MC_var_yibar_mis {SMARTp}

Estimated mean and variance of the average change in CAL for each subject

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 = \sum Y_{it}(1 - M_{it})/\sum(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