aisoph {aisoph}

Fit Additive Isotonic Proportional Hazards Model

Description

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

Usage

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

Arguments

time

survival time. It must be greater than 0.

status

censoring indication. It must be 0 or 1.

z1

First covariate under order-restriction.

z2

Second covariate under-order restriction.

x

Additional covariates (vector or data.frame). This argument is optional

shape1

Shape-restriction for z1 , "increasing" or "decreasing".

shape2

Shape-restriction for z2 , "increasing" or "decreasing".

K1

anchor constraint for z1 .

K2

anchor constraint for z2 .

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, x)=\lambda0(t)exp(\psi1(z1)+\psi2(z2)+\beta x),

where \lambda0 is an unspecified baseline hazard function, \psi1 and \psi2 are monotone increasing (or decreasing) functions in z1 and z2, respectively, x is a covariate, and \beta is a regression paramter. If x is omitted in the formulation above, \psi1 and \psi2 are only estimated.

The model is not identifiable without the anchor constraint, \psi1(K1)=0 and \psi2(K2)=0. By default, K1 and K2 are set to medians of z1 and z2 values, respectively. The choice of the anchor points is less important in the sense that hazard ratios do not depend on the anchors.

Value

A list of class isoph:

iso1

data.frame estimated \psi1, estimated \exp(\psi1), and cens at z1, where \exp(\psi1) is a hazard ratio between z1 and K1, and cens="no" if (at least one) subject is not censored at z1 or cens="yes" otherwise.

iso2

data.frame estimated \psi2, estimated \exp(\psi2), and cens at z2, where \exp(\psi2) is a hazard ratio between z2 and K2, and cens="no" if (at least one) subject is not censored at z2 or cens="yes" otherwise.

est

data.frame with estimated \beta, and \exp(\beta).

conv

status of algorithm convergence.

shape1

shape-constrain for \psi1.

shape2

shape-constrain for \psi2.

K1

anchor point for K1.

K2

anchor point for K2.

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, 
              shape1="increasing", shape2="increasing")

# 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, x=trt,
              shape1="increasing", shape2="increasing")

# 2.3. print result
res2

#2.4. plot
plot(res2)