# powerCalData: Calculate the power for testing delta=0 based on a dataset In riskPredictClustData: Assessing Risk Predictions for Clustered Data

## Description

Calculate the power for testing delta=0 based on a dataset.

## Usage

 ```1 2 3 4 5``` ```powerCalData( nSubj, triangle, frame, alpha = 0.05) ```

## Arguments

 `nSubj` integer. number of subjects to be generated. Assume each subject has two observations. `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 `frame` A data frame with 5 columns: cid, subuid, status, score1, and score2. `cid` indicates cluster id; `subuid` indicates unit ID within a cluster; `status=1` indicates an eye is progressed; `status=0` indicates an eye is not progressed; `score1` represents the score based on prediction rule 1. `score2` represents the score based on prediction rule 2. `alpha` type I error rate

## Value

A list with 11 elements.

 `power` the esstimated power `rho` rho=corr(H(Z_{ij}), H(Z_{k ell})) , where H=Phi^{-1} is the probit transformation. `rho11` rho_{11}=corr(H_{ij}^{(1)}, H_{i ell}^{(1)}) , where H=Phi^{-1} is the probit transformation. `rho22` rho_{22}=corr(H_{ij}^{(2)}, H_{i ell}^{(2)}) , where H=Phi^{-1} is the probit transformation. `rho12` rho_{12}=corr(H_{ij}^{(1)}, H_{i ell}^{(2)}) , 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. `p00` p_{00}=Pr(delta_{i1}=0 & delta_{i2}=0) , where delta_{ij}=1 if the j-th subunit of the i-th cluster has progressed. `mu1` mu_1=H(Y)-H(Y_c) is the difference between probit transformation H(Y) and probit-shift alternative H(Y_c) for the first prediction score, 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. `mu2` mu_2=H(Y)-H(Y_c) is the difference between probit transformation H(Y) and probit-shift alternative H(Y_c) for the second prediction score, 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.

## Author(s)

Bernard Rosner <stbar@channing.harvard.edu>, Weiliang Qiu <Weiliang.Qiu@gmail.com>, Meiling Ting Lee <MLTLEE@umd.edu>

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```set.seed(1234567) datFrame = genSimDataGLMEM(nSubj = 30, beta0 = -6, sd.beta0i = 1.58, beta1 = 1.58, beta2 = -3.95, beta3 = 3.15, beta4 = 2.06, beta5 = 0.51, beta6 = 1.47, beta7 = 3.11, p.smkcur = 0.08, p.inieye31 = 0.44, p.inieye32 = 0.42, p.inieye41 = 0.12, p.inieye42 = 0.11, sd.lncalorc = 0.33) print(dim(datFrame)) print(datFrame[1:2,]) # prediction rule 1 tt1 = getScore(fmla = prog~smkcur+lncalorc+inieye3+inieye4+factor(rtotfat), cidVar = "cid", subuidVar = "subuid", statusVar = "prog", datFrame = datFrame, mycorstr = "exchangeable", verbose = FALSE) myframe1=tt1\$frame print(dim(myframe1)) print(myframe1[1:3,]) #### # prediction rule 2 tt2 = getScore(fmla = prog~smkcur+lncalorc+inieye3+inieye4, cidVar = "cid", subuidVar = "subuid", statusVar = "prog", datFrame = datFrame, mycorstr = "exchangeable", verbose = FALSE) myframe2=tt2\$frame print(dim(myframe2)) print(myframe2[1:3,]) # combine scores from two prediction rules myframe12=myframe1[, c("cid", "subuid", "status")] myframe12\$score1=myframe1\$score myframe12\$score2=myframe2\$score print(dim(myframe12)) print(myframe12[1:3,]) res = powerCalData(nSubj = 30, triangle = 0.05, frame=myframe12, alpha = 0.05) print(res) ```

riskPredictClustData documentation built on May 1, 2019, 6:34 p.m.