survival (version 3.8-3)

survdiff: Test Survival Curve Differences

Description

Tests if there is a difference between two or more survival curves using the \(G^\rho\) family of tests, or for a single curve against a known alternative.

Usage

survdiff(formula, data, subset, na.action, rho=0, timefix=TRUE)

Value

a list with components:

n

the number of subjects in each group.

obs

the weighted observed number of events in each group. If there are strata, this will be a matrix with one column per stratum.

exp

the weighted expected number of events in each group. If there are strata, this will be a matrix with one column per stratum.

chisq

the chisquare statistic for a test of equality.

var

the variance matrix of the test.

strata

optionally, the number of subjects contained in each stratum.

pvalue

the p-value corresponding to the Chisquare statistic

Arguments

formula

a formula expression as for other survival models, of the form Surv(time, status) ~ predictors. For a one-sample test, the predictors must consist of a single offset(sp) term, where sp is a vector giving the survival probability of each subject. For a k-sample test, each unique combination of predictors defines a subgroup. A strata term may be used to produce a stratified test. To cause missing values in the predictors to be treated as a separate group, rather than being omitted, use the strata function with its na.group=T argument.

data

an optional data frame in which to interpret the variables occurring in the formula.

subset

expression indicating which subset of the rows of data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), a numeric vector indicating which observation numbers are to be included (or excluded if negative), or a character vector of row names to be included. All observations are included by default.

na.action

a missing-data filter function. This is applied to the model.frame after any subset argument has been used. Default is options()$na.action.

rho

a scalar parameter that controls the type of test.

timefix

process times through the aeqSurv function to eliminate potential roundoff issues.

Description

This function implements the G-rho family of Harrington and Fleming (1982), with weights on each death of \(S(t)^\rho\), where \(S(t)\) is the Kaplan-Meier estimate of survival. With rho = 0 this is the log-rank or Mantel-Haenszel test, and with rho = 1 it is equivalent to the Peto & Peto modification of the Gehan-Wilcoxon test.

Peto and Peto show that the Gehan-Wilcoxon test can be badly biased if the two groups have different censoring patterns, and proposed an alternative. Prentice and Marek later showed an actual example where this issue occurs. For most data sets the Gehan-Wilcoxon and Peto-Peto-Prentice variant will hardly differ, however.

If the right hand side of the formula consists only of an offset term, then a one sample test is done. To cause missing values in the predictors to be treated as a separate group, rather than being omitted, use the factor function with its exclude argument to recode the righ-hand-side covariate.

Note that the ordinary log-rank test is equivalent to the score test from a Cox model, using the Breslow approximation for ties. Use the Cox model form for more complex models, e.g., time-dependent covariates.

References

Harrington, D. P. and Fleming, T. R. (1982). A class of rank test procedures for censored survival data. Biometrika, 553-566.

Peto R. Peto and Peto, J. (1972) Asymptotically efficient rank invariant test procedures (with discussion), JRSSA, 185-206.

Prentice, R. and Marek, P. (1979) A qualitative discrepancy between censored data rank tests, Biometics, 861--867.

Examples

## Two-sample test
survdiff(Surv(futime, fustat) ~ rx,data=ovarian)
check <- coxph(Surv(futime, fustat) ~ rx, data=ovarian, ties="breslow")
round(summary(check)$sctest, 3)

## Stratified 8-sample test (7 df)
survdiff(Surv(time, status) ~ pat.karno + strata(inst), data=lung)
check <- coxph(Surv(time, status) ~ factor(pat.karno) + strata(inst), lung)
round(summary(check)$sctest, 3)

## Expected survival for heart transplant patients based on
## US mortality tables
expect <- survexp(futime ~ 1, data=jasa, cohort=FALSE,
                  rmap= list(age=(accept.dt - birth.dt), sex=1, year=accept.dt),
                  ratetable=survexp.us)
## actual survival is much worse (no surprise)
survdiff(Surv(jasa$futime, jasa$fustat) ~ offset(expect))

# The free light chain data set is close to the population.
e2 <- survexp(futime ~ 1, data=flchain, cohort=FALSE,
              rmap= list(age= age*365.25, sex=sex, 
                         year=as.Date(paste0(sample.yr, "-07-01"))),
              ratetable= survexp.mn)
survdiff(Surv(futime, death) ~ offset(e2), flchain)