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

 1 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.

  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 44 45 46 47 48 49 50 51 52 53 54 55 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