Fit Proportional Hazards Regression Model

DESCRIPTION:

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.

USAGE:

coxph(formula, data=sys.parent(), weights=<<see below>>, subset, 
      na.action=na.fail, init, control=coxph.control, method="efron", 
      singular.ok=T, robust=<<see below>>, model=F, x=F, y=T) 

REQUIRED ARGUMENTS:

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.

OPTIONAL ARGUMENTS:

data
a data frame in which to interpret the variables named in the formula, subset, and weights arguments.
weights
a vector of case weights. If weights is a vector of integers, the estimated coefficients are equivalent to estimating the model from data with the individual cases replicated as many times as indicated by weights. Multiplying all weights by a positive constant c does not change the estimated coefficients or the robust standard errors computed by coxph. However, the standard errors of the coefficients will decrease by a factor of sqrt(c). By default, no weights are included in the model.
subset
an expression indicating which subset of the rows in data should be used in the fit. This can be a logical vector, which is replicated to have length equal to the number of observations, a numeric vector indicating which observation numbers are to be included (or excluded if negative), or a character vector of row names to be included. 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. The default is na.fail, which returns an error if any missing values are found. An alternative is na.exclude, which deletes observations that contain one or more missing values.
init
a vector of initial values for the iteration. The default is zero for all variables.
control
a list of control values to be used in the iteration. See coxph.control for the available control options and their default settings.
method
a character string specifying the method for tie handling. The choices are "efron", "breslow", and "exact". If there are no tied death times, all the methods are equivalent. Nearly all Cox regression programs use the Breslow method by default, but S-PLUS uses the Efron approximation. The Efron method 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 x. If singular.ok=TRUE, the program automatically skips over columns of x that are linear combinations of earlier columns. In this case, the coefficients for such columns are NA and the variance matrix contains zeros. For ancillary calculations such as the linear predictor, the missing coefficients are treated as zeros.
robust
logical value. If TRUE, a robust variance estimate is returned. The default is TRUE if the model includes a cluster operative and FALSE otherwise.
model
logical value. If TRUE, the model frame is returned in the component named model. By default, model=FALSE.
x
logical value. If TRUE, the model matrix is returned in the component named x. By default, x=FALSE.
y
logical value. If TRUE, the response is returned in the component named y. By default, y=TRUE.

VALUE:

an object of class "coxph" representing the fit. See coxph.object for details.

SIDE EFFECTS:

Depending on the call, the predict, residuals, and survfit routines may need to reconstruct the model 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 Guide to Statistics for details.

DETAILS:

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 observation interval (start, stop].

There are two special terms that may be used in the model equation. A strata term identifies a stratified Cox model, in which 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 id==unique(id), is equivalent to specifying the robust=T argument and produces an approximate jackknife estimate of the variance. If the values in id are not unique, but instead identify clusters of correlated observations, then the variance estimate is based on a grouped jackknife.

In certain cases, the actual maximum likelihood 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 exists 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's hardware, or the maximum number of interactions is exceeded. The routine attempts to detect when this has happened, but is not always successful.

REFERENCES:

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., and Fleming. T. (1990). Martingale based residuals for survival models. Biometrika 77: 147-160.

SEE ALSO:

, , , , , , .

EXAMPLES:

# 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), data = 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, data = test2)) 

# Fit a stratified model, clustered on patients 
bladder1 <- bladder 
bladder1$start <- NULL 
bladder1 <- bladder1[bladder1$enum < 5, ] 
coxph(Surv(stop, event) ~ (rx + size + number) * strata(enum) + 
      cluster(id), data = bladder1, method = "breslow")