How does lifelines calculate baseline hazard in CoxPHFitter?

Question

I have learnt that the baseline hazard function in the Cox PH Model is unspecified. Does it mean that I can specify it as any functions and select the best one during experiments?

I also see that the CoxPHFitter function in the lifelines does not have any parameters where I can specific my baseline hazard function. So how does Lifelines calculate it?

Cam.Davidson.Pilon · Accepted Answer · 2021-01-07T14:33:15.030

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I'm the author of lifelines and can help you.

Does it mean that I can specify it as any functions and select the best one during experiments?

Not normally, no. (In fact, if you could, that would make the Cox model fully parametric, and not semi parametric). It being "unspecified" means it is non-parametric. If you strongly have a prior assumption on what the baseline might be, there are other models (like AFT models) that could be used.

To answer your second question, how lifelines calculates the baseline survival, we use the formula on page 15 here. In code, this is represented here.

edited Jan 07 '21 at 14:33

answered Apr 27 '18 at 01:16

Cam.Davidson.Pilon

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Thanks for the reply. Does it mean the h0 is a vector with len(T), in which each element is a number corresponds to the h0 at time t? Since we are not sure how h0 changes with t, it is better to make it non-parametric. Correct? – Munichong Apr 27 '18 at 16:37
That’s exactly correct – Cam.Davidson.Pilon Apr 28 '18 at 00:04
Is it possible that t is a continuous variable? In my application, the time t is a float variable. Can lifelines handle it? – Munichong Apr 29 '18 at 00:42
Yup, it can. That should be no problem. – Cam.Davidson.Pilon Apr 29 '18 at 04:49
Hey @Cam.Davidson.Pilon, the link to the formula [for baseline survival calc used in lifelines] seems to have expired. Do you perhaps have another link that details the calc used? Many thanks ! – Mike Tauber Jan 07 '21 at 13:23
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@MikeTauber thanks for the ping - it's fixed now – Cam.Davidson.Pilon Jan 07 '21 at 14:33

How does lifelines calculate baseline hazard in CoxPHFitter?

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