ssize.reference.range {MKpower}

Power Calculations for Two-sample Hsu t Test

Description

Compute the sample size for reference range studies, or determine parameters for a given sample size; see Jennen-Steinmetz and Wellek (2005).

Usage

ssize.reference.range(n = NULL, delta = NULL, ref.prob = 0.95, conf.prob = NULL,
                      alternative = c("two.sided", "one.sided"),
                      method = "parametric", exact = TRUE, 
                      tol = .Machine$double.eps^0.5)

Arguments

n

number of observations

delta

difference between empirical and target coverage of reference range

ref.prob

target coverage of reference range

conf.prob

confidence probability to acchieve given difference between empirical and target coverage

alternative

a character string specifying "two.sided" (default), or one-sided reference ranges. You can specify just the initial letter.

method

either "parametric" or "nonparametric"; see details

exact

use exact or approximate method

tol

numerical tolerance used in root finding, the default providing (at least) eight significant digits.

Details

Exactly one of the parameters n, delta, ref.prob and conf.prob must be passed as NULL, and that parameter is determined from the others. In case of ref.prob NULL must be explicitly passed if you want to compute it.

If method "parametric" a normal distribution is assumed for the investigated quantity.

If method "nonparametric" an arbitrary continuous probability distribution is assumed.

If exact = TRUE is used, the computations use the exact formulas (5) and (9) of Jennen-Steinmetz and Wellek (2005).

If exact = FALSE is used, the computations use the approximate formulas (6) and (10) of Jennen-Steinmetz and Wellek (2005).

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 the equations 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

C. Jennen-Steinmetz, S. Wellek (2005). A new approach to sample size calculation for reference interval studies. Statistics in Medicine 24:3199-3212.

See Also

uniroot

Examples

  ## see Table 1 in Jennen-Steinmetz and Wellek (2005)
  ssize.reference.range(delta = 0.03, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ## 135 vs 125 (error in Table 1)
  ssize.reference.range(delta = 0.03, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.03, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.03, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.025, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.025, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.025, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.025, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.02, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ## 314 vs. 305 (error Table 1?)
  ssize.reference.range(delta = 0.02, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.02, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.02, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.015, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.01, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.9, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.015, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.015, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.0125, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.0125, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.0125, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.0125, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.01, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.01, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.0075, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.0075, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.0075, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.0075, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  ssize.reference.range(delta = 0.005, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE)
  ssize.reference.range(delta = 0.005, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE)
  ssize.reference.range(delta = 0.005, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE)
  ssize.reference.range(delta = 0.005, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE)
  
  
  ## results are equivalent to one-sided reference range with coverage of 
  ## 95 percent instead of 90 percent; for example
  ssize.reference.range(delta = 0.03, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = TRUE, alternative = "one.sided")
  ## 135 vs 125 (error in Table 1)
  ssize.reference.range(delta = 0.03, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = TRUE, alternative = "one.sided")
  ssize.reference.range(delta = 0.03, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "parametric", exact = FALSE, alternative = "one.sided")
  ssize.reference.range(delta = 0.03, ref.prob = 0.95, conf.prob = 0.9, 
                        method = "nonparametric", exact = FALSE, alternative = "one.sided")