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After fitting my model to a time varying cox regression, let's say I have a continuos variable $ X $. The hazard ratio of this variable will be higher than 1 (about 2 and it is significantly significant). Is it safe to say that an increase in $ X $ will increase the risk by a factor of two ?

I'm not so sure about this, because this is a time varying covariates.

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    $\begingroup$ I agree with Maarten. Using time-dependent covariates allows for specification of individuals going from one hazard level to another during follow-up. I.e individuals are allowed to jump between hazard levels during specific time-intervals. It does not affect the interpretation of the hazard ratio for that variable. HR of 2 equals two times as great a risk. $\endgroup$ Feb 5, 2015 at 9:05

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There is no problem with that conclusion. In fact, I would say it is especially meaningful for time varying covariates. Think of a time constant covariate like sex: would someone ever experience what happens if she became a he or the reverse (ignoring sex-change operations)? So time-constant covariates are basically group comparisons, but you would not expect someone to experience such a change in group membership. In case of time-varying covariates it is usually realistic for a person to experience such a change (how else could it vary over time?).

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