lin.simulation {agreement}R Documentation

Performs a summary of the simulation

Description

In order to analyze the problem we take a bivariate gaussian distribution on (X,Y). It is true under the null hypothesis (no agreement) and the alternative (yes agreement).

Usage

lin.simulation(NUM_CAMP = 5000, NUM = 30, matH0, matH1, underH0 = TRUE, ALPHA_CI = 0.05, la_CP1 = 0.9)

Arguments

NUM_CAMP number of samples to simulate. Its default value is 5000
NUM sample size. Its default value is 30
matH0 matrix of parameters under null hypothesis. It has 2 rows and 3 columns. See Details.
matH1 matrix of parameters under alternative hypothesis . It has exactly the same structure of matH0
underH0 logical parameter to determine what condition to simulate. Its default value is TRUE (simulation under null hypothesis)
ALPHA_CI level of significance. Its default value is 0.05
la_CP1 the threshold used for TDI. Its default value is 0.9

Details

The first column of table object is the theoretical value of the indices (Th val) while the second column (Thr) represent the threshold used to determine the rejection region. Theoretical values of alpha and 1 - beta are reported in the third column (Th prob). The fourth column (Mean of est) represents the inverse transformation of the mean estimate of the agreement measure. We expect the first and the fourth columns to be similar in order to consider the estimate robust. The same conclusion is made between the fifth and the sixth columns which represent the standard deviation of the transformation (Std of est) and the mean of the standard deviation (Mean of std) respectively. In the seventh column (Prop rej) it is calculated the proportion between NUM_CAMP runs fall in the rejection region. If we simulate under H0 then we expect that this value is about alpha = 0.05 (type one error probability) while we expect it is about the true value 1 - beta (power) if we simulate under H1.

matH0 is a matrix of six elements. In the first row we have the variance of X, the covariance between X and Y and the expected value of X respectively. In the second row we have the covariance between X and Y, the variance of Y and the expected value of Y respectively. matH1 has exactly the same structure of matH0.

Value

table it is a matrix with 6 rows and 7 columns. Each row represents a measure of agreement and each column a summary for the simulation. See Details.
underH0 see above
matH0 see above
matH1 see above
NUM_CAMP see above
NUM see above
alpha see above
rho is the value for the correlation coefficient under null hypothesis (if underH0 = TRUE) or alternative hypothesis (if underH0 = FALSE)

Author(s)

Fabio Frascati fabio.frascati@studenti.unimi.it

References

D. G. Altman, J. M. Bland (1983): Measurement in Medicine: The Analysis of Method Comparison Studies, The Statistician, 32, 302–317

L. Lin (1989): A Concordance Correlation Coefficient to Evaluate Reproducibility, Biometrics, 45, 255–258

L. Lin, A. Heyadat, B. Sinha, M. Yang (2002): Statistical methods in assessing agreement: Models, issues, and tools, JASA, 97, 257–270

Examples

## we define the matrix of parameters under H0
sigma2x0   <- 1 / 1.15
sigma2y0   <- 1.15
covxy0     <- 0.95 * sqrt(1 / 1.15 * 1.15)
mux0       <- 0
muy0       <- 0.15
matH0      <- matrix(0,nrow = 2,ncol = 3)
matH0[1,1] <- sigma2x0
matH0[1,2] <- covxy0
matH0[1,3] <- mux0
matH0[2,1] <- covxy0
matH0[2,2] <- sigma2y0
matH0[2,3] <- muy0
## we define the matrix of parameters under H1
sigma2x1   <- 1 / 1.1
sigma2y1   <- 1.1
covxy1     <- 0.9662055 * sqrt(1 / 1.1 * 1.1)
mux1       <- 0
muy1       <- 0.1
matH1      <- matrix(0,nrow = 2,ncol = 3)
matH1[1,1] <- sigma2x1
matH1[1,2] <- covxy1
matH1[1,3] <- mux1
matH1[2,1] <- covxy1
matH1[2,2] <- sigma2y1
matH1[2,3] <- muy1
## we run lin.simulation()
lin.simulation(matH0 = matH0,matH1 = matH1,NUM = 30,NUM_CAMP = 5000,underH0 = TRUE)

[Package agreement version 1.0-1 Index]