MRMC study power (Obuchowski-Rockette mixed model, paired-patient paired-reader design)

Computes the power of a multi-reader multi-case study to detect a given difference in accuracy (e.g. ROC area) with J readers, using the non-central F framework of Zhou et al. (2011) Eq 6.32 with the Table 6.4 parameterisation for the paired-patient, paired-reader design (rho1 > rho2 > rho3 > 0, rho_b > 0).

Usage

mrmc_power(
  n,
  J,
  delta,
  sigma_b2,
  sigma_w2,
  sigma_c2,
  rho1,
  rho2,
  rho3,
  rho_b = NULL,
  alpha = 0.05,
  n_repeats = 1
)

Arguments

n

Patients with the condition (paired-patient design: the same patients are imaged under both tests)

J

Number of readers per test; integer >= 2 (the F test needs J-1 df).

delta

Difference in accuracy to detect; number > 0 (on the AUC or accuracy metric scale, e.g. 0.10).

sigma_b2

Between-reader variance component; number >= 0. Planning heuristic: (accuracy range / 4)^2 (Zhou p. 223, Beam 1996).

sigma_w2

Within-reader (occasion) variance component; number >= 0.

sigma_c2

Patient-sampling (case) variance component; number >= 0. This is the variance of the accuracy estimate attributable to sampling patients, i.e. V(A)/n (Zhou p. 221), so it already carries the sample size. For the mammography example it is 0.00196 at n = 50.

rho1

Correlation, same reader different tests; in [0, 1).

rho2

Correlation, different readers same test; in [0, 1).

rho3

Correlation, different readers different tests; in [0, 1). The paired-patient, paired-reader parameterisation expects rho1 > rho2 > rho3 > 0 (Zhou Table 6.4); violated orderings warn.

rho_b

Correlation between the same readers' accuracies on the two tests (Zhou Table 6.3 p_b); in [0, 1). Defaults to rho1, which is the value implied when a single "same reader, different test" correlation is supplied. For the Zhou mammography example the book sets rho_b = 0.75.

alpha

Type I error of the two-sided F test; in (0, 1), default 0.05.

n_repeats

Reading occasions per reader-test (Q); integer >= 1, usually 1.

Value

Numeric power (0-1), invisible. The full result object (parameters, formula, noncentrality) is attached as a sample_size_result.

Details

Eq 6.32 as printed (Zhou 2011, p. 221):

  lambda = J (v1 - v2)^2 / (2 * {
    sigma_b2 (1 - rho_b) + sigma_w2 / Q +
    sigma_c2 [(1 - rho1) + (J - 1)(rho2 - rho3)] })

Note the two features that distinguish it from simpler MRMC formulae: the between-reader term is weighted by (1 - rho_b), the correlation between the same readers' accuracies on the two tests, and the patient-sampling term sigma_c2 is NOT divided by n (sigma_c2 is already the patient-sampling variance component, computed as V(A)/n; see Zhou p. 221).

Anchor: Zhou 2011 p. 225 (mammography example) - n = 50 malignant and 50 benign patients, J = 8 readers, delta = 0.10, sigma_b2 = 0.00123, sigma_w2 = 0.00087, sigma_c2 = 0.00196 (from Eq 6.5 with n = 50), rho1 = 0.5, rho2 = 0.3, rho3 = 0.25, rho_b = 0.75 -> power = 0.893, which reproduces the book's "89% power".

Examples

# Mammography MRMC planning (Zhou 2011 pp. 221-225): 50 malignant plus 50
# benign patients, 8 readers, detect an AUC difference of 0.10. Power
# reproduces the book's 89%.
mrmc_power(
  n = 50, J = 8, delta = 0.10,
  sigma_b2 = 0.00123, sigma_w2 = 0.00087, sigma_c2 = 0.00196,
  rho1 = 0.50, rho2 = 0.30, rho3 = 0.25, rho_b = 0.75
)