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I'm reading a paper which gives "Risk ratios from Cox hazard models with time-varying covariates".

Time-varying covariates just means that, for example if $X_i$ is a covariate for person $i$ then it might be $0$ at some time and $1$ at another time.

I understand that we can specify this model by saying that the $i$-th person's hazard rate at time t, for the decrement we're interested in, is:

$$\lambda_i(t) = \lambda_0(t)e^{\beta X_i(t)}$$

(i.e. there is only one covariate in the model)

In this case, the hazard ratio is $e^{\beta X_i(t)}$ but it's not clear to me what the author means by giving a risk ratio.

Can anyone help?

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A couple of weeks ago I had a similar problem. Why don't you take a look, it might help you Relative Risk with Log-rank test

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    $\begingroup$ So, basically it's a hazard ratio but the person is confused? $\endgroup$ – Stanley Jun 25 '15 at 14:32
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    $\begingroup$ Actually, in that case it was calculated the Risk Ratio but presented in the section of survival analysis (near Kaplan-Meier estimates and was said that it was used log-rank test). What I learn is that nowadays statistics is being used in many different areas by people with very different backgrounds. That results that many definitions will be "lost in translation" when people try to transpose knowledge. Sometimes people will call nectarine to a peach. Other times, they call potato to a peach. Therefore, be very careful with what you read and verify the information in more than one source. $\endgroup$ – yohanna Jun 25 '15 at 15:05

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