mets (version 1.3.11)

gof.phreg: Goodness-of-Fit for Cox PH Regression (Proportionality)

Description

Performs cumulative score process residual tests for the proportional hazards (PH) assumption in Cox regression. The test statistics are based on the cumulative score process: $$ U(t) = \int_0^t (X_i - E(t) ) d \hat M_i(s) $$ where \(\hat M_i(s)\) are the martingale residuals.

Usage

# S3 method for phreg
gof(object, n.sim = 1000, silent = 1, robust = NULL, ...)

Value

An object of class "gof.phreg" containing:

jumptimes

Event times used in the process.

supUsim

Matrix of simulated supremum values for each covariate.

res

Matrix with observed supremum (Sup|U(t)|) and p-values.

supU

Observed supremum values.

pvals

Vector of p-values for each covariate.

score

Cumulative score process values over time.

simUt

Simulated score processes.

type

Type of test performed ("prop").

robust

Logical flag indicating if robust simulation was used.

Arguments

object

A fitted phreg object (from mets or survival).

n.sim

Number of simulations for the resampling procedure (default 1000).

silent

Logical; if TRUE, suppresses timing estimates for long jobs.

robust

Logical; if TRUE, uses robust martingale-based simulations. If NULL, defaults to TRUE if a cluster term is detected in the model call.

...

Additional arguments passed to lower-level functions.

Author

Thomas Scheike and Klaus K. Holst

Details

P-values are computed using the Lin, Wei, and Ying (1993) resampling method, which simulates the asymptotic distribution of the supremum of the score process under the null hypothesis of proportional hazards.

The function supports two types of simulation:

• Standard: Uses \(dN_i\) (counting process increments) for simulation.

• Robust: Uses \(\hat M_i(t)\) (martingale residuals) adjusted for clustering if a cluster() term is present in the model.

References

Lin, D. Y., Wei, L. J., & Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80(3), 557-572.

See Also

gofM_phreg, gofZ_phreg

Examples

data(sTRACE)

m1 <- phreg(Surv(time,status==9)~vf+chf+diabetes, data=sTRACE) 
gg <- gof(m1)
gg
par(mfrow=c(1,3))
plot(gg)

m1 <- phreg(Surv(time,status==9)~strata(vf)+chf+diabetes, data=sTRACE) 
gg <- gof(m1)

## Robust simulations with cluster
sTRACE$id <- 1:500
m1 <- phreg(Surv(time,status==9)~vf+chf+diabetes+cluster(id), data=sTRACE) 
gg <- gof(m1)
gg