isoph (version 0.3)

isoph: Fit Isotonic Proportional Hazards Model

Description

Nonparametric estimation of an isotonic covariate effect for Cox's partial likelihood.

Usage

isoph(formula, data, shape, K, maxiter, eps, maxdec)

Arguments

formula

a formula object: a response ~ a univariate covariate. The response must be survival outcome unsing the Surv function. For interval data, each subject's starting time must be set to 0.

data

data.frame or list that includes variables named in the formula argument.

shape

direction of the covariate effect on the hazard function, "increasing" or "decreasing"

K

anchor constraint (default is 0).

maxiter

maximum number of iteration (default is 10^5).

eps

stopping convergence criteria (default is 10^-3).

maxdec

maximum number of decisimal for output (default is 2).

Details

The isoph function of isoph allows to analyze isotonic proportional hazards model, defined as $$\lambda(t|z)=\lambda0(t)exp(\psi(Z)),$$ where $\lambda0$ is a baseline hazard function and $\psi$ is an isotonic function. Correspondingly, the partial likelihood is well defined, and thus, $\psi$ can be computed by maximizing the partial likelihood over an isotonic constraint.

As similar to a reference cell conding in the standard Cox's proportional hazard model, one point has to be fixed with $\psi(K)=0$, where $K$ is called an anchor point. A direction of $\psi$ should be defined as monotone increasing or monotone decreasing in $Z$. Time-dependent covariate is allowed with interval data, where each subject's starting time must be set to zero.

Pseudo iterative convex minorant algorithm is used.

References

Yunro Chung, Anastasia Ivanova, Michael M. Hudgens, Jason P. Fine, Partial likelihood estimation of isotonic proportional hazards models (under revision).

Examples

#require(survival)
#require(Iso)

###
# 1. Time-independent covariate with monotone increasing effect
###
# 1.1. Create a test data set 1
test1=list(
  time=  c(2, 5, 1, 7, 9, 5, 3, 6, 8, 9, 7),
  status=c(1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1),
  z=     c(2, 1, 1, 3, 5, 6, 7, 9, 3, 0, 2)
)

# 1.2. Fit isotonic proportional hazards model
res1 = isoph(Surv(time, status)~z, data=test1, shape="increasing")

# 1.3. Print result
res1

# 1.4 Figure
plot(res1, which=1) #which=1 for psi (default)
plot(res1, which=2) #which=2 for psiexp(psi.hat)

###
# 2. Test 2: Time-dependent covariate with monotone decreasing effect
###
# 2.1. Create a test data set 2
test2=list(
  start= c(0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2),
  stop=  c(5, 2, 6, 3, 8, 1, 2, 5, 7, 2 ,2, 8),
  status=c(1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1),
  z=     c(1, 2, 1, 3, 5, 3, 1, 3, 2, 8, 5, 7)
)

# 2.2. Fit isotonic proportional hazards model
res2 = isoph(Surv(start,stop,status)~z, data=test2, shape="decreasing")

# 2.3. Print result
res2

# 2.4. Figure
plot(res2, which=1) #which=1 for psi (default)
plot(res2, which=2) #which=2 for psiexp(psi.hat)

###
#3. More arguments for plot.isoph
###
#3.1. removes labels
plot(res2, main=NA, ylab=NA, xlab=NA, lglab=NA)

#3.2. renames labels
plot(res2, main="Iso PH", ylab="Iso", xlab="Cov", lglab="Cov wt obs", lgloc="center", lgcex=1.5)

#3.3. adjust xlim and ylim, with change in line and point
plot(res2, xlim=c(2,4), ylim=c(-2,0), lty=2, lcol=2, lwd=2, pch=3, pcol=4, pcex=1.5)