How does cox.zph deal with time-dependent covariates?

Question

I have a coxph model with 5 time-dependent and 2 time-independent variables. I want to test the assumption of proportional hazards and, apart from the rest of the martingale and deviation, using cox.zph. My question is: how does this function work with time-dependent covariates?

After reading Grant et al., 2014 , I'm not sure if this is the recommended good faith criterion for evaluating the PH assumption of time-varying covariates.

Model:

teste<-coxph(Surv(tempo1,tempo2,status)~sexo+CODE_06+factor(clima)+TP_media7
             +ndvi+peso+epoca,data=newftable,na.action=na.fail)

> cox.zph(teste)
                         rho    chisq      p
sexoM                 0.0844  0.32363 0.5694
CODE_06Regadio        0.1531  0.66865 0.4135
CODE_06Sequeiro       0.2278  1.65735 0.1980
factor(clima)8       -0.1823  1.16522 0.2804
factor(clima)9        0.1051  0.24456 0.6209
factor(clima)15      -0.0193  0.00945 0.9226
TP_media7(12,22]      0.1689  0.75604 0.3846
TP_media7(22,32]      0.1797  1.03731 0.3084
TP_media7(32,41]      0.1060  0.34036 0.5596
ndvi(3e+03,4e+03]    -0.1595  1.00006 0.3173
ndvi(4e+03,5e+03]     0.0421  0.05233 0.8191
ndvi(5e+03,6e+03]     0.1750  0.98816 0.3202
ndvi(6e+03,8.05e+03] -0.0311  0.02880 0.8653
peso[850,1005]        0.2534  3.34964 0.0672
epocamid_inv_rep      0.0193  0.01219 0.9121
epocamid_pos_inv     -0.2193  0.93355 0.3339
epocamid_rep_pos      0.0231  0.01341 0.9078
epocapos_repr         0.2073  1.09893 0.2945
epocarepr             0.0766  0.12905 0.7194
GLOBAL                    NA 19.79229 0.4072

Answer 1

, cox.zph - , . , , . , , Cross Validated.

Therneau:

library(survival)
veteran$celltype <- relevel(veteran$celltype, ref="adeno")
f1 <- coxph(Surv(time, status) ~
            trt + celltype + karno + diagtime + age + prior,
            data=veteran)
(z1 <- cox.zph(f1, transform="log"))

                       rho   chisq        p
trt               -0.01561  0.0400 0.841486
celltypesquamous  -0.16278  3.8950 0.048431
celltypesmallcell -0.11908  2.2199 0.136238
celltypelarge      0.00942  0.0121 0.912551
karno              0.29329 11.8848 0.000566
diagtime           0.11317  1.6951 0.192930
age                0.20984  6.5917 0.010245
prior             -0.16683  3.9873 0.045844
GLOBAL                  NA 27.5319 0.000572

rho - Shoenfeld g (t), g - ( -, log, x ). , . , , chisq.

@Didi Ingabire - :

, p- low :

• , /
• ( coxph)

:

for (i in 1:(nrow(z1$table)-1)){
    plot(z1[i], main="Scaled Schoenfeld residuals by time with smooth spline
If <0 indicates protective effect")
    graphics::abline(a=0, b=0, col="black")
}

, :

@JMarcelino. , cox.zph - , , .

( ), . , p, .

, , ?. , ( ), . , , .

, karno , , :

f2 <- coxph(Surv(time, status) ~
            trt + celltype + log(karno * time) + diagtime + age + prior,
            data=veteran)
(z2 <- cox.zph(f2, transform="log"))

                      rho  chisq     p
trt                0.0947 1.4639 0.226
celltypesquamous  -0.0819 1.1085 0.292
celltypesmallcell -0.0897 1.3229 0.250
celltypelarge      0.0247 0.0968 0.756
log(karno * time) -0.0836 0.6347 0.426
diagtime           0.0463 0.2723 0.602
age                0.0532 0.3493 0.554
prior             -0.0542 0.3802 0.538
GLOBAL                 NA 7.6465 0.469

, . log(karno * time) .

Answer 2

, PH.

. ; . (), , .

:

• : - , (, ).

• : / , , (, , , , ).

, , PH. , , , , PH. , Cox (, ).

: Cox , PH cox.zph Thernau. SAS " ph/resample". PH, () .

. :

Survival = age + sex + blood_pressure

, PH → :

Survival = age + sex + blood_pressure*survival_time_variable

, , .

, , (.. ).