ratesci (version 0.5.0)

pairbinci: Confidence intervals for comparisons of paired binomial rates.

Description

Confidence intervals for the rate (or risk) difference ('RD'), rate ratio ('RR') or odds ratio ('OR'), for paired binomial data. (For paired Poisson rates, suggest use the tdasci function with distrib = "poi", and weighting = "MH", with pairs as strata.) This function applies the score-based Tango and Tang methods for RD and RR respectively, with iterative and closed-form versions, as well as an experimental method using the stratified TDAS method with pairs as strata. Also includes MOVER options using the Method of Variance Estimates Recovery for paired RD and RR. For OR, intervals are produced based on transforming various intervals for the single proportion, including SCAS, mid-p and Jeffreys. All methods have options for continuity correction, and the magnitude of correction can be customised.

Usage

pairbinci(
  x,
  contrast = "RD",
  level = 0.95,
  cc = FALSE,
  cctype = "constant",
  method_RD = "Score_closed",
  method_RR = "Score_closed",
  method_OR = "SCAS",
  moverbase = "SCAS",
  theta0 = NULL,
  precis = 6
)

Value

A list containing the following components:

data

the input data in 2x2 matrix form

estimates

the requested contrast, with its confidence interval and the specified confidence level

pval

the corresponding 2-sided significance test against the null hypothesis that p_1 = p_2 (McNemar's test), and one-sided significance tests against the null hypothesis that theta >= or <= theta0 as specified

Arguments

x

A numeric vector object specified as c(a, b, c, d) where: a is the number of pairs with the event (e.g. success) under both conditions (e.g. treated/untreated, or case/control) b is the count of the number with the event on condition 1 only (= n12) c is the count of the number with the event on condition 2 only (= n21) d is the number of pairs with no event under both conditions (Note the order of a and d is only important for contrast="RR".)

contrast

Character string indicating the contrast of interest: "RD" = rate difference (default), "RR" = rate ratio, "OR" = odds ratio.

level

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

cc

Number or logical (default FALSE) specifying (amount of) continuity correction. When a score-based method is used, cc = 0.5 corresponds to the continuity-corrected McNemar test.

cctype

Character string indicating the type of continuity correction ("constant" or "delrocco") to be applied for contrast = "RR". (Note: both options produce non-equivariant intervals, an improved correction is currently under evaluation - watch this space.)

method_RD

Character string indicating the confidence interval method to be used for contrast = "RD". "Score" = iterative Tango asymptotic score, "Score_closed" = closed form solution for Tango interval (default), "MOVER" = hybrid MOVER method for paired RD (as per "method 8" in Newcombe, but with a choice of input methods - see moverbase), "MOVER_newc" = hybrid MOVER method with "correction" to correlation estimate (Newcombe's "method 10"), "TDAS" = t-distribution asymptotic score (experimental method, seems to struggle with low numbers).

method_RR

Character string indicating the confidence interval method to be used for contrast = "RR". "Score" = iterative Tang asymptotic score, "Score_closed" = closed form solution for Tang interval (default), "MOVER" = hybrid MOVER method for paired RR, "MOVER_newc" = hybrid MOVER method with "correction" to correlation estimate from Newcombe's RD method, "TDAS" = t-distribution asymptotic score (experimental method, seems to struggle with low numbers).

method_OR

Character string indicating the confidence interval method to be used for contrast = "OR", all of which are based on transformation of an interval for a single proportion b/(b+c): "SCAS" = transformed skewness-corrected score (default), "jeff" = transformed Jeffreys, "midp" = transformed mid-p, "wilson" = transformed Wilson score - included for reference only, not recommended.

moverbase

Character string indicating the base method used as input for the MOVER methods (when method_RR or method_RD = "MOVER"): "wilson" = Wilson score (not recommended, known to be skewed), "jeff" = Jeffreys equal-tailed interval, "midp" = mid-p, "SCAS" = skewness-corrected score (default)

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. NB: can also be used for a superiority test by setting theta0 = 0.

precis

Number (default 6) specifying precision (i.e. number of decimal places) to be used in optimisation subroutine for the confidence interval.

Author

Pete Laud,

References

Tango T. Equivalence test and confidence interval for the difference in proportions for the paired-sample design. Statistics in Medicine 1998; 17:891-908

Newcombe RG. Improved confidence intervals for the difference between binomial proportions based on paired data. Statistics in Medicine 1998; 17:2635-2650

Tango T. Improved confidence intervals for the difference between binomial proportions based on paired data by Robert G. Newcombe, Statistics in Medicine, 17, 2635-2650 (1998). Statistics in Medicine 1999; 18(24):3511-3513

Nam J-M, Blackwelder WC. Analysis of the ratio of marginal probabilities in a matched-pair setting. Stat Med 2002; 21(5):689–699

Tang N-S, Tang M-L, Chan ISF. On tests of equivalence via non-unity relative risk for matched-pair design. Statistics in Medicine 2003; 22:1217-1233

Agresti A, Min Y. Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 2005; 24:729-740

Tang M-L, Li H-Q, Tang N-S. Confidence interval construction for proportion ratio in paired studies based on hybrid method. Statistical Methods in Medical Research 2010; 21(4):361-378

Tang N-S et al. Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data. Statistical Methods in Medical Research. 2011; 20(3):233-259

Yang Z, Sun X and Hardin JW. A non-iterative implementation of Tango's score confidence interval for a paired difference of proportions. Statistics in Medicine 2013; 32:1336-1342

Fagerland MW, Lydersen S, Laake P. Recommended tests and confidence intervals for paired binomial proportions. Statistics in Medicine 2014; 33(16):2850-2875

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

DelRocco N et al. New Confidence Intervals for Relative Risk of Two Correlated Proportions. Statistics in Biosciences 2023; 15:1–30

Chang P et al. Continuity corrected score confidence interval for the difference in proportions in paired data. Journal of Applied Statistics 2024; 51-1:139-152

Examples

# Data example from Agresti-Min 2005
pairbinci(x = c(53, 16, 8, 9), contrast = "RD", method_RD = "Score")
pairbinci(x = c(53, 16, 8, 9), contrast = "RD", method_RD = "TDAS")
pairbinci(x = c(53, 16, 8, 9), contrast = "RR", method_RR = "Score")
pairbinci(x = c(53, 16, 8, 9), contrast = "RR", method_RR = "TDAS")
pairbinci(x = c(53, 16, 8, 9), contrast = "OR", method_OR = "SCAS")
# Example from Fagerland et al 2014
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method_RD = "Score_closed")
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method_RD = "MOVER_newc", moverbase = "wilson")
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method_RD = "MOVER_newc", moverbase = "SCAS")
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method_RR = "Score_closed")
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method_RR = "MOVER_newc", moverbase = "wilson")
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method_RR = "MOVER_newc", moverbase = "SCAS")
pairbinci(x = c(1, 1, 7, 12), contrast = "OR", method_OR = "wilson")
pairbinci(x = c(1, 1, 7, 12), contrast = "OR", method_OR = "midp")
pairbinci(x = c(1, 1, 7, 12), contrast = "OR", method_OR = "SCAS")