# Main effect required for time-varying covariate?

I'm modeling a multivariable proportional hazards model (competing risks), and I want to include an internal time-varying covariate.

1. Should I include a main effect for this time-varying covariate in the model? (I'm not trying to test the proportionality assumption here)
2. How does one report the overall value and significance of this time-varying variable?
• I think the answer depends on exactly what model are you fitting. Some software estimates time-varying effects nonparametrically, and some parametrically. – Aniko Aug 21 '13 at 13:34
• @Aniko I'll be more specific: I'm fitting a Fine & Gray semiparametric proportional hazards model for the subdistribution of a competing risk. In Stata, this is the stcrreg command. – Nicole Aug 21 '13 at 16:43

Based on the help file forstccreg, if $X$ is declared a time-dependent covariate, then the time-dependence is modeled parametrically as $X(t) = X\cdot f(t)$, where the default is $f(t)=t$. That means that at time 0, the time-dependent portion has no effect, and then the effect increases/decreases linearly in time (on the log-hazard scale). So in this case, omitting the $X$ as a time-invariant predictor has the same effect as omitting the intercept from a linear regression model: you are eliminating any immediate ($t\approx 0$) effect of $X$. This is probably unwise unless specifically desired.
Stata will allow you to change the multiplier $f$ function, so the interpretation of the time-invariant part might change, but $f$ will always have to be a predefined function with no unknown parameters.
As for testing, if Stata does not give a test in the default output, you could fit the model with and without the time-varying part, and do a likelihood-ratio test with 1 degree of freedom (assuming $X$ has one degree of freedom).