| predict.coxph {survival} | R Documentation |
Predictions for a Cox model
Description
Compute fitted values and regression terms for a model fitted by
coxph
Usage
## S3 method for class 'coxph'
predict(object, newdata,
type=c("lp", "risk", "expected", "terms", "survival"),
se.fit=FALSE, na.action=na.pass, terms=names(object$assign), collapse,
reference=c("strata", "sample", "zero"), ...)
Arguments
object |
the results of a coxph fit. |
newdata |
Optional new data at which to do predictions. If absent predictions are for the data frame used in the original fit. When coxph has been called with a formula argument created in another context, i.e., coxph has been called within another function and the formula was passed as an argument to that function, there can be problems finding the data set. See the note below. |
type |
the type of predicted value.
Choices are the linear predictor ( |
se.fit |
if TRUE, pointwise standard errors are produced for the predictions. |
na.action |
applies only when the |
terms |
if type="terms", this argument can be used to specify which terms should be included; the default is all. |
collapse |
optional vector of subject identifiers. If specified, the output will contain one entry per subject rather than one entry per observation. |
reference |
reference for centering predictions, see details below |
... |
For future methods |
Details
The Cox model is a relative risk model; predictions
of type "linear predictor", "risk", and "terms" are all
relative to the sample from which they came. By default, the reference
value for each of these is the mean covariate within strata.
The underlying reason is both statistical and practial.
First, a Cox model only predicts relative risks
between pairs of subjects within the same strata, and hence the addition
of a constant to any covariate, either overall or only within a
particular stratum, has no effect on the fitted results.
Second, downstream calculations depend on the risk score exp(linear
predictor), which will fall prey to numeric overflow for a linear
predictor greater than .Machine\$double.max.exp.
The coxph routines try to approximately center the predictors out
of self protection.
Using the reference="strata" option is the safest centering,
since strata occassionally have different means.
When the results of predict are used in further calculations it
may be desirable to use a single reference level for all observations.
Use of reference="sample" will use object$means, which agrees
with the linear.predictors component of the coxph object.
Predictions of type="terms" are almost invariably passed
forward to further calculation, so for these we default to using
the sample as the reference.
A reference of "zero" causes no centering to be done.
Predictions of type "expected" or "survival" incorporate the baseline
hazard and are thus absolute instead of relative; the
reference option has no effect on these.
These values depend on the follow-up time for the future subjects as
well as covariates so the newdata argument needs to include both
the right and left hand side variables from the formula.
(The status variable will not be used, but is required since the
underlying code needs to reconstruct the entire formula.)
Models that contain a frailty term are a special case: due
to the technical difficulty, when there is a newdata argument the
predictions will always be for a random effect of zero.
For predictions of type expected a user will normally want to use
\Lambda(t_i), i.e., the cumulative hazard at the individual
follow-up time t_iof each individual subject.
This is E in the martingale residual O-E and plays a natural role in
assessments of model validation (Crowson 2016).
For predictions of type survival, on the other hand, a user
will normally want S(tau), where tau is a single pre-specified time
point which is the same for all subjects, e.g., predicted 5 year
survival. The newdata data set should contain actual survival
time(s) for each subject for the first case, as the survival time variable(s),
and the target time tau in the second case; (0, tau) for (time1, time2) data.
Value
a vector or matrix of predictions, or a list containing the predictions (element "fit") and their standard errors (element "se.fit") if the se.fit option is TRUE.
Note
Some predictions can be obtained directly from the coxph object, and for
others it is necessary for the routine to have the entirety of the
original data set, e.g., for type = terms or if standard errors
are requested.
This extra information is saved in the coxph object if
model=TRUE, if not the original data is reconstructed.
If it is known that such residuals will be required overall execution will be
slightly faster if the model information is saved.
In some cases the reconstruction can fail.
The most common is when coxph has been called inside another function
and the formula was passed as one of the arguments to that enclosing
function. Another is when the data set has changed between the original
call and the time of the prediction call.
In each of these the simple solution is to add model=TRUE to the
original coxph call.
References
C Crowson, E Atkinson and T Therneau, Assessing calibration of prognostic risk scores, Stat Methods Med Res, 2016.
See Also
Examples
options(na.action=na.exclude) # retain NA in predictions
fit <- coxph(Surv(time, status) ~ age + ph.ecog + strata(inst), lung)
#lung data set has status coded as 1/2
mresid <- (lung$status-1) - predict(fit, type='expected') #Martingale resid
predict(fit,type="lp")
predict(fit,type="expected")
predict(fit,type="risk",se.fit=TRUE)
predict(fit,type="terms",se.fit=TRUE)
# For someone who demands reference='zero'
pzero <- function(fit)
predict(fit, reference="sample") + sum(coef(fit) * fit$means, na.rm=TRUE)