Comparison of the accuracy of two tests using relative sensitivity and specificity

Calculates two-sided Wald confidence intervals and performs a Wald test for the relative sensitivity and specificity of two binary diagnostic tests in a paired study design.

Usage

sesp.rel(tab, alpha)

Arguments

tab: an object of class tab.paired.
alpha: significance level alpha used to compute two-sided 100(1-alpha)%-confidence intervals, the default is 0.05.

Value

A list containing:

sensitivity: a named vector containing test1 (the sensitivity for test 1), test2 (the sensitivity for test 2), rel.sens (the relative difference between the two sensitivities, computed as test2/test1), se.log.rel.sens (the standard error for log(rel.sens)), lcl.rel.sens (the lower confidence limit for rel.sens), ucl.rel.sens (the upper confidence limit for rel.sens), and pval.rel.sens (the p-value from the test for the null hypothesis: relative sensitivity=1).
specificity: a named vector containing test1 (the specificity for test 1), test2 (the specificity for test 2), rel.spec (the relative difference between the two specificities, computed as test2/test1), se.log.rel.spec (the standard error for log(rel.spec)), lcl.rel.spec (the lower confidence limit for rel.spec), ucl.rel.spec (the upper confidence limit for rel.spec), and pval.rel.spec (the p-value from the test for the null hypothesis: relative specificity=1).
alpha: significance level alpha for 100(1-alpha)%-confidence intervals for rel.sens and rel.spec.

Details

If relative sensitivity>1, the percentage increase in sensitivity for test2 relative to test1 is computed as 100(relative sensitivity-1)%. If relative sensitivity<1 the percentage decrease in sensitivity for test2 relative to test1 is computed as 100(1-relative sensitivity)%. Percentage increase/decrease in specificity is computed in an analogous fashion.

Given the independence of relative sensitivity and relative specificity, a possible joint 100(1-alpha)% confidence region for {relative sensitivity, relative specificity} is formed by the rectangle {lcl.rel.sens, ucl.rel.sens} x {lcl.rel.spec, ucl.rel.spec}, where {lcl.rel.sens, ucl.rel.sens} and {lcl.rel.spec, ucl.rel.spec} are 100(1-alpha*)% confidence intervals for relative sensitivity and relative specificity, respectively, and alpha*=1-sqrt(1-alpha).

The McNemar's test implemented in sesp.mcnemar is asymptotically equivalent to the Wald test implemented here.

References

Alonzo, T. A., Pepe, M. S., & Moskowitz, C. S. (2002). Sample size calculations for comparative studies of medical tests for detecting presence of disease. Statistics in medicine, 21(6), 835-852.

Examples

data(Paired1) # Hypothetical study data
ftable(Paired1)
#>      y2   0   1
#> d y1           
#> 0 0     155  22
#>   1      53  31
#> 1 0      32  22
#>   1      78 319
paired.layout <- tab.paired(d=d, y1=y1, y2=y2, data=Paired1)
paired.layout 
#> Two binary diagnostic tests (paired design)
#> 
#> Test1: 'y1'
#> Test2: 'y2'
#> 
#> Diseased:
#>            Test1 pos. Test1 neg. Total
#> Test2 pos.        319         22   341
#> Test2 neg.         78         32   110
#> Total             397         54   451
#> 
#> Non-diseased:
#>            Test1 pos. Test1 neg. Total
#> Test2 pos.         31         22    53
#> Test2 neg.         53        155   208
#> Total              84        177   261
#> 
sesp.rel.results <- sesp.rel(paired.layout)
str(sesp.rel.results)
#> List of 3
#>  $ sensitivity: Named num [1:7] 0.8803 0.7561 0.8589 0.0272 0.8144 ...
#>   ..- attr(*, "names")= chr [1:7] "test1" "test2" "rel.sens" "se.log.rel.sens" ...
#>  $ specificity: Named num [1:7] 0.6782 0.7969 1.1751 0.0451 1.0757 ...
#>   ..- attr(*, "names")= chr [1:7] "test1" "test2" "rel.spec" "se.log.rel.spec" ...
#>  $ alpha      : num 0.05
sesp.rel.results
#> $sensitivity
#>           test1           test2        rel.sens se.log.rel.sens    lcl.rel.sens 
#>    8.802661e-01    7.560976e-01    8.589421e-01    2.717863e-02    8.143843e-01 
#>    ucl.rel.sens   pval.rel.sens 
#>    9.059378e-01    2.211197e-08 
#> 
#> $specificity
#>           test1           test2        rel.spec se.log.rel.spec    lcl.rel.spec 
#>    0.6781609195    0.7969348659    1.1751412429    0.0451348840    1.0756505055 
#>    ucl.rel.spec   pval.rel.spec 
#>    1.2838342322    0.0003493056 
#> 
#> $alpha
#> [1] 0.05
#>