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   Zarate-Herrada, David A.; Santos, Lea F.; Torres-Herrera, E. Jonathan (February 2023, Entropy)

   Survival probability measures the probability that a system taken out of equilibrium has not yet transitioned from its initial state. Inspired by the generalized entropies used to analyze nonergodic states, we introduce a generalized version of the survival probability and discuss how it can assist in studies of the structure of eigenstates and ergodicity. 

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2. Conformalized survival analysis

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   Candès, Emmanuel; Lei, Lihua; Ren, Zhimei (January 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank. 

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3. Survival dynamical systems: individual-level survival analysis from population-level epidemic models

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   KhudaBukhsh, Wasiur R.; Choi, Boseung; Kenah, Eben; Rempała, Grzegorz A. (December 2019, Interface Focus)

   In this paper, we show that solutions to ordinary differential equations describing the large-population limits of Markovian stochastic epidemic models can be interpreted as survival or cumulative hazard functions when analysing data on individuals sampled from the population. We refer to the individual-level survival and hazard functions derived from population-level equations as a survival dynamical system (SDS). To illustrate how population-level dynamics imply probability laws for individual-level infection and recovery times that can be used for statistical inference, we show numerical examples based on synthetic data. In these examples, we show that an SDS analysis compares favourably with a complete-data maximum-likelihood analysis. Finally, we use the SDS approach to analyse data from a 2009 influenza A(H1N1) outbreak at Washington State University. 

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4. Multi-task Survival Analysis

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5. Survival of the Systems

   https://doi.org/10.1016/j.tree.2020.12.003  

   Lenton, Timothy M.; Kohler, Timothy A.; Marquet, Pablo A.; Boyle, Richard A.; Crucifix, Michel; Wilkinson, David M.; Scheffer, Marten (April 2021, Trends in Ecology & Evolution)

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