ARpMMEC.est {ARpLMEC}

Censored Mixed-Effects Models with Autoregressive Correlation Structure and DEC for Normal and t-Student Errors

Description

This functino fits left, right or intervalar censored mixed-effects linear model, with autoregressive errors of order p, using the EM algorithm. It returns estimates, standard errors and prediction of future observations.

Usage

ARpMMEC.est(
  y,
  x,
  z,
  tt,
  cc,
  nj,
  struc = "UNC",
  order = 1,
  initial = NULL,
  nu.fixed = TRUE,
  typeModel = "Normal",
  cens.type = "left",
  LI = NULL,
  LS = NULL,
  MaxIter = 200,
  error = 1e-04,
  Prev = FALSE,
  step = NULL,
  isubj = NULL,
  xpre = NULL,
  zpre = NULL
)

Arguments

y

Vector 1 x n of censored responses, where n is the sum of the number of observations of each individual

x

Design matrix of the fixed effects of order n x s, corresponding to vector of fixed effects.

z

Design matrix of the random effects of ordern x b, corresponding to vector of random effects.

tt

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

cc

Vector of censoring indicators of length n, where n is the total of observations. For each observation: 0 if non-censored, 1 if censored.

nj

Vector 1 x m with the number of observations for each subject, where m is the total number of individuals.

struc

UNC,ARp,DEC,SYM or DEC(AR) for uncorrelated ,autoregressive, DEC(phi1,phi2), DEC(phi1,phi2=1), DEC(DEC(phi1,phi2=1)) structure, respectively

order

Order of the autoregressive process. Must be a positive integer value.

initial

List with the initial values in the next orden: betas,sigma2,alphas,phi and nu. If it is not indicated it will be provided automatically. Default is NULL

nu.fixed

Logical. Should estimate the parameter "nu" for the t-student distribution?. If is False indicates the value in the list of initial values. Default is FALSE

typeModel

Normal for Normal distribution and Student for t-Student distribution. Default is Normal

cens.type

left for left censoring, right for right censoring and interval for intervalar censoring. Default is left

LI

Vector censoring lower limit indicator of length n. For each observation: 0 if non-censored, -inf if censored. It is only indicated for when cens.type is both. Default is NULL

LS

Vector censoring upper limit indicator of length n. For each observation: 0 if non-censored, inf if censored.It is only indicated for when cens.type is both. Default is NULL

MaxIter

The maximum number of iterations of the EM algorithm. Default is 200

error

The convergence maximum error. Default is 0.0001

Prev

Indicator of the prediction process. Available at the moment only for the typeModel=normal case. Default is FALSE

step

Number of steps for prediction. Default is NULL

isubj

Vector indicator of subject included in the prediction process. Default is NULL

xpre

Design matrix of the fixed effects to be predicted. Default is NULL.

zpre

Design matrix of the random effects to be predicted. Default is NULL.

Value

returns list of class “ARpMMEC”:

FixEffect

Data frame with: estimate, standar errors and confidence intervals of the fixed effects.

Sigma2

Data frame with: estimate, standar errors and confidence intervals of the variance of the white noise process.

Phi

Data frame with: estimate, standar errors and confidence intervals of the autoregressive parameters.

RandEffect

Data frame with: estimate, standar errors and confidence intervals of the random effects.

nu

the parameter "nu" for the t-student distribution

Est

Vector of parameters estimate (fixed Effects, sigma2, phi, random effects).

SE

Vector of the standard errors of (fixed Effects, sigma2, phi, random effects).

Residual

Vector of the marginal residuals.

loglik

Log-likelihood value.

AIC

Akaike information criterion.

BIC

Bayesian information criterion.

AICc

Corrected Akaike information criterion.

iter

Number of iterations until convergence.

Yfit

Vector "y" fitted

MI

Information matrix

Prev

Predicted values (if xpre and zpre is not NULL).

time

Processing time.

others

The first and second moments of the random effect and vector Y

References

Olivari, R. C., Garay, A. M., Lachos, V. H., & Matos, L. A. (2021). Mixed-effects models for censored data with autoregressive errors. Journal of Biopharmaceutical Statistics, 31(3), 273-294. doi:10.1080/10543406.2020.1852246

Examples

## Not run: 
p.cens   = 0.1
m           = 10
D = matrix(c(0.049,0.001,0.001,0.002),2,2)
sigma2 = 0.30
phi    = 0.6
beta   = c(1,2,1)
nj=rep(4,10)
tt=rep(1:4,length(nj))
x<-matrix(runif(sum(nj)*length(beta),-1,1),sum(nj),length(beta))
z<-matrix(runif(sum(nj)*dim(D)[1],-1,1),sum(nj),dim(D)[1])
data=ARpMMEC.sim(m,x,z,tt,nj,beta,sigma2,D,phi,struc="ARp",typeModel="Normal",p.cens=p.cens)

teste1=ARpMMEC.est(data$y_cc,x,z,tt,data$cc,nj,struc="ARp",order=1,typeModel="Normal",MaxIter = 2)
teste2=ARpMMEC.est(data$y_cc,x,z,tt,data$cc,nj,struc="ARp",order=1,typeModel="Student",MaxIter = 2)

xx=matrix(runif(6*length(beta),-1,1),6,length(beta))
zz=matrix(runif(6*dim(D)[1],-1,1),6,dim(D)[1])
isubj=c(1,4,5)
teste3=ARpMMEC.est(data$y_cc,x,z,tt,data$cc,nj,struc="ARp",order=1,typeModel="Normal",
                  MaxIter = 2,Prev=TRUE,step=2,isubj=isubj,xpre=xx,zpre=zz)
teste3$Prev


## End(Not run)