Package 'aisoph'

Additive Isotonic Proportional Hazards Model

Description

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

Details

Package:	aisoph
Type:	Package
Version:	0.4
Date:	2023-03-03
License:	GPL (>= 2)

Author(s)

Yunro Chung [aut, cre] Maintainer: Yunro Chung <[email protected]>

References

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

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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)

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