aisoph {aisoph} | R Documentation |
Nonparametric estimation of additive isotonic covariate effects for proportional hazards model.
aisoph(time, status, z1, z2, trt, shape1, shape2, K1, K2, maxdec, maxiter, eps)
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 |
shape2 |
Direction for |
K1 |
anchor constraint for |
K2 |
anchor constraint for |
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). |
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.
A list of class isoph:
est1 |
data.frame with estimated |
est2 |
data.frame with estimated |
psi1 |
estimated |
psi2 |
estimated |
exp.beta |
estimated |
z1 |
Sorted z1. |
z2 |
Sorted z2. |
z1.range |
Range of z1. |
z2.range |
Range of z2. |
conv |
Algorithm convergence status. |
K1 |
anchor point satisfying |
K2 |
anchor point satisfying |
call |
formulation. |
Yunro Chung [aut, cre]
Yunro Chung, Anastasia Ivanova, Jason P. Fine, Additive isotonic proportional hazards models (working in progress).
#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)