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Compute Expected Survival

Usage

survexp(formula, data, weights, subset, na.action,
 times, cohort=T, conditional=T,
 ratetable=survexp.us, scale=1, se.fit, model=F, x=F, y=F)

Arguments

formula a formula object. The response variable will be a vector of follow-up times, and is optional. The predictors will consist of optional grouping variables separated by + operators (exactly as in survfit), along with a ratetable() term. This latter matches each subject to his/her expected cohort.
data, as in other modeling routines. Weights are currently ignored.
times an optional vector of times at which the resulting survival curve should be evaluated. If absent, the result will be reported for each unique value of the vector of follow-up times.
cohort If false, each subject is treated as a subgroup of size 1.
conditional If y is missing in the formula, this argument is ignored. Otherwise it is an indicator of whether y includes death times, which leads to conditional expected survival, or y includes only the potential censoring times.
ratetable a table of event rates, such as survexp.uswhite, or a fitted Cox model.
scale a scaling for the results. As most rate tables are in units/day, a value of 365.24 would cause the output to be reported in years.
npoints calculate intermediate results at npoints values, evenly spaced on the range of y. The usual (exact) calculation is done at each unique 'y' value; for very large data sets this may incur too much storage for the scratch array. For a prediction from a Cox model this arument 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, 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.

Description

Individual expected survival is ususally 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 onto the study,sex and actual survival time are all known for a group of subjects. The 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 Verhuel 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=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.

References

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 Cnacer Inst Monogr 1961, 6:101-21. T. Hakulinen. Cancer survival corrected for heterogeneity in patient withdrawal. Biometrics 1892, 38:933. H. Verheul, E. Dekker, P. Bossuyt, A. Moulijn, and A. Dunning. Backround mortality in clinical survival studies. Lancet 1993, 341:872-5.

See Also

survfit, survexp.us, survexp.fit, personyr, date

Examples

efit <- survexp( ~ ratetable(sex=sex, year=entry.dt, age=entry.dt-birth.dt))
plot(survfit(Surv(futime, status) ~1))
lines(efit)