powerCal {riskPredictClustData}

Calculate the power for testing \delta=0

Description

Calculate the power for testing \delta=0.

Usage

powerCal(
  nSubj, 
  mu1, 
  triangle, 
  rho, 
  rho11, 
  rho22, 
  rho12, 
  p11, 
  p10, 
  p01, 
  alpha = 0.05)

Arguments

nSubj

integer. number of subjects to be generated. Assume each subject has two observations.

mu1

\mu_1=H(Y)-H(Y_c) is the difference between probit transformation H(Y) and probit-shift alternative H(Y_c), where Y is the prediction score of a randomly selected progressing subunit, and Y_c is the counterfactual random variable obtained if each subunit that had progressed actually had not progressed.

triangle

the difference of the expected value the the extended Mann-Whitney U statistics between two prediction rules, i.e., \triangle = \eta^{(1)}_c - \eta^{(2)}_c

rho

\rho=corr\left(H\left(Z_{ij}\right), H\left(Z_{k\ell}\right)\right), where H=\Phi^{-1} is the probit transformation.

rho11

\rho_{11}=corr\left(H_{ij}^{(1)}, H_{i\ell}^{(1)}\right), where H=\Phi^{-1} is the probit transformation.

rho22

\rho_{22}=corr\left(H_{ij}^{(2)}, H_{i\ell}^{(2)}\right), where H=\Phi^{-1} is the probit transformation.

rho12

\rho_{12}=corr\left(H_{ij}^{(1)}, H_{i\ell}^{(2)}\right), where H=\Phi^{-1} is the probit transformation.

p11

p_{11}=Pr(\delta_{i1}=1 \& \delta_{i2}=1), where \delta_{ij}=1 if the j-th subunit of the i-th cluster has progressed.

p10

p_{10}=Pr(\delta_{i1}=1 \& \delta_{i2}=0), where \delta_{ij}=1 if the j-th subunit of the i-th cluster has progressed.

p01

p_{01}=Pr(\delta_{i1}=0 \& \delta_{i2}=1), where \delta_{ij}=1 if the j-th subunit of the i-th cluster has progressed.

alpha

type I error rate

Value

the power

Author(s)

Bernard Rosner <[e-mail]>, Weiliang Qiu <[e-mail]>, Meiling Ting Lee <[e-mail]>

References

Rosner B, Qiu W, and Lee MLT. Assessing Discrimination of Risk Prediction Rules in a Clustered Data Setting. Lifetime Data Anal. 2013 Apr; 19(2): 242-256.

Examples

 

set.seed(1234567)
mu1 = 0.8

power = powerCal(nSubj = 30, mu1 = mu1, 
  triangle = 0.05, rho = 0.93, rho11 = 0.59, rho22 = 0.56, rho12 = 0.52,
  p11 = 0.115, p10 = 0.142, p01 = 0.130, alpha = 0.05)

print(power)