Survival Analysis – Madhav Prashanth

Hazard functions, parametric distributions, Kaplan-Meier, Cox proportional hazards. Motivated by predictive maintenance in industrial systems.

Code: blog

Part 1: Introduction to Survival Analysis

A note on platform and process. Part 0 of this series was published on Medium. Starting from Part 1, I have moved to Quarto on GitHub Pages for one reason: proper LaTeX…

Madhav Prashanth Ramachandran

Part 2: Distributions in Survival Analysis

In Part 1, we established why survival analysis exists as a separate field- regression breaks, censoring is real and the functions we care about for survival analysis are…

Madhav Prashanth Ramachandran

Part 3: Fitting Survival Distributions to Data

In Part 2, we built a vocabulary of survival distributions — the Exponential for constant hazard, the Rayleigh for linearly increasing hazard, and the Weibull as the…

Madhav Prashanth Ramachandran

Part 4: The Kaplan-Meier Estimator

In Part 3, we derived the likelihood function for censored data from first principles, fit a Weibull distribution to our synthetic machine fleet, and assessed the quality of…

Madhav Prashanth Ramachandran

Part 5: The Cox Proportional Hazards Model

In Part 4, we derived the Kaplan-Meier estimator from scratch using conditional probability and a counting argument, proved Greenwood’s formula for its variance, and closed…

Madhav Prashanth Ramachandran