EM_fit {PenIC}

EM algorithm for fitting generalized odds-rate model with specified link function (i.e., alpha value) under interval-censored data

Description

Fits the generalized odds-rate model based on penalized B-splines to interval censored data via an EM algorithm.

Usage

EM_fit(g0,b0,d1,d2,d3,Li,Ri,Z,nsub,alpha,qn,order,t.seq,tol=1e-5,itmax=500,lamu=1e5)

Arguments

g0

initial estimate of the spline coefficients; should be of length qn+order+1.

b0

initial estimate of regression coefficients; should be of length dim(Z)[2].

d1

vector indicating whether an observation is left-censored (1) or not (0).

d2

vector indicating whether an observation is interval-censored (1) or not (0).

d3

vector indicating whether an observation is right-censored (1) or not (0).

Li

the left endpoint of the observed interval; if an observation is left-censored, its corresponding entry should be 0.

Ri

the right endpoint of the observed interval; if an observation is right-censored, its corresponding entry should be Inf.

Z

design matrix of predictor variables (in columns); should be specified without an intercept term.

nsub

size of observed dataset.

alpha

parameter of link function; alpha=0 for the PH model and alpha=1 for the PO model.

qn

the number of interior knots to be used; should not exceed square root of sample size.

order

the order of the basis functions; order=3 for cubic spline.

tol

the convergence criterion of the EM algorithm.

t.seq

an increasing sequence of points at which the cumulative baseline hazard function is evaluated.

itmax

maximum iterations of EM procedure.

lamu

upper limit of smoothing parameter.

Details

The above function fits the generalized odds-rate model (with specified value of alpha) to interval censored data via an EM algorithm using penalized monotone B-splines.

Value

b

estimates of the regression coefficients.

g

estimates of the spline coefficients.

se

the standard deviation of b.

base

estimated cumulative baseline hazard function evaluated at the points t.seq.

lambda

final value of smooth parameter.

flag

the indicator whether the procedure converged; 0 if converged.

References

Lu, M., Liu, Y., Li, C. and Sun, J. (2019+). An efficient penalized estimation approach for a semi-parametric linear transformation model with interval-censored data. arXiv:1912.11703.

Examples

set.seed(1)
case  <- 2
nsub  <- 35

# Generate interval-censored data under PH model

dat <- dataPA(nsub,case,alpha=0)
rp  <- c(mean(dat$d1),mean(dat$d2),mean(dat$d3))
rp

# [1] 0.2571429 0.3428571 0.4000000

t.seq <- seq(0.01,4,0.01)

# number of interior knots to be used
qn    <- ceiling(nsub^(1/3))-2
order <- 3
d1    <- dat$d1
d2    <- dat$d2
d3    <- dat$d3
Ri    <- dat$Ri
Li    <- dat$Li
Z     <- dat$Z
p     <- ncol(Z)
b0    <- rep(0,p)
g0    <- sort(runif(qn+order+1,-1,1))

# Fit data under PH model

fit <- EM_fit(g0,b0,d1,d2,d3,Li,Ri,Z,nsub,alpha=0,qn,order,t.seq,tol=1e-2,itmax=100,lamu=1e5)
cbind(fit$b,fit$se)


#           [,1]      [,2]
#[1,] -1.0655212 0.5021835
#[2,]  0.7649178 0.3185045