mets (version 1.3.11)

gofM_phreg: Goodness-of-Fit for Cox Covariates (Model Matrix)

Description

Tests the functional form of covariates in a Cox PH model by computing cumulative residuals against a user-specified model matrix. This helps detect non-linear effects or time-varying coefficients (interaction with time).

Usage

gofM_phreg(
  formula,
  data,
  offset = NULL,
  weights = NULL,
  modelmatrix = NULL,
  n.sim = 1000,
  silent = 1,
  ...
)

Value

An object of class "gof.phreg" containing:

jumptimes

Event times.

supUsim

Simulated supremum values.

res

Matrix with observed supremum and p-values for each column of modelmatrix.

score

Cumulative score process.

simUt

Simulated processes.

Utlast, pval.last

Supremum and p-value for the final time point (covariate direction).

type

Type of test ("modelmatrix").

Arguments

formula

Formula for the Cox regression model.

data

Data frame.

offset

Offset vector.

weights

Weights vector.

modelmatrix

Matrix for cumulating residuals. Typically constructed using cumContr() or manually (e.g., quartiles of a continuous covariate).

n.sim

Number of simulations (default 1000).

silent

Logical; suppresses timing estimates if TRUE.

...

Additional arguments passed to phreg.

Author

Thomas Scheike and Klaus K. Holst

Details

The test statistic is: $$ U(t) = \int_0^t K^T d \hat M $$ where \(K\) is the model matrix (e.g., a set of basis functions for a continuous covariate) and \(\hat M\) are the martingale residuals.

P-values are based on the Lin, Wei, and Ying (1993) resampling method. The plot shows whether the residuals are consistent with the model across the range of the covariate.

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

gof.phreg, gofZ_phreg, cumContr

Examples

data(TRACE)
set.seed(1)
TRACEsam <- blocksample(TRACE, idvar="id", replace=FALSE, 100)
dcut(TRACEsam) <- ~. 
mm <- model.matrix(~-1+factor(wmicat.4), data=TRACEsam)
m1 <- gofM_phreg(Surv(time,status==9)~vf+chf+wmi, data=TRACEsam, modelmatrix=mm)
summary(m1)
if (interactive()) {
par(mfrow=c(2,2))
plot(m1)
}

## Cumulative sums in covariates via design matrix
mm <- mets:::cumContr(TRACEsam$wmi, breaks=10, equi=TRUE)
m1 <- gofM_phreg(Surv(time,status==9)~strata(vf)+chf+wmi, data=TRACEsam,
         modelmatrix=mm, silent=0)
summary(m1)