These functions calculate the precision or sample size for likelihood ratios (LRs).
prec_lr is a generalized method for that can be used for positive and
negative LRs as well as conditional LRs.
prec_pos_lr is a wrapper to prec_lr to ease
calculations for positive likelihood ratios by allowing sensitivity and
specificity to be given explicitly.
prec_neg_lr is a wrapper to prec_lr to ease
calculations for negative likelihood ratios by allowing sensitivity and
specificity to be given explicitly.
Usage
prec_lr(prev, p1, p2, n = NULL, conf.width = NULL, conf.level = 0.95, ...)
prec_pos_lr(
prev,
sens,
spec,
n = NULL,
conf.width = NULL,
conf.level = 0.95,
...
)
prec_neg_lr(
prev,
sens,
spec,
n = NULL,
conf.width = NULL,
conf.level = 0.95,
...
)Arguments
- prev
disease/case prevalence in the study group.
- p1
proportion of positives in group 1 (e.g. sensitivity).
- p2
proportion of positives in group 2 (e.g. 1 - specificity).
- n
total group size.
- conf.width
precision (the full width of the confidence interval).
- conf.level
confidence level (defaults to 0.95).
- ...
other arguments to uniroot (e.g.
tol).- sens
sensitivity.
- spec
specificity.
Value
Object of class "presize", a list of arguments (including the computed one) augmented with method and note elements.
Details
These functions implement formula 10 from Simel et al 1991.
prec_lr is a generalized function allowing for many scenarios, while
prec_pos_lr and prec_neg_lr are specific to positive and
negative likelihood ratios in the 2*2 setting (e.g. disease status and test
positive/negative).
For the positive likelihood ratio (LR+), in a 2x2 style experiment, p1
should be sensitivity, p2 should be 1-specificity. Alternatively, use
prec_pos_lr.
For the negative likelihood ratio (LR-), in a 2x2 style experiment, p1
should be 1-sensitivity, p2 should be specificity. Alternatively, use
prec_neg_lr.
For conditional likelihood ratios with 3x2 tables, such as positive or
negative tests against inconclusive ones (yields), p1 would be the
proportion of positive or negative tests in the diseased group and p2
would be the proportion of positive or negative tests in the non-diseased group.
References
Simel, DL, Samsa, GP and Matchar, DB (1991) Likelihood ratios with confidence: Sample size estimation for diagnostic test studies. J Clin Epidemiol 44(8), 763-770
Examples
# equal numbers of diseased/non-diseased, 80% sens, 73% spec, 74 participants total
prec_lr(.5, .8, .27, 74)
#>
#> precision for likelihood ratios
#>
#> prev p1 p2 n n1 n2 lr lwr upr conf.width conf.level
#> 1 0.5 0.8 0.27 74 37 37 2.962963 1.703046 5.15497 3.451925 0.95
# Simel et al 1991, problem 1 - LR+ CI width from N
# Sensitivity of a new test is at least 80%, specificity is 73% and the LR+
# is 2.96 (= 0.8/(1-0.73)). We have as many diseased as not diseased
# (n1 = n2, n = 2*n1 = 146.8, prevalence = .5)
prec_lr(prev = .5, p1 = .8, p2 = 1-.73, n = 146.8)
#>
#> precision for likelihood ratios
#>
#> prev p1 p2 n n1 n2 lr lwr upr conf.width
#> 1 0.5 0.8 0.27 146.8 73.4 73.4 2.962963 1.999739 4.390147 2.390407
#> conf.level
#> 1 0.95
prec_pos_lr(prev = .5, sens = .8, spec = .73, n = 146.8)
#>
#> precision for positive likelihood ratio
#>
#> prev p1 p2 n n1 n2 lr lwr upr conf.width
#> 1 0.5 0.8 0.27 146.8 73.4 73.4 2.962963 1.999739 4.390147 2.390407
#> conf.level
#> 1 0.95
# problem 1 of Simel et al actually derives n1 rather than the width of the
# confidence interval (ie N from CI width). If we know that the lower limit
# of the CI should be 2.0, the confidence interval width is approximately
# exp(2*(log(2.96) - log(2))) = 2.19 (approximate because the CI Of the LR
# is only symetrical on the log(LR) scale), which we can put in conf.width
prec_lr(prev = .5, p1 = .8, p2 = 1-.73, conf.width = 2.2)
#>
#> sample size for likelihood ratios
#>
#> prev p1 p2 n n1 n2 lr lwr upr
#> 1 0.5 0.8 0.27 172.0183 86.00915 86.00915 2.962963 2.060562 4.260562
#> conf.width conf.level
#> 1 2.2 0.95
# same, but using the wrapper to specify sens and spec
prec_pos_lr(prev = .5, sens = .8, spec = .73, conf.width = 2.2)
#>
#> sample size for positive likelihood ratio
#>
#> prev p1 p2 n n1 n2 lr lwr upr
#> 1 0.5 0.8 0.27 172.0183 86.00915 86.00915 2.962963 2.060562 4.260562
#> conf.width conf.level
#> 1 2.2 0.95
# Simel et al 1991, problem 2 - LR- CI width from N
# p1 = 1 - sens = .1, p2 = spec = .5
# n1 = n2, n = 160, prev = .5
prec_lr(prev = .5, p1 = .1, p2 = .5, n = 160)
#>
#> precision for likelihood ratios
#>
#> prev p1 p2 n n1 n2 lr lwr upr conf.width conf.level
#> 1 0.5 0.1 0.5 160 80 80 0.2 0.1000195 0.3999219 0.2999024 0.95
# same, but using the wrapper to specify sens and spec
prec_neg_lr(prev = .5, sens = .9, spec = .5, n = 160)
#>
#> precision for negative likelihood ratio
#>
#> prev p1 p2 n n1 n2 lr lwr upr conf.width conf.level
#> 1 0.5 0.1 0.5 160 80 80 0.2 0.1000195 0.3999219 0.2999024 0.95