| survexp {survival} | R Documentation |
Returns either the expected survival of a cohort of subjects, or the individual expected survival for each subject.
survexp(formula, data, weights, subset, na.action, times, cohort=TRUE,
conditional=FALSE, ratetable=survexp.us, scale=1, npoints,
se.fit=, model=FALSE, x=FALSE, y=FALSE)
formula |
formula object. The response variable is a vector of follow-up times
and is optional. The predictors consist of optional grouping variables
separated by the + operator (as in survfit), along with a ratetable
term. The ratetable term matches each subject to his/her expected cohort.
|
data |
data frame in which to interpret the variables named in
the formula, subset and weights arguments.
|
weights |
case weights. |
subset |
expression indicating a subset of the rows of data to be used in the fit.
|
na.action |
function to filter missing data. This is applied to the model frame after
subset has been applied. Default is options()$na.action. A possible
value for na.action is na.omit, which deletes observations that contain
one or more missing values.
|
times |
vector of follow-up times at which the resulting survival curve is
evaluated. If absent, the result will be reported for each unique
value of the vector of follow-up times supplied in formula.
|
cohort |
logical value: if FALSE, each subject is treated as a subgroup of size 1.
The default is TRUE.
|
conditional |
logical value: if TRUE, the follow-up times supplied in formula
are death times and conditional expected survival is computed.
If FALSE, the follow-up times are potential censoring times.
If follow-up times are missing in formula, this argument is ignored.
|
ratetable |
a table of event rates, such as survexp.uswhite, or a fitted Cox model.
|
scale |
numeric value to scale the results. If ratetable is in units/day,
scale = 365.25 causes the output to be reported in years.
|
npoints |
number of points at which to calculate intermediate results, evenly spaced
over the range of the follow-up times. The usual (exact) calculation is done
at each unique follow-up time. For very large data sets specifying npoints
can reduce the amount of memory and computation required.
For a prediction from a Cox model npoints is ignored.
|
se.fit |
compute the standard error of the predicted survival. The default is to compute this whenever the routine can, which at this time is only for the Ederer method and a Cox model as the rate table. |
model,x,y |
flags to control what is returned. If any of these is true, then the model frame, the model matrix, and/or the vector of response times will be returned as components of the final result, with the same names as the flag arguments. |
Individual expected survival is usually used in models or testing, to
'correct' for the age and sex composition of a group of subjects. For
instance, assume that birth date, entry date into the study, sex and
actual survival time are all known for a group of subjects.
The survexp.uswhite population tables contain expected death rates
based on calendar year, sex and age. Then
haz <- -log(survexp(death.time ~ ratetable(sex=sex, year=entry.dt, age=(birth.dt-entry.dt)), cohort=F))
gives for each subject the total hazard experienced up to their observed
death time or censoring time.
This probability can be used as a rescaled time value in models:
glm(status ~ 1 + offset(log(haz)), family=poisson)
glm(status ~ x + offset(log(haz)), family=poisson)
In the first model, a test for intercept=0 is the one sample log-rank
test of whether the observed group of subjects has equivalent survival to
the baseline population. The second model tests for an effect of variable
x after adjustment for age and sex.
Cohort survival is used to produce an overall survival curve. This is then added to the Kaplan-Meier plot of the study group for visual comparison between these subjects and the population at large. There are three common methods of computing cohort survival. In the "exact method" of Ederer the cohort is not censored; this corresponds to having no response variable in the formula. Hakulinen recommends censoring the cohort at the anticipated censoring time of each patient, and Verheul recommends censoring the cohort at the actual observation time of each patient. The last of these is the conditional method. These are obtained by using the respective time values as the follow-up time or response in the formula.
if cohort=T an object of class survexp, otherwise a vector of per-subject
expected survival values. The former contains the number of subjects at
risk and the expected survival for the cohort at each requested time.
G. Berry. The analysis of mortality by the subject-years method. Biometrics 1983, 39:173-84. F Ederer, L Axtell, and S Cutler. The relative survival rate: a statistical methodology. Natl Cancer Inst Monogr 1961, 6:101-21. T. Hakulinen. Cancer survival corrected for heterogeneity in patient withdrawal. Biometrics 1982, 38:933. H. Verheul, E. Dekker, P. Bossuyt, A. Moulijn, and A. Dunning. Background mortality in clinical survival studies. Lancet 1993, 341:872-5.
survfit, survexp.us, survexp.fit, pyears, date
## comparing data to population
data(ratetables)
data(cancer)
## compare survival to US population
cancer$year<-rep(as.date("1/1/1980"),nrow(cancer))
efit <- survexp( ~ ratetable(sex=sex, year=year, age=age*365), times=(1:4)*365,data=cancer)
plot(survfit(Surv(time, status) ~1,data=cancer))
lines(efit)
## compare data to Cox model
## Mayo PBC data
data(pbc)
## fit to randomised patients
m<-coxph(Surv(time,status)~edtrt+log(bili)+log(protime)+age+platelet,data=pbc,
subset=trt>0)
##compare Kaplan-Meier to fitted model for 2 edema groups in
##unrandomised patients
plot(survfit(Surv(time,status)~edtrt,data=pbc,subset=trt==-9))
lines(survexp(~edtrt+ratetable(edtrt=edtrt,bili=bili,platelet=platelet,age=age,
protime=protime),data=pbc,subset=trt==-9,ratetable=m,cohort=TRUE),col="purple")