I am new to R and I just wanted to know if it is possible to test an interaction between a time-varying covariate and a time-invariant covariate in survival analysis?

A related question is, can you plot the time-dependent covariate effect on survival for different groups?

Thanks!

`coxph4b <- coxph(Surv(start, stop, frust_event) ~ avoid + newSDQtgr + avoid:newSDQtgr + frailty(id), ties = c ("efron"), data = frustrec2a) summary(coxph4b) frust.surv<-survfit(coxph4b) frust.surv <- survfit(Surv(second, frust_event) ~ avoid:newSDQtgr, data = frustrec2) plot(frust.surv, lty = 2:3) legend(100, .9, c("avoid", "no avoid"), lty = 2:3) title("Kaplan-Meier Curves for children's recurring aggression") lsurv2 <- survfit(Surv(second, frust_event) ~ avoid*newSDQtgr, frustrec2, type='fleming') plot(lsurv2, lty=2:3, fun="cumhaz", xlab="Seconds", ylab="Cumulative Hazard") `

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#### Best Answer

Survival analysis is performed at event times. What matters *at each event time* in a Cox proportional hazards regression is the set of *current* values of covariates for the case that had the event, versus *current* covariate values for those still at risk who didn't have the event.

A regression coefficient and interaction terms involving a time-varying covariate are thus no different from those for a time-invariant covariate. The regression coefficients and associated hazard ratios are still constant over time. That means that the effect on survival associated with any *particular value* of the time-varying covariate is constant over time. All that differs is that the values of the time-varying covariates can vary with time.

Once you have a model you certainly can plot predicted survival for members of any particular groups or combinations of covariate values, and you can even allow for time-varying values of covariates in the new data that you provide to the model if you format the data properly. This can be done, for example, with the `survfit.coxph()`

function in the R `survival`

package. The help page includes the following critical warning, however:

… although predictions with a time-dependent covariate path can be useful, it is very easy to create a prediction that is senseless. Users are encouraged to seek out a text that discusses the issue in detail.

Things are more complicated if you are considering time-varying *coefficients* for covariates. The time-dependent vignette provided with the `survival`

package is an introduction to issues with respect to time-dependent covariates and coefficients.

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