Bayesian Censored Mixed-Effects Models with Damped Exponential Correlation Structures for Scale Mixture of Normal distributions error

Description

This function fits left, right censored mixed-effects linear model, with scale mixture of normal distribution errors, using the Stan. It returns estimates, standard errors and LPML, AIC, BIC and DIC.

Usage

SMNlmec.est(
  ID,
  x_set,
  z_set,
  tt,
  y_complete,
  censor_vector,
  dist = "Normal",
  struc = "UNC",
  direction = "left",
  thin_num = 1,
  chains_num = 1,
  iter_num = 3000,
  burn_percen = 0.1,
  seed_set = NULL,
  adapt_delta_set = 0.8
)

Arguments

Value

Return a S4 class SMNlmecfit object. Using function SMNlmec.summary() to obtain the estimation of parameters and model selection criteria. The SMNlmecfit include:

References

Kelin Zhong, Fernanda L. Schumacher, Luis M. Castro and Victor H. Lachos. Bayesian analysis of censored linear mixed-effects models for heavy-tailed irregularly observed repeated measures. Statistics in Medicine, 2025. doi:10.1002/sim.10295

Examples

require(rstan)
require(StanHeaders)
require(MASS)
require(tmvtnorm)
require(mvtnorm)
require(mnormt)

data("UTIdata_sub")
data1 <- UTIdata_sub
y1 <- c(log10(data1$RNA))
cc <- (data1$RNAcens==1)+0
y_com<-as.numeric(y1)
rho_com<-as.numeric(cc)
x <- cbind(
 (data1$Fup==0)+0,
 (data1$Fup==1)+0,
 (data1$Fup==3)+0,
 (data1$Fup==6)+0,
 (data1$Fup==9)+0,
 (data1$Fup==12)+0,
 (data1$Fup==18)+0,
 (data1$Fup==24)+0
 )
z <- matrix(rep(1, length(y1)), ncol=1)

UTI_T_DEC <- SMNlmec.est(ID = data1$Patid, x_set = x, z_set = z,
                         tt = data1$Fup, y_complete = y_com,
                         censor_vector = rho_com, dist = "Student",
                         struc = "DEC", direction = "left",
                         thin_num = 1, chains_num = 1, iter_num = 3000,
                         burn_percen = 0.1, seed_set = 9955,
                         adapt_delta_set = 0.8)

SMNlmec.summary(UTI_T_DEC)

Generating Censored UNC, DEC, CAR errors with Mixed Effects, for normal, student's-t and slash distribution.

Description

Generating Censored UNC, DEC, CAR errors with Mixed Effects, for normal, student's-t and slash distribution.

Usage

SMNlmec.sim(
  m,
  x,
  z,
  tt,
  nj,
  beta,
  sigma2,
  D,
  phi,
  struc = "UNC",
  typeModel = "Normal",
  p.cens = 0.1,
  n.cens = NULL,
  cens_type = "right",
  nu_set = NULL
)

Arguments

Value

return list:

Examples

p.cens <- 0.1
m <- 50
D <- matrix(c(0.049,0.001,0.001,0.002),2,2)
sigma2_set <- 0.15
beta <- c(-2.83,-0.18)
nu <- 2
phi <- c(0.6,2)
nj <- rep(6,m)
tt <- rep(1:6,length(nj))
X1 <- rep(1,sum(nj))
X2 <- tt
x <- as.matrix(cbind(X1,X2))
Z1 <- rep(1,sum(nj))
Z2 <- tt
z <- as.matrix(cbind(Z1,Z2))

ID_sim <- rep(0,length(tt))
ID_log <- 0
for(i in 1:m) {
  for(j in 1:nj[i]) {
    ID_sim[ID_log + j] <- i
  }
  ID_log <- ID_log + nj[i]
}

Slash_DEC_sim <- SMNlmec.sim(m = m,x = x,z = z,tt = tt,nj = nj,beta = beta,
                      sigma2 = sigma2_set,D = D,phi= phi,struc ="DEC",
                      typeModel="Slash",p.cens = p.cens,n.cens = NULL,
                      cens_type="right",nu_set=nu)

head(Slash_DEC_sim$cc)
sum(Slash_DEC_sim$cc)/length(Slash_DEC_sim$cc)

head(Slash_DEC_sim$y_cc)


y_com <- as.numeric(Slash_DEC_sim$y_cc)
rho_com <- as.numeric(Slash_DEC_sim$cc)
tem <- tt

Slash_DEC_est <- SMNlmec.est(ID = ID_sim, x_set = x, z_set = z,
                         tt = tem, y_complete = y_com,
                         censor_vector = rho_com, dist = "Slash",
                         struc = "DEC", direction = "right",
                         thin_num = 1, chains_num = 1, iter_num = 3000,
                         burn_percen = 0.1, seed_set = 9955,
                         adapt_delta_set = 0.8)

SMNlmec.summary(Slash_DEC_est)

SMNlmecfit Summary

Description

A generic function to provide a summary for objects of class SMNlmecfit.

Usage

SMNlmec.summary(object)

Arguments

Value

A summary of model estimations, R-hats, standard errors, and criteria.

S4 method for summarizing SMNlmecfit objects

Description

S4 method for summarizing SMNlmecfit objects

Fitted SMNlmec Model Object

Description

An S4 class returned by SMNlmec.est(). Users usually do not need to create objects of this class directly.

Slots

stan_object

stanfit object from rstan.

model_criteria

list, model selection criteria.

dist_set

character, the name of distribution.

struc_set

character, the name of correlation structure.

Data set for Unstructured Treatment Interruption Study

Description

Data set from a study of Unstructured Treatment Interruption in HIV-infected adolescents in four institutions in the US. The main outcome is the HIV-1 RNA viral load, which is subject to censoring below the lower limit of detection of the assay (50 copies/mL). The censored observations are indicated by the variable RNAcens.

Usage

data(UTIdata)

Format

A data frame with 373 observations on the following 5 variables.

Patid

patient ID

Days.after.TI

days after treatment interruption.

Fup

follow-up months

RNA

viral load RNA

RNAcens

censoring indicator for viral load

References

Saitoh, A., Foca, M, et al. (2008), Clinical outcome in perinatally acquired HIV-infected children and adolescents after unstructured treatment interruption, Pediatrics,121, e513-e521.

Sub data set for Unstructured Treatment Interruption Study

Description

Data set from a study of Unstructured Treatment Interruption in HIV-infected adolescents in four institutions in the US. The main outcome is the HIV-1 RNA viral load, which is subject to censoring below the lower limit of detection of the assay (50 copies/mL). The censored observations are indicated by the variable RNAcens. Excluding subjects whose observations are less than 2 and with missing RNA (excluding subject ID C6 T16).

Usage

data(UTIdata_sub)

Format

A data frame with 360 observations on the following 5 variables.

Patid

patient ID

Days.after.TI

days after treatment interruption.

Fup

follow-up months

RNA

viral load RNA

RNAcens

censoring indicator for viral load

References

Saitoh, A., Foca, M, et al. (2008), Clinical outcome in perinatally acquired HIV-infected children and adolescents after unstructured treatment interruption, Pediatrics,121, e513-e521.