aisoph {aisoph}R Documentation

Fit Additive Isotonic Proportional Hazards Model

Description

Nonparametric estimation of additive isotonic covariate effects for proportional hazards model.

Usage

  aisoph(time, status, z1, z2, trt, shape1, shape2, K1, K2, maxdec, maxiter, eps)

Arguments

time

survival time. It must be greater than 0.

status

censoring indication. It must be 0 or 1.

z1

First covariate.

z2

Second covariate.

trt

Treatment group variable. It must be 0 or 1. This argument is optional.

shape1

Direction for z1 , "increasing" or "decreasing".

shape2

Direction for z1 , "increasing" or "decreasing.

K1

anchor constraint for z1 (default is 0).

K2

anchor constraint for z2 (default is 0).

maxdec

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

maxiter

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

eps

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

Details

The aisoph function allows to analyze additive isotonic proportional hazards model, which is defined as

\lambda(t|Z1, Z2, trt)=\lambda0(t)exp(\psi1(Z1)+\psi2(Z2)+\beta trt),

where \lambda0 is a unspecified baseline hazard function, \psi1 and \psi2 are monotone increasing (or decreasing) functions, trt is a binary variable coded as 0 and 1, e.g. 1 for treatment and 0 for placebo, and \beta is a regression paramter. If trt is omitted in the formulation above, \psi1 and \psi2 are estimated as right continuous increasing (or left continuous decreasing) step functions. Otherwise, \psi1, \psi2 and trt are estimated.

For the anchor constraint, one point has to be fixed with \psi1(K1)=0 to solve the identifiability problem, e.g. \lambda0(t)exp(\psi1(z1)+\psi2(z2)+\beta trt)=(\lambda0(t)exp(-c))exp(\psi1(z)+c+\psi2(z2)+\beta trt) for any constant c. Similarly, \psi2(K2)=0. K1 and K2 are called anchor points. By default, we set K1 and K2 as medians of z1 s and z2 values, respectively. The choise of anchor points are less importants because hazars ratios are not affected by anchor points.

Value

A list of class isoph:

est1

data.frame with estimated \psi1, \exp(\psi1), level set of z1.

est2

data.frame with estimated \psi1, \exp(\psi2), level set of z2.

psi1

estimated \psi1 at sorted z1.

psi2

estimated \psi1 at sorted z2.

exp.beta

estimated \exp(\beta).

z1

Sorted z1.

z2

Sorted z2.

z1.range

Range of z1.

z2.range

Range of z2.

conv

Algorithm convergence status.

K1

anchor point satisfying \psi1(K1)=0.

K2

anchor point satisfying \psi2(K2)=0.

call

formulation.

Author(s)

Yunro Chung [aut, cre]

References

Yunro Chung, Anastasia Ivanova, Jason P. Fine, Additive isotonic proportional hazards models (working in progress).

Examples

#require(survival)
#require(Iso)

###
# 1. time-independent covariate with monotone increasing effect
###
# 1.1. create a test data set 1
time=  c(1, 6, 3, 6, 7, 8, 1, 4, 0, 2, 1, 5, 8, 7, 4)
status=c(1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
z1=     c(3, 1, 2, 4, 8, 3, 3, 4, 1, 9, 4, 2, 2, 8, 5)
z2=     c(1, 3, 5, 6, 1, 7, 6, 8, 3, 4, 8, 8, 5, 2, 3)

# 1.2. Fit isotonic proportional hazards model
res1 = aisoph(time=time, status=status, z1=z1, z2=z2)

# 1.3. print result
res1

#1.4. plot
plot(res1)

###
# 2. time-independent covariate with monotone increasing effect
###
# 2.1. create a test data set 1
time=  c(0,4,8,9,5,6,9,8,2,7,4,2,6,2,5,9,4,3,8,2)
status=c(0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1)
z1=    c(3,2,1,1,3,1,8,4,3,6,2,9,9,0,7,7,2,3,4,6)
z2=    c(3,6,9,9,4,3,9,8,4,7,2,3,1,3,7,0,1,6,4,1)
trt=   c(0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1)

# 2.2. Fit isotonic proportional hazards model
res2 = aisoph(time=time, status=status, z1=z1, z2=z2, trt=trt)

# 2.3. print result
res2

#2.4. plot
plot(res2)

[Package aisoph version 0.2 Index]