prec_riskdiff returns the risk difference and the sample size or the
precision for the provided proportions.
prec_riskdiff(
p1,
p2,
n1 = NULL,
conf.width = NULL,
r = 1,
conf.level = 0.95,
method = c("newcombe", "mn", "ac", "wald"),
...
)risk among exposed.
risk among unexposed.
number of patients in exposed group.
precision (the full width of the confidence interval).
allocation ratio (relative size of exposed and unexposed cohort
(n1 / n2)).
confidence level.
Exactly one of newcombe (default), mn
(Miettinen-Nurminen), ac (Agresti-Caffo), wald. Methods can
be abbreviated.
other options to uniroot (e.g. tol)
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.
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.
# proportions of 40 and 30\%, 50 participants, how wide is the CI?
prec_riskdiff(p1 = .4, p2 = .3, n1 = 50)
#> Warning: more than one method was chosen, 'newcombe' will be used
#>
#> precision for a risk difference with newcombe confidence interval
#>
#> p1 p2 n1 n2 ntot r delta lwr upr conf.width conf.level
#> 1 0.4 0.3 50 50 100 1 0.1 -0.08510109 0.2759788 0.3610798 0.95
# 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)
#> Warning: more than one method was chosen, 'newcombe' will be used
#>
#> sample size for a risk difference with newcombe confidence interval
#>
#> p1 p2 n1 n2 ntot r delta lwr upr conf.width
#> 1 0.4 0.3 169.8394 169.8394 339.6787 1 0.1 -0.001408915 0.1985911 0.2
#> conf.level
#> 1 0.95
# Validate Newcombe (1998)
prec_riskdiff(p1 = 56/70, p2 = 48/80, n1 = 70, r = 70/80, met = "newcombe") # Table IIa
#>
#> precision for a risk difference with newcombe confidence interval
#>
#> p1 p2 n1 n2 ntot r delta lwr upr conf.width conf.level
#> 1 0.8 0.6 70 80 150 0.875 0.2 0.05243147 0.3338727 0.2814412 0.95
prec_riskdiff(p1 = 10/10, p2 = 0/10, n1 = 10, met = "newcombe") # Table IIh
#>
#> precision for a risk difference with newcombe confidence interval
#>
#> p1 p2 n1 n2 ntot r delta lwr upr conf.width conf.level
#> 1 1 0 10 10 20 1 1 0.6075094 1 0.3924906 0.95
# 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")
#>
#> precision for a risk difference with wald confidence interval
#>
#> p1 p2 n1 n2 ntot r delta lwr upr
#> 1 0.80000000 0.6000000 70 80 150 0.875000 0.20000000 0.05750490 0.3424951
#> 2 0.90000000 0.3000000 10 10 20 1.000000 0.60000000 0.26052428 0.9394757
#> 3 0.85714286 0.2857143 7 7 14 1.000000 0.57142857 0.14811614 0.9947410
#> 4 0.08928571 0.0000000 56 29 85 1.931034 0.08928571 0.01460024 0.1639712
#> conf.width conf.level
#> 1 0.2849902 0.95
#> 2 0.6789514 0.95
#> 3 0.8466249 0.95
#> 4 0.1493709 0.95