pairbinci: Confidence intervals for comparisons of paired binomial...

In ratesci: Confidence Intervals and Tests for Comparisons of Binomial Proportions or Poisson Rates

Confidence intervals for comparisons of paired binomial rates.

Description

Confidence intervals for the rate (or risk) difference ("RD"), rate ratio ("RR") or conditional 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, and an added skewness correction for improved one-sided coverage. Also includes MOVER options using the Method of Variance Estimates Recovery for paired RD and RR, incorporating Newcombe's correlation correction, and some simpler methods by Bonett & Price for RD and RR. For OR, intervals are produced based on transforming various intervals for the single proportion, including SCASp, mid-p and Jeffreys. All methods have options for continuity adjustment, and the magnitude of adjustment can be customised.

Usage

pairbinci(
  x,
  level = 0.95,
  contrast = "RD",
  method = ifelse(contrast == "OR", "SCASp", "Score"),
  moverbase = ifelse(method %in% c("MOVER", "MOVER_newc", "BP"), "jeff", NULL),
  bcf = TRUE,
  skew = TRUE,
  cc = FALSE,
  theta0 = NULL,
  precis = 6,
  warn = TRUE,
  method_RD = NULL,
  method_RR = NULL,
  method_OR = NULL,
  cctype = NULL,
  ...
)

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 (= x12) c is the count of the number with the event on condition 2 only (= x21) 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".)
level	Number specifying confidence level (between 0 and 1, default 0.95).
contrast	Character string indicating the contrast of interest: "RD" = rate difference (default); "RR" = rate ratio; "OR" = conditional odds ratio.
method	Character string indicating the confidence interval method to be used. The following are available for contrast = "RD" or "RR": "Score" = (default) asymptotic score class of methods including Tango (for RD) / Tang (for RR), by iterative calculations, with optional skewness correction; "Score_closed" = closed form solution for Tango/Tang intervals (without skewness correction); "MOVER" = hybrid MOVER method (as per "method 8" in Newcombe, but with a choice of input methods - see moverbase); "MOVER_newc" = hybrid MOVER methods with correction to correlation estimate (Newcombe's "method 10"); "TDAS" = t-distribution asymptotic score (experimental method, now deprecated); "BP" = Wald with Bonett-Price adjustment for RD, or Hybrid Bonett-Price method for RR. For contrast = "OR", one of the following methods may be selected, all of which are based on transformation of an interval for a single proportion b/(b+c): "SCASp" = 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 for RD or RR (when method = "MOVER" or "MOVER_newc"), and for the Hybrid BP method for RR: "jeff" = Jeffreys equal-tailed interval (default), "SCASp" = skewness-corrected score, "midp" = mid-p, "wilson" = Wilson score (not recommended, known to be skewed).
bcf	Logical (default FALSE) indicating whether to apply variance bias correction in the score denominator. (Under evaluation, manuscript under review.)
skew	Logical (default TRUE) indicating whether to apply skewness correction or not. (Under evaluation, manuscript under review.) Only applies for the iterative method = "Score".
cc	Number or logical (default FALSE) specifying (amount of) continuity adjustment. When a score-based method is used, cc = 0.5 corresponds to the continuity-corrected McNemar test.
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.
warn	Logical (default TRUE) giving the option to suppress warnings.
method_RD	(deprecated: parameter renamed to method)
method_RR	(deprecated: parameter renamed to method)
method_OR	(deprecated: parameter renamed to method)
cctype	(deprecated: new equivariant cc method implemented instead.)
...	Other arguments.

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, along with estimates of the marginal probabilities and the correlation coefficient (uncorrected and corrected).

pval

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

call

details of the function call.

Author(s)

Pete Laud, [e-mail]

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

Bonett DG, Price RM. Confidence intervals for a ratio of binomial proportions based on paired data. Statistics in Medicine 2006; 25:3039-3047

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

Laud PJ. Comments on "New Confidence Intervals for Relative Risk of Two Correlated Proportions" (2023). Statistics in Biosciences 2025; https://doi.org/10.1007/s12561-025-09479-4

Laud PJ. Improved confidence intervals and tests for paired binomial proportions. (2025, Under review)

Examples

# Example from Fagerland et al 2014
# SCAS method for RD
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method = "Score")
# Tango method
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method = "Score", skew = FALSE, bcf = FALSE)
# MOVER-NJ method
pairbinci(x = c(1, 1, 7, 12), contrast = "RD", method = "MOVER_newc", moverbase = "jeff")
# SCAS for RR
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method = "Score")
# Tang method
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method = "Score", skew = FALSE, bcf = FALSE)
# MOVER-NJ
pairbinci(x = c(1, 1, 7, 12), contrast = "RR", method = "MOVER_newc", moverbase = "jeff")
# Transformed SCASp method for OR
pairbinci(x = c(1, 1, 7, 12), contrast = "OR", method = "SCASp")
# Transformed Wilson method
pairbinci(x = c(1, 1, 7, 12), contrast = "OR", method = "wilson")

ratesci documentation built on June 21, 2025, 1:07 a.m.