Goodness-of-Fit for Cox Covariates (Linearity)

Tests the functional form of continuous covariates in a Cox PH model to check for linearity. It computes cumulative residuals evaluated at a grid of covariate values $z$.

Usage

gofZ_phreg(
  formula,
  data,
  vars = NULL,
  offset = NULL,
  weights = NULL,
  breaks = 50,
  equi = FALSE,
  n.sim = 1000,
  silent = 1,
  ...
)

Arguments

formula: Formula for the Cox regression.
data: Data frame.
vars: Vector of variable names to test. If NULL, automatically detects continuous covariates with more than 2 levels.
offset: Offset vector.
weights: Weights vector.
breaks: Number of break points for the grid (default 50).
equi: Logical; if TRUE, uses equidistant breaks; if FALSE, uses quantiles.
n.sim: Number of simulations (default 1000).
silent: Logical; suppresses timing estimates.
...: Additional arguments passed to gofM_phreg.

Value

An object of class "gof.phreg" with type "Zmodelmatrix" containing:

res: Matrix of p-values for each tested variable.
Zres: List of gof.phreg objects, one for each variable.
type: Type of test ("Zmodelmatrix").

Details

The test statistic is: $$ U(z, \tau) = \int_0^\tau K(z)^T d \hat M $$ where $K(z)$ is a design matrix based on indicator functions $I(Z_i \leq z_l)$ for a grid of points $z_l$.

The p-value is valid but depends on the chosen grid. As the number of break points increases, this test converges to the original Lin, Wei, and Ying test for linearity.

Author

Thomas Scheike and Klaus K. Holst

Examples

data(TRACE)
set.seed(1)
TRACEsam <- blocksample(TRACE, idvar="id", replace=FALSE, 100)

## Test linearity of continuous covariates
 ## Reduce Ex.Timings
m1 <- gofZ_phreg(Surv(time,status==9)~strata(vf)+chf+wmi+age, data=TRACEsam)
summary(m1) 
#> Cumulative residuals versus modelmatrix :
#>     Sup_z |U(tau,z)|  pval
#> wmi         3.891570 0.331
#> age         5.665722 0.093
plot(m1, type="z")