Can anyone help me out with plotting a Hazard Ratio Plot for a Weibull distribution. The following link specifies how a Hazard Ratio could be plotted for a Cox PH model:

Plot of the estimated log hazard ratio in R


I think you're confusing hazards with hazard ratios. The cox model estimates a constant hazard ratio in the sense that comparing any two groups over time, the ratio of hazards for certain exposures remains constant.

What are you seeing in the linked plot is post-estimates of the baseline hazard function, since hazards are bound to go up or down over time. The term "baseline" is ill chosen, and yet seems to be prevalent in the literature (baseline would suggest time=0, but this hazard function varies over time). What is actually meant is the hazard over time among individuals with all covariates set to 0, like an intercept in a regular parametric model.

For a Weibull survival regression model, the baseline hazard function is easily obtained from the model parameter estimates. The hazard function for a Weibull family RV is $p\lambda^pt^{p-1}$. So just use your estimates of $\lambda$ and $p$ and graph this function. It is log-linear in time, a rather strong assumption that is easily relaxed with Cox models or piecewise-parametric survival models.

  • $\begingroup$ Thanks for the reply. Really appreciate it. How about Accelerated Failure Time Models (i.e. AFT Weibull)? In this case, the Hazard Ratios are not constant over time for two groups? $\endgroup$
    – esh88
    Nov 11 '16 at 22:21

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