Running and interpreting time varying covariates -tvc( )-

[Nate Fitzpatrick]

Hello, I am currently running a competing risks analysis looking at the occurrence of an adverse event in the presence of competing risks (death).

I am planning to compare the cause-specific (stcox) and subdistribution hazard (stcrreg) models, but realized I have a time varying covariate (cumulativedose) I'm not sure how to interpret the results (I can't post my data as it is locked in a virtual machine).

1. What is the difference between running the stcox model with the covariate as a main effect AND a tvc effect? The survival analysis manual presents the age drug1 and drug2 dataset with using: stcox age drug1 drug2, tvc(drug1 drug2) AND stcox age, tvc(drug1 drug2), but I don't really understand the distinction between interpretation.

Fore my model It would be:

stcox sex, tvc(cum_dose)

or

stcox sex cum_dose, tvc(cum_dose)

From what I can understand, the first model just gives a more conservative "average" of how the hazard ratio would change the risk of the event accounting for sex. while in the second model the main effect estimates a different baseline hazard at t0 compared to the reference group, and the tvc effect estimates the change in risk (HR) at each time point compared to the reference group. Is there a way to convert the baseline to 0?

2. Can a variate model be done for a time varying covariate?

From what I can tell, stata will run a univariate subdistribution hazard model (stcrreg) for a TVC, but not an cause-specific (stcox) model.

Working stcrreg command:

stcrreg, tvc(cum_dose) texp(_t)

Error stcox command:

stcrreg, tvc(cum_dose) texp(_t)

Assuming both assume proportional hazards, and assuming this model would immediately violate this assumption, why can one be run and not the other?

3. What is the most efficient way of reporting these results in a table. I assume it's not sufficient to post the TVC effect as the relative hazard ratio is multiplicative of a reference hazard other than 0, but I have not seen tabular results presented this way.

Thank you!

[Daniel Shin]

1. The difference between the two codes is that the second code is that it is adding an interaction term of cum_dose and analysis time, which is a way of testing the PH assumption for cum_dose. The first code specifies cum_dose as a TVC.

2. I'm assuming you meant stcox, tvc(cum_dose) texp(_t). It is curious why Stata throws an error, but functionally this would be the equivalent:

gen id=_n
streset, id(id)
stsplit, at(failures)
gen cum_dose_tvc = cum_dose*_t
stcox cum_dose_tvc

3. The TVCs could be reported as "variable x g(t)" for whichever function you're using. I've seen them being omitted from main tables since they're usually not the main effects of interest, with full model estimates included as supplementary material.