disoph {isoSurv} | R Documentation |
Fit Double Isotonic Proportional Hazards Model
Description
Nonparametric estimation of monotone baseline hazard and monotone covariate effect functions in the proportional hazards model.
Usage
disoph(formula, bshape, data, maxiter, eps)
Arguments
formula |
formula object: response ~ iso( |
bshape |
direnction of the baseline hazard function ( |
data |
data.frame includes variables named in the formula argument. |
maxiter |
maximum number of iteration (default is |
eps |
stopping convergence criteria (default is |
Details
The disoph function computes (\lambda0, \psi, \beta
) in the isotonic proportional hazards model, defined as
\lambda(t|z,x)=\lambda0(t)exp(\psi(z)+\beta_1x_1+\beta_2x_2+...+\beta_px_p),
based on the full likelihood, where \lambda0
is a monotone increasing (or decreasing) baseline hazard function, \psi
is a monotone increasing (or decreasing) covariate effect function, z
is a univariate variable, (x_1,x_2,...,x_p
) is a set of covariates, and \beta=(\beta_1,\beta_2,...,\beta_p
) is a set of corresponding regression parameters. It allows to estimate (\lambda0, \beta)
only if iso(z
,shape="increasing") is removed in the formula object. Likewise, It allows to estimate (\lambda0, \psi)
only if x
is removed in the formula object. Using the nonparametric maximum likelihood approaches, estimated \lambda0
and \psi
are right continuous increasing (or left continuos decreasing) step functions. Compared to the standard partial likelihood approach, the full likelihood approach in the disoph function additionally use shape-information on \lambda0
, resulting in more efficient estimators especially for a finate sampe size.
For the anchor constraint, one point has to be fixed with \psi(K)=0
to solve the identifiability problem, e.g. \lambda0(t)exp(\psi(z))=(\lambda0(t)exp(-c))(exp(\psi(z)+c))
for any constant c
. K
is called an anchor point. By default, we set K
as a median of values of z
's. The choice of anchor points are not important because, for example, different anchor points results in the same hazard ratios.
Value
A list of class fisoph:
iso.bh |
data.frame with |
iso.cov |
data.frame with |
beta |
estimated |
conv |
algorithm convergence status. |
iter |
total number of iterations. |
Zk |
anchor satisfying estimated |
shape.bh |
order restriction on |
shape.cov |
order restriction on |
Author(s)
Yunro Chung [auth, cre]
References
Yunro Chung, Double Isotonic Proportional Hazards Models with Applications to Dose-Finding Studies. In preparation.
Examples
#test1
test1=data.frame(
time= c(2, 5, 1, 7, 9, 5, 3, 6, 8, 9, 7, 4, 5, 2, 8),
status=c(0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1),
z= c(2, 1, 1, 3, 5, 6, 7, 9, 3, 0, 2, 7, 3, 9, 4)
)
disoph.fit1=disoph(Surv(time, status)~iso(z,shape="inc"),bshape="inc",data=test1)
print(disoph.fit1)
plot(disoph.fit1)
#test2
test2=data.frame(
time= c(2, 5, 1, 7, 9, 5, 3, 6, 8, 9, 7, 4, 5, 2, 8),
status=c(0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1),
z= c(2, 1, 1, 3, 5, 6, 7, 9, 3, 0, 2, 7, 3, 9, 4),
trt= c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0),
x= c(1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6)
)
disoph.fit2=disoph(Surv(time, status)~iso(z,shape="inc")+trt+x,bshape="inc",data=test2)
print(disoph.fit2)
plot(disoph.fit2)