Test the Proportional Hazards Assumption of a Cox Regression

Test the proportional hazards assumption for a Cox regression model fit (coxph).

Usage

cox.zph(fit, transform="km", terms=TRUE, singledf=FALSE, global=TRUE)

Arguments

fit

the result of fitting a Cox regression model, using the coxph or coxme functions.

transform

a character string specifying how the survival times should be transformed before the test is performed. Possible values are "km", "rank", "identity" or a function of one argument.

terms

if TRUE, do a test for each term in the model rather than for each separate covariate. For a factor variable with k levels, for instance, this would lead to a k-1 degree of freedom test. The plot for such variables will be a single curve evaluating the linear predictor over time.

singledf

use a single degree of freedom test for terms that have multiple coefficients, i.e., the test that corresponds most closely to the plot. If terms=FALSE this argument has no effect.

global

should a global chi-square test be done, in addition to the per-variable or per-term tests tests.

Value

an object of class "cox.zph", with components:

table

a matrix with one row for each variable, and optionally a last row for the global test. Columns of the matrix contain a score test of for addition of the time-dependent term, the degrees of freedom, and the two-sided p-value.

x

the transformed time axis.

time

the untransformed time values; there is one entry for each event time in the data

strata

for a stratified coxph model, the stratum of each of the events

y

the matrix of scaled Schoenfeld residuals. There will be one column per term or per variable (depending on the terms option above), and one row per event. The row labels are a rounded form of the original times.

var

a variance matrix for the covariates, used to create an approximate standard error band for plots

transform

the transform of time that was used

call

the calling sequence for the routine.

Details

The computations require the original x matrix of the Cox model fit. Thus it saves time if the x=TRUE option is used in coxph. This function would usually be followed by both a plot and a print of the result. The plot gives an estimate of the time-dependent coefficient \(\beta(t)\). If the proportional hazards assumption holds then the true \(\beta(t)\) function would be a horizontal line. The table component provides the results of a formal score test for slope=0, a linear fit to the plot would approximate the test.

Random effects terms such a frailty or random effects in a coxme model are not checked for proportional hazards, rather they are treated as a fixed offset in model.

If the model contains strata by covariate interactions, then the y matrix may contain structural zeros, i.e., deaths (rows) that had no role in estimation of a given coefficient (column). These are marked as NA. If an entire row is NA, for instance after subscripting a cox.zph object, that row is removed.

Note

In versions of the package before survival3.0 the function computed a fast approximation to the score test. Later versions compute the actual score test.

References

P. Grambsch and T. Therneau (1994), Proportional hazards tests and diagnostics based on weighted residuals. Biometrika, 81, 515-26.

See also

coxph, Surv.

Examples

fit <- coxph(Surv(futime, fustat) ~ age + ecog.ps,  
             data=ovarian) 
temp <- cox.zph(fit) 
print(temp)                  # display the results 
#>         chisq df    p
#> age     0.698  1 0.40
#> ecog.ps 2.371  1 0.12
#> GLOBAL  3.633  2 0.16
plot(temp)                   # plot curves