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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?
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  • $\begingroup$ I think the answer depends on exactly what model are you fitting. Some software estimates time-varying effects nonparametrically, and some parametrically. $\endgroup$ – Aniko Aug 21 '13 at 13:34
  • $\begingroup$ @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. $\endgroup$ – Nicole Aug 21 '13 at 16:43
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The short answer is: you do need the "main", i.e. non-time varying effect of the covariate.

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).

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  • $\begingroup$ Thanks for your help. Looking through Stata's survival analysis manual pages 12-14, they show Cox models with and without the time-invariate component ("main effect"), differentiating between models fit with time-varying covariates (without main effect) and time-varying coefficients (with main effect). I think this covariate/coefficient distinction may be the source of my confusion. From the manual's suggestion, it seems like adding the main effect will only test the PH assumption of the coefficient. $\endgroup$ – Nicole Aug 21 '13 at 23:16

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