Confidence Intervals for Differences in Sensitivity and Specificity

Calculates confidence intervals for differences in sensitivity and specificity of two binary diagnostic tests in a paired study design.

Usage

sesp.diff.ci(tab, ci.method, alpha, cont.corr)

Arguments

tab: An object of class tab.paired.
ci.method: The available methods are “wald” (Altman, 1991), “agresti-min” (Agresti and Min, 2005), “bonett-price” (Bonett and Price, 2011), and “tango” (Tango, 1998), the default is “wald”.
alpha: Significance level alpha for 100(1-alpha)%-confidence intervals for the difference in sensitivity and specificity, the default is 0.05.
cont.corr: A logical value indicating whether the continuity correction should be used (only available for ci.method="wald"), the default is FALSE.

Details

For details and recommendations see Newcombe (2012) and Wenzel and Zapf (2013).

Value

A list containing:

sensitivity: A vector containing test1 (the sensitivity of test 1), test2 (the specificity of test 2), diff (the difference between the two sensitivities, computed as test2 - test1), diff.se (the standard error of diff), diff.lcl (the lower confidence limit of diff) and diff.ucl (the upper confidence limit of diff).
specificity: A vector containing test1 (specificity of test 1), test2 (specificity of test 2), diff (the difference between the two specificities, computed as test2 - test1), diff.se (the standard error of diff), diff.lcl (the lower confidence limit of diff) and diff.ucl (the upper confidence limit of diff).
ci.method: The name of the method used to calculate confidence intervals.
alpha: The level alpha used to compute 100(1-alpha)%-confidence intervals.
cont.corr: A logical value indicating whether the continuity correction was applied.

References

Altman, D.G. (1991). Practical statistics for medical research. Chapman & Hall, London.

Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions. Stat Med, 24(5): 729-40.

Bonett, D.G., and Price, R.M. (2011). Adjusted Wald confidence intervals for a difference of binomial proportions based on paired data. J Educ Behav Stat, 37(4): 479-488.

Newcombe R.G. (2012). Confidence intervals for proportions and related measures of effect size. Chapman and Hall/CRC Biostatistics Series.

Tango, T. (1998). Equivalence test and confidence interval for the difference in proportions for the paired-sample design. Stat Med, 17(8): 891-908.

Wenzel, D., and Zapf, A. (2013). Difference of two dependent sensitivities and specificities: comparison of various approaches. Biom J, 55(5): 705-718.

Examples

library(DTComPair)
t1 <- read.tab.paired(18, 14, 0, 18,
                      18, 12, 2, 18)
t1
#> Two binary diagnostic tests (paired design)
#> 
#> Test1: 'Noname 1'
#> Test2: 'Noname 2'
#> 
#> Diseased:
#>            Test1 pos. Test1 neg. Total
#> Test2 pos.         18         14    32
#> Test2 neg.          0         18    18
#> Total              18         32    50
#> 
#> Non-diseased:
#>            Test1 pos. Test1 neg. Total
#> Test2 pos.         18         12    30
#> Test2 neg.          2         18    20
#> Total              20         30    50
#> 
sesp.diff.ci(t1, ci.method="wald", cont.corr=FALSE)
#> $sensitivity
#>      test1      test2       diff    diff.se   diff.lcl   diff.ucl 
#> 0.36000000 0.64000000 0.28000000 0.06349803 0.15554615 0.40445385 
#> 
#> $specificity
#>       test1       test2        diff     diff.se    diff.lcl    diff.ucl 
#>  0.60000000  0.40000000 -0.20000000  0.06928203 -0.33579029 -0.06420971 
#> 
#> $ci.method
#> [1] "wald"
#> 
#> $alpha
#> [1] 0.05
#> 
#> $cont.corr
#> [1] FALSE
#> 
sesp.diff.ci(t1, ci.method="wald", cont.corr=TRUE)
#> $sensitivity
#>      test1      test2       diff    diff.se   diff.lcl   diff.ucl 
#> 0.36000000 0.64000000 0.28000000 0.08349803 0.11634687 0.44365313 
#> 
#> $specificity
#>       test1       test2        diff     diff.se    diff.lcl    diff.ucl 
#>  0.60000000  0.40000000 -0.20000000  0.08928203 -0.37498957 -0.02501043 
#> 
#> $ci.method
#> [1] "wald"
#> 
#> $alpha
#> [1] 0.05
#> 
#> $cont.corr
#> [1] TRUE
#> 
sesp.diff.ci(t1, ci.method="agresti-min")
#> $sensitivity
#>      test1      test2       diff    diff.se   diff.lcl   diff.ucl 
#> 0.36000000 0.64000000 0.28000000 0.06444681 0.15368658 0.40631342 
#> 
#> $specificity
#>       test1       test2        diff     diff.se    diff.lcl    diff.ucl 
#>  0.60000000  0.40000000 -0.20000000  0.06954236 -0.33630053 -0.06369947 
#> 
#> $ci.method
#> [1] "agresti-min"
#> 
#> $alpha
#> [1] 0.05
#> 
#> $cont.corr
#> [1] FALSE
#> 
sesp.diff.ci(t1, ci.method="tango")
#> $sensitivity
#>     test1     test2      diff   diff.se  diff.lcl  diff.ucl 
#> 0.3600000 0.6400000 0.2800000        NA 0.1747417 0.4166512 
#> 
#> $specificity
#>       test1       test2        diff     diff.se    diff.lcl    diff.ucl 
#>  0.60000000  0.40000000 -0.20000000          NA -0.34470882 -0.06111243 
#> 
#> $ci.method
#> [1] "tango"
#> 
#> $alpha
#> [1] 0.05
#> 
#> $cont.corr
#> [1] FALSE
#>