Linear Mixed-Effects Models with Censored Responses

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Description

This generic function fits a linear mixed-effects model in the formulation described in Laird and Ware (1982) but allowing for censored normal responses. In this version, the with-in group errors are assumed independent and identically distributed.

Usage

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lmec(yL, cens, X, Z, cluster, maxstep = 200, varstruct = "unstructured", init, method = "ML", epsstop = 0.001, abspmv = 0.001, mcmc0 = 100, sdl = 0.1, iter2 = 15, trs = 5, pls = 5, mcmcmax = 1000)

Arguments

yL

Observed left-censored response vector

cens

Censoring indicator: if yL>ytrue, then cens=1

X

Design matrix for the fixed-effects model, it needs to include a column of 1's if the intercept is present

Z

If the design matrix for the random-effects is diag(Z1, Z2, ..., Zm), then Z=(Z1',Z2', ..., Zm')'

cluster

Cluster indicator taking values between 1 and m

maxstep

The maximum number of EM iterations

varstruct

Variance structure for random effects, current options are unstructured and diagonal.

init

Intial estimated parameters (it is optional), it is a list with components beta, bi, sigma and Delta.

method

Options are ML, REML and MLmcmc

epsstop

The threshold for the difference between two consecutive likelihood values in EM sequence

abspmv

Absolute error tolerance for pmvnorm() function

mcmc0

The burn-in MCMC sample size for E-step of EM

sdl

The target standard deviation for the log-likelihood

iter2

Number of steps in stage 2 for evaluating standard deviation of log-likelihhood

trs

Number of increase in sample size during transition face

pls

Number of steps in plateau face of MCEM

mcmcmax

Maximum MCEM sample size

Value

beta

Estimated fixed effects

bi

Estimated random effects

sigma

Residual standard deviation

Psi

Variance matrix of random effects

Delta

Matrix such that Delta'*Delta=sigma2*solve(Psi)

loglik

Maximum log-likelihood value (or surrogate objective function)

varFix

Variance matrix for fixed effects

method

Options are ML, REML and MLmcmc

varstruct

Variance structure for random effects, current options are unstructured and diagonal

step

Number of EM iterations

likseq

Log-likelihood EM sequence

Author(s)

Florin Vaida (fvaida@ucsd.edu) and Lin Liu (linliu@ucsd.edu)

References

Vaida, Florin and Liu, Lin, Fast Implementation For Normal Mixed Effects Models with Censored Response (submitted).

Vaida, Florin and Fitzgerald, Anthony and DeGruttola, Victor (2007), Efficient Hybrid EM for nonlinear mixed effects models with censored response, Computational Statistics and Data Analysis, 51, 5718-5730.

Examples

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data(UTIdata)
UTIdata <- subset(UTIdata, !is.na(RNA))
o <- order(UTIdata$Patid, UTIdata$Fup)
UTIdata <- UTIdata[o,]
cens = (UTIdata$RNAcens==1)+0
y = log10(UTIdata$RNA)
X = cbind((UTIdata$Fup==0)+0, (UTIdata$Fup==1)+0, (UTIdata$Fup==3)+0, (UTIdata$Fup==6)+0, (UTIdata$Fup==9)+0, (UTIdata$Fup==12)+0, (UTIdata$Fup==18)+0, (UTIdata$Fup==24)+0)
Z = matrix(rep(1, length(y)), ncol=1)
cluster = as.numeric(UTIdata$Patid)
fit = lmec(yL=y,cens=cens, X=X, Z=Z, cluster=cluster, method='ML', maxstep=40)