Confidence intervals for conditional odds ratio (OR) with paired binomial rates.

Confidence intervals for comparisons of two binomial rates from paired data. This convenience wrapper function produces a selection of the methods below for the conditional odds ratio (OR) contrast, with or without optional continuity adjustment (where available).

Transformed SCAS (skewness-corrected asymptotic score)
Transformed Wilson Score method
Transformed mid-P
Transformed Jeffreys
Approximate log-normal (Wald) method

Usage

orpairci(x, level = 0.95, std_est = TRUE, cc = FALSE, precis = 8)

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).
std_est: logical, specifying if the crude point estimate for the contrast value should be returned (TRUE, default) or the method-specific alternative point estimate consistent with a 0% confidence interval (FALSE).
cc: Number or logical (default FALSE) specifying (amount of) continuity adjustment. Numeric value between 0 and 0.5 is taken as the gamma parameter in Laud 2017, Appendix S2 (cc = TRUE translates to 0.5 for 'conventional' Yates adjustment).
precis: Number (default 6) specifying precision (i.e. number of decimal places) to be used in output.

Value

A list containing the following components:

data: the input data in 2x2 matrix form.
estimates: an array containing the confidence interval for paired OR using various methods. The methods shown depends on the cc argument (if cc = TRUE then the continuity-adjusted methods are given).
call: details of the function call.

References

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. Improved confidence intervals and tests for paired binomial proportions. (2026, Under review)

Author

Pete Laud, p.j.laud@sheffield.ac.uk

Examples

# Example data from Fagerland et al 2014
orpairci(x = c(1, 1, 7, 12), precis = 3)
#> [[1]]
#>          Test_2
#> Test_1    Success Failure
#>   Success       1       1
#>   Failure       7      12
#> 
#> $estimates
#>                      lower   est upper
#> Transformed SCASp    0.008 0.143 0.912
#> Transformed midp     0.006 0.143 0.924
#> Transformed Wilson   0.023 0.143 0.890
#> Transformed Jeffreys 0.014 0.143 0.831
#> Wald                 0.018 0.143 1.161
#> 
#> $call
#> level    cc 
#>  0.95  0.00 
#> 
# with conventional continuity adjustment
orpairci(x = c(1, 1, 7, 12), precis = 3, cc = TRUE)
#> [[1]]
#>          Test_2
#> Test_1    Success Failure
#>   Success       1       1
#>   Failure       7      12
#> 
#> $estimates
#>                             lower   est upper
#> Transformed SCASp_cc        0.000 0.143 1.204
#> Transformed Clopper-Pearson 0.003 0.143 1.112
#> Transformed Wilson_cc       0.007 0.143 1.142
#> Transformed Jeffreys_cc     0.003 0.143 1.112
#> 
#> $call
#> level    cc 
#>  0.95  0.50 
#> 
# with intermediate continuity adjustment
orpairci(x = c(1, 1, 7, 12), precis = 3, cc = 0.25)
#> [[1]]
#>          Test_2
#> Test_1    Success Failure
#>   Success       1       1
#>   Failure       7      12
#> 
#> $estimates
#>                               lower   est upper
#> Transformed SCASp_cc(0.25)    0.002 0.143 1.052
#> Transformed midp_cc(0.25)     0.004 0.143 1.029
#> Transformed Wilson_cc(0.25)   0.014 0.143 1.009
#> Transformed Jeffreys_cc(0.25) 0.008 0.143 0.966
#> 
#> $call
#> level    cc 
#>  0.95  0.25 
#>