MC_var_yibar_mis: Estimated mean and variance of the average change in CAL for...

In SMARTp: Sample Size for SMART Designs in Non-Surgical Periodontal Trials

Description

The estimated Monte Carlo mean and variance of the average change in clinical attachment level (CAL) for each subject

Usage

MC_var_yibar_mis(mu, Sigma, sigma1, lambda, nu, sigma0, Num, a0, b0, cutoff)

Arguments

mu	Mean matrix, where row represents each treatment path, and column represents each cluster unit
Sigma	Within-mouth teeth covariance matrix
sigma1	Standard deviation of the residual for the continuous outcome Y_{it}
lambda	The skewness parameter of the residual for the continuous outcome Y_{it}
nu	The degree freedom, or kurtosis parameter of the residual for the continuous outcome Y_{it}
sigma0	Standard deviation of the residual for the binary outcome M_{it}
Num	Number of samples to estimate mean or variance of \bar{Y}_i
a0	Intercept parameter in the probit model for the binary outcome M_{it}
b0	Slope parameter corresponding to the spatial random effect in the probit model for the binary outcome M_{it}
cutoff	Cut-off value in the binary outcome regression

Details

MC_var_yibar_mis computes the Monte-Carlo estimates of expectation and variance of the sample mean among the teeth within each mouth, i.e \bar{Y}_i = ∑ Y_{it}(1 - M_{it})/∑(1 - M_{it}), where Y_{it} is the change in CAL (measured in mm) for patient i and tooth t, and M_{it} is the misingness indicator, i.e., M_{it} = 1 implies tooth t in subject i is mising. The joint regression models for Y_{it} and M_{it} are available in Reich & Bandyopadhyay (2010, Annals of Applied Statistics).

Value

The simulated dataset of CAL change "Y_{it}", missingness "M_{it}" and function inside the indicator of "M_{it} I_{it}" for each tooth of each patient, with the corresponding estimated mean "mY_i", variance "VarY_i" and missing proportion "PM" for each patient

Author(s)

Jing Xu, Dipankar Bandyopadhyay, Douglas Azevedo, Bibhas Chakraborty

References

Besag, J., York, J. & Mollie, A. (1991), "Bayesian image restoration, with two applications in spatial statistics (With Discussion)", Annals of the Institute of Statistical Mathematics 43, 159.

Reich, B. & Bandyopadhyay, D. (2010), "A latent factor model for spatial data with informative missingness", The Annals of Applied Statistics 4, 439–459.

See Also

CAR_cov_teeth, SampleSize_SMARTp

Examples

m <- 28
Num <- 1000
cutoff <- 0
sigma1 <- 0.95
sigma0 <- 1
lambda <- 0
nu <- Inf
b0 <- 0.5
a0 <- -1.0
rho <- 0.975
tau <- 0.85
del1 <- 0.5
del2 <- 2

Sigma <- CAR_cov_teeth(m, rho, tau)
Sigma_comp <- array(Sigma, c(m, m, 4))
Sigma_sim <- array(Sigma, c(m, m, 10))

mu_comp <- array(0, c(2, m, 2))
mu_comp[, , 1] <- rbind(rep(0, m), rep(del1, m))
mu_comp[, , 2] <- rbind(rep(0, m), rep(del2, m))

VarYitd1R = MC_var_yibar_mis(mu = mu_comp[1, , 1], Sigma = Sigma,
                             sigma1 = sigma1,
                             lambda = lambda, nu = nu,
                             sigma0 = sigma0, Num = Num, a0 = a0, b0 = b0,
                             cutoff = cutoff)
PM <- VarYitd1R$PM
VarYid1R <- VarYitd1R$VarYi
mYid1R <- VarYitd1R$mYi
VarYitd1NR <- MC_var_yibar_mis(mu = mu_comp[2, , 1], Sigma = Sigma,
                               sigma1 = sigma1,
                               lambda = lambda, nu = nu,
sigma0 = sigma0, Num = Num, a0 = a0, b0 = b0, cutoff = cutoff)

PM <- VarYitd1NR$PM
VarYid1NR <- VarYitd1NR$VarYi
mYid1NR <- VarYitd1NR$mYi
VarYitd3R <- MC_var_yibar_mis(mu = mu_comp[1, , 2], Sigma = Sigma,
                              sigma1 = sigma1,
                              lambda = lambda, nu = nu,
                              sigma0 = sigma0, Num = Num, a0 = a0, b0 = b0,
                              cutoff = cutoff)

PM <- VarYitd3R$PM
VarYid3R <- VarYitd3R$VarYi
mYid3R <- VarYitd3R$mYi
VarYitd3NR <- MC_var_yibar_mis(mu = mu_comp[2,,2], Sigma = Sigma,
                               sigma1 = sigma1,
                               lambda = lambda, nu = nu,
sigma0 = sigma0, Num = Num, a0 = a0, b0 = b0, cutoff = cutoff)

PM <- VarYitd3NR$PM
VarYid3NR <- VarYitd3NR$VarYi
mYid3NR <- VarYitd3NR$mYi

SMARTp documentation built on May 17, 2019, 9 a.m.