CPHshape (version 1.0.1)

CPHshape-package: Compute the MLE in the Cox proportional hazard model with shape constrained baseline

Description

This package calculates the semi-parametric maximum likelihood estimator (MLE) of the effect parameters and the nonparametric hazard constrained to be either increasing, decreasing, unimodal, or u-shaped. We assume that the times are continuous, and allow for right-censoring.

Details

Package:

CPHshape

Type:

Package

Version:

1.0

Date:

2012-03-06

License:

GPL (>=2)

LazyLoad:

yes

The two main function in the package is find.shapeCPH: Compute the maximum likelihood estimator of the effect parameters and the nonparametric shape constrained hazard in the proportional hazard model.

The package also provides the function:

find.shapeMLE: Compute the MLE of a nonparametric shape-constrained hazard.

References

Grenander, U. (1956) On the theory of mortality measurement II. Skand. Aktuarietidskr. 39: 125-153. Hui, R. and Jankowski, H. (2012). Maximum likelihood estimation of a shape-constrained hazard in the proportional hazard model. Technical Report. http://www.math.yorku.ca/~hkj/ Jankowski, H. and Wellner, J. (2007) Nonparametric Estimation of a convex bathtub-shaped hazard function. University of Washington Technical Report no. 521. http://www.stat.washington.edu/tech.reports/ Mykytyn, S. and Santner, T. (1981) Maximum likelihood estimation of the survival function based on censored data under hazard rate assumptions. Comm. Statist. A - Theory and Methods 10 (14): 1369-1387. Lopuhaa, H.P., Nane, G.F., Shape constrained nonparametric estimators of the baseline distribution in Cox proportional hazards model (2011). Preprint.

Examples

# random sample from the proportional hazard model
n	<-	200
beta1	<-	1
beta2	<-	2
z1	<-	rbinom(n,1,0.5)
z2	<-	runif(n,-1,1)
w	<-	exp(beta1*z1+beta2*z2)
x	<-	rexp(n, rate=0.3*w)
delta	<-	1*(x<=2.5)
x	<-	pmin(x,2.5)

# compute MLE
mle	<-	find.shapeCPH(x, cbind(z1,z2) , delta, print=TRUE, type="decreasing")

# estimates of the effect parameter
mle$beta

# plot resulting estimate of baseline hazard

plot(mle)
abline(h=0.3, col="red") # add true baseline
rug(x)