riskPredictClustData (version 0.2.6)

powerCal: 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

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

# NOT RUN {
 

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)



# }