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Type:

Package

Title:

Scale Mixture of Normal Distribution in Linear Mixed-Effects Model

Version:

1.0.0

Maintainer:

Kelin Zhong <kelin.zhong@uconn.edu>

Description:

Bayesian analysis of censored linear mixed-effects models that replace Gaussian assumptions with a flexible class of distributions, such as the scale mixture of normal family distributions, considering a damped exponential correlation structure which was employed to account for within-subject autocorrelation among irregularly observed measures. For more details, see Kelin Zhong, Fernanda L. Schumacher, Luis M. Castro, Victor H. Lachos (2025) <doi:10.1002/sim.10295>.

Depends:

R (≥ 4.2)

Imports:

rstan (≥ 2.26.23), StanHeaders (≥ 2.26.28), MASS (≥ 7.3-60), tmvtnorm (≥ 1.5), mvtnorm (≥ 1.2-3), mnormt (≥ 2.1.1), methods, stats, LaplacesDemon (≥ 16.1.6), TruncatedNormal (≥ 2.2.2), numDeriv (≥ 2016.8-1.1)

URL:

https://github.com/KelinZhong/SMNlmec

BugReports:

https://github.com/KelinZhong/SMNlmec/issues

License:

GPL-3

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.3.1

NeedsCompilation:

Packaged:

2025-01-30 00:21:04 UTC; Colin

Author:

Kelin Zhong [aut, cre], Fernanda L. Schumacher [aut], Luis M. Castro [aut], Victor H. Lachos [aut], Jalmar M.F. Carrasco [aut]

Repository:

CRAN

Date/Publication:

2025-01-30 08:10:02 UTC

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

ID

Vector N x 1 of the ID of the data set, specifying the ID for each measurement.

x_set

Design matrix of the fixed effects of order N x p.

z_set

Design matrix of the random effects of order N x d.

tt

Vector N x 1 with the time the measurements were made, where N is the total number of measurements for all individuals. Default it's considered regular times.

y_complete

Vector N x 1 of the complete responses.

censor_vector

Vector N x 1 of the indicator vector of censored responses.

dist

Distribution of the random effects and random error. Available options are Normal, Student and Slash.

struc

Structure of the correlation structure. Available options are UNC, DEC, CAR.

direction

Direction of censoring type. Available options are left and right.

thin_num

A positive integer specifying the period for saving samples. The default is 5. See more details in rstan::stan().

chains_num

A positive integer specifying the number of chains generating by rstan::stan(). The default is 3.

iter_num

A positive integer specifying the number of iterations for each chain (including warmup). The default is 5000.

burn_percen

A percentage of the warm-up iterations in each chain the Stan. The default is 0.1.

seed_set

A random seed. The default is NULL.

adapt_delta_set

A parameter to control the sampler's behavior. The default is 0.8. See rstan::stan() for more details.

Value

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

stan_object

A stanfit object from rstan::stan().

model_criteria

A list includes LPML, DIC, EAIC, EBIC, K-L divergence.

dist_set

The setting of distribution of the stan model.

struc_set

The setting of correlation structure of the stan model.

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

m

Number of individuals.

x

Design matrix of the fixed effects of order N x p, corresponding to vector of fixed effects.

z

Design matrix of the random effects of orderN x d, corresponding to vector of random effects.

tt

Vector N x 1 with the time the measurements were made, where N is the total number of measurements for all individuals.

nj

Vector m x 1 with the number of measurements of each individual, where m is the total number of individuals.

beta

Vector of values fixed effects.

sigma2

Values of the scalar of the variance matrix.

D

Variance matrix of the random effects of order d x d.

phi

Vector of parameter in the DEC and CAR structure. NULL for UNC, c(phi_1,phi_2) for DEC and c(phi_1,1) for CAR.

struc

Structure for the simulated data. Available options are UNC, DEC and CAR.

typeModel

Distribution of the simulated data. Available options are Normal, Student and Slash.

p.cens

Percentage of censored measurements in the responses. The default value is 0.1.

n.cens

Number of censored measurements in the responses. The default value is NULL.

cens_type

The direction of cesoring. Available options are left and right.

nu_set

degrees of freedom for student's-t or slash simulated data. The default value is NULL.

Value

return list:

cc

Vector of censoring indicators.

y_cc

Vector of responses censoring.

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)

## S4 method for signature 'SMNlmecfit'
SMNlmec.summary(object)

Arguments

object

An object of class SMNlmecfit.

Value

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

A printed summary of the SMNlmecfit object.

SMNlmecfit Class

Description

SMNlmecfit Class

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.

Create SMNlmecfit Objects

Description

A function to create objects of class SMNlmecfit.

Usage

SMNlmecfit.creator(stan_object, model_criteria, dist_set, struc_set)

Arguments

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.

Value

A SMNlmecfit object containing:

stan_object

A stanfit object from rstan::stan().

model_criteria

A list includes LPML, DIC, EAIC, EBIC, K-L divergence.

dist_set

The setting of distribution of the stan model.

struc_set

The setting of correlation structure of the stan model.

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

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.