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, times, cohort=T,
        conditional=F, ratetable=survexp.us, scale=1, npoints,
        se.fit=<>, model=F, x=F, y=F)

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), along with a ratetable term.

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

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 miss

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

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.

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.

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.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.

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 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.