sampleSize_MRMC {MRMCsamplesize}

Estimate sample sizes for MRMC studies

Description

sampleSize_MRMC This function returns number of cases required for a MRMC study for a given number of readers.

Usage

sampleSize_MRMC(
  endpoint = "auc",
  J,
  delta,
  rangeb,
  rangew,
  theta,
  R = 1,
  r1,
  r2 = 0.3,
  r3 = 0.3,
  rb = 0.8,
  K = 1,
  power = 0.8,
  alpha = 0.05,
  nu1 = 1,
  var_auc = "obuchowski",
  reader_var_estimation_method = "normal",
  n_reading_sessions_per_reader = 2,
  corr = FALSE,
  ICC = NULL,
  s = NULL
)

Arguments

endpoint

Character string to inform what is the Figure-of-Merit (FOM) which will be used as the endpoint of the MRMC study. Values can be either auc or sensitivity.

J

The number of readers for the study. It is recommended to have minimum 5 readers in any MRMC study.

delta

Effect size denoting the anticipated difference in the endpoint between the two interventions/imaging-modalities/techniques. Typically chosen values are 0.04, 0.05 and 0.06. Should be between 0 and 1.

rangeb

Inter-reader variability range (sometimes referred to as between-reader variability) denoting the anticipated difference between the highest accuracy of any reader in the study and the lowest accuracy of any reader in the study. Should be a numeric value between 0 and 1.

rangew

Intra-reader variability range (sometimes referred to as within-reader variability) denoting the anticipated difference between the accuracies of a reader who interprets the same images using the same imaging technique at two different times. Should be a numeric value between 0 and 1.

theta

Expected average value of the FOM for the J readers.

R

Ratio of non-diseased cases to diseased cases. Defaults to 1.

r1

Correlation between FOMs of readers when same cases are evaluated by the same reader using different modalities.

r2

Correlation between FOMs when the same cases are evaluated by different readers using the same modality. It is assumed that r2 = r3 for default calculations.

r3

Correlation between FOMs when the same cases are evaluated by different readers using different modalities. It is assumed that r2 = r3 for default calculations.

rb

Correlation between FOMs when the same readers evaluate cases using different modalities. The default value is 0.8.

K

Number of times each reader interprets the same case from the same modality. This is always equal to 1 in a fully-crossed paired-reader paired-case study design with two modalities.

power

Power to detect delta given all other assumptions. Default value is 0.8 corresponding to 80 percent power.

alpha

The type I error rate. Default value is 0.05 corresponding to 5 percent type I error (significance level).

nu1

Numerator degrees of freedom of the F-distribution which will be used to estimate the non-centrality parameter (lambda).

var_auc

Variance estimation method when endpoint is auc. Defaults to the string obuchowski. If value is changed to blume, then method proposed by Blume (2009) will be used to estimate the variance.

reader_var_estimation_method

A value = normal uses the assumption that the accuracy of readers are distributed normally and thus the relationship between range and standard deviation can be used to estimate the inter and intra reader variances from rangeb and rangew. Any other value will use a rule of thumb to estimate inter and intra reader variances by dividing rangeb and rangew by 4 followed by squaring it. normal method is typically more conservative especially when J is less than 30-35.

n_reading_sessions_per_reader

Number of times each reader interprets each case. Defaults to 2 which corresponds to a typical MRMC study with 2 modalities.

corr

Logical value indicating if ICC (intra-cluster correlation) has to be adjusted (TRUE) or not (FALSE). Defaults to FALSE.

ICC

A numerical value between 0 and 1 indicating the expected ICC if corr is TRUE.

s

Average number of lesions in diseased cases. This must be a numeric value greater than or equal to 1.

Details

When corr = FALSE, the nUnits_i in ORSampleSizeResults list is the number of diseased cases. The number of total cases (diseased + non-diseased; nTotal) required will depend on the the ratio R specified. When corr = TRUE, the anticipated correlation between units within the same diseased cases are adjusted and the nUnits_i in ORSampleSizeResults list is the number of units in diseased cases assuming independence. The number of diseased cases required in this scenario will be given by nCases_c. Again, nTotal required will depend on the R specified.

Value

A list within a list object with two named lists

• varComponents - A list containing the estimated values of the OR variances and correlation components.

• ORSampleSizeResults - A list containing the sample size results.

Author(s)

Dennis Robert [e-mail]

References

• Obuchowski NA, Hillis SL. Sample size tables for computer-aided detection studies. AJR Am J Roentgenol. 2011 Nov;197(5):W821-8. doi: 10.2214/AJR.11.6764. PMID: 22021528; PMCID: PMC3494304

• Obuchowski NA. & Rockette HE. (1995) Hypothesis testing of diagnostic accuracy for multiple readers and multiple tests an anova approach with dependent observations, Communications in Statistics - Simulation and Computation, 24:2, 285-308, DOI: 10.1080/03610919508813243

• Obuchowski NA. Sample size tables for receiver operating characteristic studies. AJR Am J Roentgenol. 2000;175(3):603-608. doi:10.2214/ajr.175.3.1750603

• Rockette HE, Campbell WL, Britton CA, Holbert JM, King JL, Gur D. Empiric assessment of parameters that affect the design of multireader receiver operating characteristic studies. Acad Radiol. 1999;6(12):723-729. doi:10.1016/s1076-6332(99)80468-1

• Blume JD. Bounding Sample Size Projections for the Area Under a ROC Curve. J Stat Plan Inference. 2009 Mar 1;139(1):711-721. doi: 10.1016/j.jspi.2007.09.015. PMID: 20160839; PMCID: PMC2631183.

Examples

library("MRMCsamplesize")
result1 <- sampleSize_MRMC(endpoint = 'auc',J = 10,delta = 0.10,theta = 0.75,
rangeb = 0.1, rangew = 0.05, R = 1, r1 = 0.47,corr = FALSE)
result2 <- sampleSize_MRMC(endpoint = 'auc',J = 20,delta = 0.05,theta = 0.75,
rangeb = 0.2, rangew = 0.05, R = 1, r1 = 0.47,corr = TRUE, ICC = 0.5, s = 1.25)
result3 <- sampleSize_MRMC(endpoint = 'se',J = 15, delta = 0.05, theta = 0.75,
rangeb = 0.2, rangew = 0.025, R = 1, r1 = 0.5, corr = TRUE, ICC = 0.5, s = 1.25)