survexp Compute Expected Survival

Description

Returns either the expected survival of a cohort of subjects, or the individual expected survival for each subject.

Usage

survexp(formula, data, weights, subset, na.action, rmap, times,
        method=c("ederer", "hakulinen", "conditional", "individual.h",
                 "individual.s"),
        cohort=TRUE, conditional=FALSE,
        ratetable=survival::survexp.us, scale=1,
        se.fit, model=FALSE, x=FALSE, y=FALSE)

Arguments

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), and is often ~1, i.e., expected survival for the entire group.
data	data frame in which to interpret the variables named in the formula, subset and weights arguments.
weights	case weights. This is most useful when conditional survival for a known population is desired, e.g., the data set would contain all unique age/sex combinations and the weights would be the proportion of each.
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.
rmap	an optional list that maps data set names to the ratetable names. See the details section below.
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 times supplied in the response value of the formula.
method	computational method for the creating the survival curves. The individual option does not create a curve, rather it retrieves the predicted survival individual.s or cumulative hazard individual.h for each subject. The default is to use method='ederer' if the formula has no response, and method='hakulinen' otherwise.
cohort	logical value. This argument has been superseded by the method argument. To maintain backwards compatability, if is present and FALSE, it implies method='individual.s'.
conditional	logical value. This argument has been superseded by the method argument. To maintain backwards compatability, if it is present and TRUE it implies method='conditional'.
ratetable	a table of event rates, such as survexp.mn, or a fitted Cox model. Note the survival:: prefix in the default argument is present to avoid the (rare) case of a user who expects the default table but just happens to have an object named "survexp.us" in their own directory.
scale	numeric value to scale the results. If ratetable is in units/day, scale = 365.25 causes the output to be reported in years.
se.fit	compute the standard error of the predicted survival. This argument is currently ignored. Standard errors are not a defined concept for population rate tables (they are treated as coming from a complete census), and for Cox models the calculation is hard. Despite good intentions standard errors for this latter case have not been coded and validated.
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.

Details

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.us population tables contain expected death rates based on calendar year, sex and age. Then

  haz <- survexp(fu.time ~ 1, data=mydata, 
                      rmap = list(year=entry.dt, age=(birth.dt-entry.dt)),
                      method='individual.h')) 

gives for each subject the total hazard experienced up to their observed death time or last follow-up time (variable fu.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.

The ratetable being used may have different variable names than the user's data set, this is dealt with by the rmap argument. The rate table for the above calculation was survexp.us, a call to summary{survexp.us} reveals that it expects to have variables age = age in days, sex, and year = the date of study entry, we create them in the rmap line. The sex variable was not mapped, therefore the function assumes that it exists in mydata in the correct format. (Note: for factors such as sex, the program will match on any unique abbreviation, ignoring case.)

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, for this case no response variable is required 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.

Value

if cohort=TRUE 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. The cohort survival is the hypothetical survival for a cohort of subjects enrolled from the population at large, but matching the data set on the factors found in the rate table.

References

Berry, G. (1983). The analysis of mortality by the subject-years method. Biometrics, 39:173-84.

Ederer, F., Axtell, L. and Cutler, S. (1961). The relative survival rate: a statistical methodology. Natl Cancer Inst Monogr, 6:101-21.

Hakulinen, T. (1982). Cancer survival corrected for heterogeneity in patient withdrawal. Biometrics, 38:933-942.

Therneau, T. and Grambsch, P. (2000). Modeling survival data: Extending the Cox model. Springer. Chapter 10.

Verheul, H., Dekker, E., Bossuyt, P., Moulijn, A. and Dunning, A. (1993). Background mortality in clinical survival studies. Lancet, 341: 872-875.

See Also

survfit, pyears, survexp.us, ratetable, survexp.fit.

Examples

# 
# Stanford heart transplant data
#  We don't have sex in the data set, but know it to be nearly all males.
# Estimate of conditional survival  
fit1 <- survexp(futime ~ 1, rmap=list(sex="male", year=accept.dt,   
          age=(accept.dt-birth.dt)), method='conditional', data=jasa)
summary(fit1, times=1:10*182.5, scale=365) #expected survival by 1/2 years

# Estimate of expected  survival stratified by prior surgery 
survexp(~ surgery, rmap= list(sex="male", year=accept.dt,  
	age=(accept.dt-birth.dt)), method='ederer', data=jasa,
        times=1:10 * 182.5) 

## Compare the survival curves for the Mayo PBC data to Cox model fit
## 
pfit <-coxph(Surv(time,status>0) ~ trt + log(bili) + log(protime) + age +
                platelet, data=pbc)
plot(survfit(Surv(time, status>0) ~ trt, data=pbc), mark.time=FALSE)
lines(survexp( ~ trt, ratetable=pfit, data=pbc), col='purple')