From KM and Cox back to the question

Bring the geometry home to time-to-event analysis: choose the target, inspect who remains at risk, and separate a hazard ratio from a survival contrast.

Further reading: Hernán: The hazards of hazard ratios; Efron (1967), The two sample problem with censored data (redistribute to the right); Satten and Datta (2001), The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average, Am Stat 55(3). Numerical values are generated by the accompanying scientific kernels; these finite examples illustrate the theory under the assumptions stated beside each experiment.