prec_lr {presize}

Sample size or precision for likelihood ratios

Description

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.

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.

Value

Object of class "presize", a list of arguments (including the computed one) augmented with method and note elements.

Functions

• prec_pos_lr(): "Positive likelihood ratio"

• prec_neg_lr(): "Negative likelihood ratio"

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)

# 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)
prec_pos_lr(prev = .5, sens = .8, spec = .73, n = 146.8)

# 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)
# same, but using the wrapper to specify sens and spec
prec_pos_lr(prev = .5, sens = .8, spec = .73, conf.width = 2.2)

# 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)
# same, but using the wrapper to specify sens and spec
prec_neg_lr(prev = .5, sens = .9, spec = .5, n = 160)