| coxph {survival} | R Documentation |
Fits a Cox proportional hazards regression model. Time dependent variables, time dependent strata, multiple events per subject, and other extensions are incorporated using the counting process formulation of Andersen and Gill.
coxph(formula, data=, weights, subset,
na.action, init, control,
method=c("efron","breslow","exact"),
singular.ok=TRUE, robust=FALSE,
model=FALSE, x=FALSE, y=TRUE, ...)
formula |
a formula object, with the response on the left of a ~ operator, and
the terms on the right. The response must be a survival object as
returned by the Surv function.
|
data |
a data.frame in which to interpret the variables named in
the formula, or in the subset and the weights
argument.
|
weights |
vector of case weights. If weights is a vector of integers,
then the
estimated coefficients are equivalent to estimating the model from data
with the individual cases replicated as many times as indicated by
weights.
|
subset |
expression indicating which subset of the rows of data should be used in the fit. All observations are included by default. |
na.action |
a missing-data filter function. This is applied to the model.frame
after any
subset argument has been used. Default is options()\$na.action.
|
init |
vector of initial values of the iteration. Default initial value is zero for all variables. |
control |
Object of class coxph.control specifying iteration limit
and other control options. Default is coxph.control(...).
|
method |
a character string specifying the method for tie handling. If there are no tied death times all the methods are equivalent. Nearly all Cox regression programs use the Breslow method by default, but not this one. The Efron approximation is used as the default here, as it is much more accurate when dealing with tied death times, and is as efficient computationally. The exact method computes the exact partial likelihood, which is equivalent to a conditional logistic model. If there are a large number of ties the computational time will be excessive. |
singular.ok |
logical value indicating how to handle collinearity in the model matrix.
If TRUE, the program will automatically skip over columns of the X
matrix that are linear combinations of earlier columns. In this case the
coefficients for such columns will be NA, and the variance matrix will
contain zeros. For ancillary calculations, such as the linear
predictor,
the missing coefficients are treated as zeros.
|
robust |
if TRUE a robust variance estimate is returned.
Default is TRUE if the model includes a cluster
operative,
FALSE otherwise.
|
model |
logical value: if TRUE, the model frame is returned in component
model.
|
x |
logical value: if TRUE, the model frame is returned in
component x.
|
y |
logical value: if TRUE, the model frame is returned in
component y.
|
... |
Other arguments will be passed to coxph.control
|
The proportional hazards model is usually expressed in terms of a single survival time value for each person, with possible censoring. Andersen and Gill reformulated the same problem as a counting process; as time marches onward we observe the events for a subject, rather like watching a Geiger counter. The data for a subject is presented as multiple rows or "observations", each of which applies to an interval of observation (start, stop].
an object of class "coxph" representing the fit.
See coxph.object for details.
Depending on the call, the predict, residuals, and survfit routines may
need to reconstruct the x matrix created by coxph. Differences in the
environment, such as which data frames are attached or the value of
options()\$contrasts, may cause this computation to fail or worse, to be
incorrect. See the survival overview document for details.
There are two special terms that may be used in the model equation.
A strata term identifies a stratified Cox model; separate baseline
hazard functions are fit for each strata.
The cluster term is used to compute a robust variance for the model.
The term + cluster(id) where each value of id is unique is equivalent to
specifying the robust=T argument, and produces an approximate
jackknife estimate of the variance. If the id variable were not
unique, but instead
identifies clusters of correlated observations, then the variance
estimate is based on a grouped jackknife.
In certain data cases the actual MLE estimate of a coefficient is infinity, e.g., a dichotomous variable where one of the groups has no events. When this happens the associated coefficient grows at a steady pace and a race condition will exist in the fitting routine: either the log likelihood converges, the information matrix becomes effectively singular, an argument to exp becomes too large for the computer hardware, or the maximum number of interactions is exceeded. (Nearly always the first occurs.) The routine attempts to detect when this has happened, not always successfully. The primary consequence for he user is that the Wald statistic, coefficient/se(coefficient), is not valid in this case and should be ignored; the likelihood ratio and Wald tests remain valid however.
coxph can now maximise a penalised partial likelihood with
arbitrary user-defined penalty. Supplied penalty functions include
ridge regression (ridge), smoothing splines
(pspline), and frailty models (frailty).
Andersen, P. and Gill, R. (1982). Cox's regression model for counting processes, a large sample study. Annals of Statistics 10, 1100-1120.
Therneau, T., Grambsch, P., Modeling Survival Data: Extending the Cox Model. Springer-Verlag, 2000.
cluster, strata, Surv,
survfit, \code{pspline}, \code{frailty},
\code{ridge}.
# Create the simplest test data set
test1 <- list(time=c(4,3,1,1,2,2,3),
status=c(1,1,1,0,1,1,0),
x=c(0,2,1,1,1,0,0),
sex=c(0,0,0,0,1,1,1))
# Fit a stratified model
coxph(Surv(time, status) ~ x + strata(sex), test1)
# Create a simple data set for a time-dependent model
test2 <- list(start=c(1,2,5,2,1,7,3,4,8,8),
stop=c(2,3,6,7,8,9,9,9,14,17),
event=c(1,1,1,1,1,1,1,0,0,0),
x=c(1,0,0,1,0,1,1,1,0,0))
summary(coxph(Surv(start, stop, event) ~ x, test2))
#
# Create a simple data set for a time-dependent model
#
test2 <- list(start=c(1, 2, 5, 2, 1, 7, 3, 4, 8, 8),
stop =c(2, 3, 6, 7, 8, 9, 9, 9,14,17),
event=c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0),
x =c(1, 0, 0, 1, 0, 1, 1, 1, 0, 0) )
summary( coxph( Surv(start, stop, event) ~ x, test2))
# Fit a stratified model, clustered on patients
bladder1 <- bladder[bladder$enum < 5, ]
coxph(Surv(stop, event) ~ (rx + size + number) * strata(enum) +
cluster(id), bladder1)