aisoph: Fit Additive Isotonic Proportional Hazards Model

In aisoph: Additive Isotonic Proportional Hazards Model

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

λ(t|z1, z2, x)=λ0(t)exp(ψ1(z1)+ψ2(z2)+β x),

where λ0 is an unspecified baseline hazard function, ψ1 and ψ2 are monotone increasing (or decreasing) functions in z1 and z2, respectively, x is a covariate, and β is a regression paramter. If x is omitted in the formulation above, ψ1 and ψ2 are only estimated.

The model is not identifiable without the anchor constraint, ψ1(K1)=0 and ψ2(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 ψ1, estimated \exp(ψ1), and cens at z1, where \exp(ψ1) 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 ψ2, estimated \exp(ψ2), and cens at z2, where \exp(ψ2) 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 β, and \exp(β).
conv	status of algorithm convergence.
shape1	shape-constrain for ψ1.
shape2	shape-constrain for ψ2.
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)

aisoph documentation built on March 7, 2023, 6:56 p.m.