 = c(70, 10, 7, 56),
              r = c(70/80, 1, 1, 56/29),
              method = "wald")