Add baseline hazard function estimate to CoxPH model

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Cox PH models are primarily used to rank subjects by proportional hazard component of the model which is a semi-parametric product of two components (functions):

baseline hazard function (non-parametric) that depends on time only and

partial hazard (parametric and time-invariant) that depends on covariates

!image-2020-08-22-17-13-53-964.png|width=200,height=183!

The partial hazard function depends on covariates and usually suffices for many applications (commonly using hazard ratios). In cases when computing actual hazard and survival for the subjects is of interest then estimate of or parametric representation of baseline hazard function in Cox PH model is desirable.

To obtain estimate of baseline hazard function use the Nelson-Aalen estimator and Breslow estimator described in sections 1.4 and 3.6 here: [https://data.princeton.edu/pop509/NonParametricSurvival.pdf|https://data.princeton.edu/pop509/NonParametricSurvival.pdf]
Also see: [https://stats.stackexchange.com/a/36077/8464|https://stats.stackexchange.com/a/36077/8464] (Prediction in Cox regression), [https://data.princeton.edu/pop509/pop509slides2.pdf|https://data.princeton.edu/pop509/pop509slides2.pdf] (slide 26 in particular), and [https://www4.stat.ncsu.edu/~dzhang2/st745/chap9.pdf|https://www4.stat.ncsu.edu/~dzhang2/st745/chap9.pdf]

If strata present in the model then corresponding baseline hazard estimates are produced for each subset of data.

Lifelines implementation references this: [https://stats.stackexchange.com/questions/46532/cox-baseline-hazard|https://stats.stackexchange.com/questions/46532/cox-baseline-hazard]

See for more details: [DFS H2O-3|https://0xdata.atlassian.net/wiki/spaces/SE/pages/1981186151/DFS+H2O-3#Baseline-hazard-function-estimate]

[h2o-ops]

JIRA Issue Migration Info

Jira Issue: PUBDEV-7735
Assignee: Ondrej Nekola
Reporter: Gregory Kanevsky
State: Resolved
Fix Version: 3.32.1.1
Attachments: Available (Count: 1)
Development PRs: Available

Linked PRs from JIRA

#5353
#5396
#4902

Attachments From Jira

Attachment Name: image-2020-08-22-17-13-53-964.png
Attached By: Gregory Kanevsky
File Link:https://h2o-3-jira-github-migration.s3.amazonaws.com/PUBDEV-7735/image-2020-08-22-17-13-53-964.png