power.diagnostic.test {MKmisc}

Power calculations for a diagnostic test

Description

Compute sample size, power, delta, or significance level of a diagnostic test for an expected sensititivy or specificity.

Usage

power.diagnostic.test(sens = NULL, spec = NULL,
                      n = NULL, delta = NULL, sig.level = 0.05,
                      power = NULL, prev = NULL, 
                      method = c("exact", "asymptotic"),
                      NMAX = 1e4)

Arguments

sens

Expected sensitivity; either sens or spec has to be specified.

spec

Expected specificity; either sens or spec has to be specified.

n

Number of cases if sens and number of controls if spec is given.

delta

sens-delta resp. spec-delta is used as lower confidence limit

sig.level

Significance level (Type I error probability)

power

Power of test (1 minus Type II error probability)

prev

Expected prevalence, if NULL prevalence is ignored which means prev = 0.5 is assumed.

method

exact or asymptotic formula; default "exact".

NMAX

Maximum sample size considered in case method = "exact".

Details

Either sens or spec has to be specified which leads to computations for either cases or controls.

Exactly one of the parameters n, delta, sig.level, and power must be passed as NULL, and that parameter is determined from the others. Notice that sig.level has a non-NULL default so NULL must be explicitly passed if you want to compute it.

The computations are based on the formulas given in the Appendix of Flahault et al. (2005). Please be careful, in Equation (A1) the numerator should be squared, in equation (A2) and (A3) the second exponent should be n-i and not i.

As noted in Chu and Cole (2007) power is not a monotonically increasing function in n but rather saw toothed (see also Chernick and Liu (2002)). Hence, in our calculations we use the more conservative approach II); i.e., the minimum sample size n such that the actual power is larger or equal power andsuch that for any sample size larger than n it also holds that the actual power is larger or equal power.

Value

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

Note

uniroot is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.

Author(s)

Matthias Kohl [e-mail]

References

A. Flahault, M. Cadilhac, and G. Thomas (2005). Sample size calculation should be performed for design accuracy in diagnostic test studies. Journal of Clinical Epidemiology, 58(8):859-862.

H. Chu and S.R. Cole (2007). Sample size calculation using exact methods in diagnostic test studies. Journal of Clinical Epidemiology, 60(11):1201-1202.

M.R. Chernick amd C.Y. Liu (2002). The saw-toothed behavior of power versus sample size and software solutions: single binomial proportion using exact methods. Am Stat, 56:149-155.

See Also

uniroot

Examples

## see n2 on page 1202 of Chu and Cole (2007)
power.diagnostic.test(sens = 0.99, delta = 0.14, power = 0.95) # 40
power.diagnostic.test(sens = 0.99, delta = 0.13, power = 0.95) # 43
power.diagnostic.test(sens = 0.99, delta = 0.12, power = 0.95) # 47

power.diagnostic.test(sens = 0.98, delta = 0.13, power = 0.95) # 50
power.diagnostic.test(sens = 0.98, delta = 0.11, power = 0.95) # 58

## see page 1201 of Chu and Cole (2007)
power.diagnostic.test(sens = 0.95, delta = 0.1, n = 93) ## 0.957
power.diagnostic.test(sens = 0.95, delta = 0.1, n = 93, power = 0.95, 
                      sig.level = NULL) ## 0.0496
power.diagnostic.test(sens = 0.95, delta = 0.1, n = 102) ## 0.968
power.diagnostic.test(sens = 0.95, delta = 0.1, n = 102, power = 0.95, 
                      sig.level = NULL) ## 0.0471
## yields 102 not 93!
power.diagnostic.test(sens = 0.95, delta = 0.1, power = 0.95)