Censored, Not Missing
How right, left, and interval censoring change the likelihood — and why treating them as missing data breaks it
Derives why a censored observation is more informative than a missing one, and builds the censored likelihood that reflects it -- a full derivation of the Exponential MLE under right-censoring (the 'total time on test' estimator), the product-limit logic behind Kaplan-Meier, and the distinction between non-informative censoring and its MNAR-like informative counterpart. A Monte Carlo simulation shows both obvious shortcuts -- dropping censored units, or treating the censoring time as the true event time -- inflate the rate estimate by roughly 50%, while the proper censored likelihood is essentially exact.
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