EM.PScr {PScr}

Maximum likelihood estimation based on EM algorithm for the Power Series cure rate model

Description

This function provides the maximum likelihood estimation based on the EM algorithm for the Power Series cure rate model

Usage

EM.PScr(t, delta, z, model = 1, dist = 1, max.iter = 1000, 
           prec = 1e-04)

Arguments

t

observed times

delta

failure indicators

z

matrix of covariates (with n rows and r columns)

model

distribution to be used for the concurrent causes: 1 for Poisson, 2 for logarithmic, 3 for negative binomial, 4 for bernoulli and 5 for polylogarithm (Gallardo et al. 2018). 6 for Flory-Schulz (Azimi et al. 2022).

dist

distribution to be used for the time-to-event: 1 for slash half-normal (Gallardo et al., 2022), 2 for Weibull, 3 for gamma and 4 for Birnbaum-Saunders.

max.iter

maximum number of iterations to be used by the algorithm

prec

precision (in absolute value) for the parameters to stop the algorithm.

Details

The EM algorithm for the model is implemented as in Gallardo et al. (2017).

Value

estimate

a matrix containing the estimated parameters and their standard error

loglike

the estimated log-likelihood function evaluated in the maximum likelihood estimators

AIC

the Akaike information criterion

BIC

the Bayesian (also known as Schwarz) information criterion

Author(s)

Diego I. Gallardo and Reza Azimi

References

Azimi, R, Esmailian, M, Gallardo DI and Gomez HJ. (2022). A New Cure Rate Model Based on Flory-Schulz Distribution: Application to the Cancer Data. Mathematics 10, 4643

Gallardo DI, Gomez YM and De Castro M. (2018). A flexible cure rate model based on the polylogarithm distribution. Journal of Statistical Computation and Simulation 88 (11), 2137-2149

Gallardo DI, Gomez YM, Gomez HJ, Gallardo-Nelson MJ, Bourguignon M. (2022) The slash half-normal distribution applied to a cure rate model with application to bone marrow transplantation. Mathematics, Submitted.

Gallardo DI, Romeo JS and Meyer R. (2017). A simplified estimation procedure based on the EM algorithm for the power series cure rate model. Communications in Statistics-Simulation and Computation 46 (8), 6342-6359.

Examples

require(mstate)
data(ebmt4)
attach(ebmt4)
t = srv / 365.25 # Time in years
delta=srv.s
prophy=as.factor(proph)
year2=ifelse(year=="1985-1989",0,1)
z=t(model.matrix(~proph-1))
#Computes the estimation for Poisson-Slash half-normal cure rate model
EM.PScr(t, delta, z, model=1, dist=1)
#Computes the estimation for Flory-Schulz-Slash half-normal cure rate model
EM.PScr(t, delta, z, model=6, dist=1)