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,
...
)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.
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").
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.
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)
#> Cumulative residuals versus modelmatrix :
#> Sup_t |U(t)| pval
#> factor(wmicat.4)[0.4,1.1] 5.788752 0.021
#> factor(wmicat.4)(1.1,1.4] 2.633143 0.591
#> factor(wmicat.4)(1.4,1.72] 5.657370 0.038
#> factor(wmicat.4)(1.72,2] 1.227485 0.948
#>
#> Cumulative score process versus covariates (discrete z via model.matrix):
#> Sup_z |U(tau,z)| pval
#> matrixZ 1.801626 0.812
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)
#> Cumulative score process test for modelmatrix:
#> Sup_t |U(t)| pval
#> <=0.56 0.88 0.33
#> <=0.72 2.25 0.26
#> <=0.88 5.28 0.03
#> <=1.04 2.68 0.54
#> <=1.2 4.12 0.17
#> <=1.36 4.09 0.17
#> <=1.52 3.34 0.24
#> <=1.68 1.78 0.83
#> <=1.84 1.17 0.84
#> <=2 0.00 1.00
summary(m1)
#> Cumulative residuals versus modelmatrix :
#> Sup_t |U(t)| pval
#> <=0.56 0.8821214 0.327
#> <=0.72 2.2521756 0.263
#> <=0.88 5.2766972 0.031
#> <=1.04 2.6807567 0.542
#> <=1.2 4.1217296 0.174
#> <=1.36 4.0926272 0.173
#> <=1.52 3.3447151 0.242
#> <=1.68 1.7766131 0.831
#> <=1.84 1.1652990 0.839
#> <=2 0.0000000 1.000
#>
#> Cumulative score process versus covariates (discrete z via model.matrix):
#> Sup_z |U(tau,z)| pval
#> matrixZ 3.931466 0.23