Editing Survival analysis (section)

== Discrete-time survival models ==
While many parametric models assume a continuous-time, discrete-time survival models can be mapped to a binary classification problem. In a discrete-time survival model the survival period is artificially resampled in intervals where for each interval a binary target indicator is recorded if the event takes place in a certain time horizon.<ref name="KrithikaSuresh2022">Suresh, K., Severn, C. & Ghosh, D. Survival prediction models: an introduction to discrete-time modeling. BMC Med Res Methodol 22, 207 (2022). https://doi.org/10.1186/s12874-022-01679-6 , https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-022-01679-6</ref> If a binary classifier (potentially enhanced with a different likelihood to take more structure of the problem into account) is [[Calibration (statistics)|calibrated]], then the classifier score is the hazard function (i.e. the conditional probability of failure).<ref name="KrithikaSuresh2022"/>
[[File:Data resampling for discrete-time survival models.webp|thumb|Description of the transformation of continuous-time survival data to discrete-time survival data. Individual 4 is censored and for individual 5 the event happens outside the observation window 5.]]

Discrete-time survival models are connected to [[empirical likelihood]].<ref>Empirical Likelihood in Survival Analysis, Gang Li (U.S.A.), Runze Li (U.S.A.), and Mai Zhou (U.S.A.), Contemporary Multivariate Analysis and Design of Experiments. March 2005, 337-349, https://www.ms.uky.edu/~mai/research/llz.pdf</ref><ref>The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data, Bruce W. Turnbull, Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 38, No. 3 (1976), pp. 290-295 (6 pages), https://apps.dtic.mil/sti/tr/pdf/ADA030940.pdf</ref>