# Time-to-Event Prediction Task

A Time-to-Event Prediction Task is an time-series prediction task that can assign the probability value of some failure event to some time range.

**AKA:**Survival Analysis.**Context:**- Input: Time-to-Event Data.
**output:**Survival Prediction.- It can be solved by Survival Analysis System (that implements a survival analysis algorithm that might require the selection of a survival model family).
- ...

**Example(s):**- a Failure Function Modeling Task.
- a Competing Risk Analysis Task.
- a long-running Clinical Dataset, such as a Framingham Study Dataset (for a Framingham Study).
- a COVID-19 Time-to-Extinction (for the COVID-19 Pandemic).
- ...
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**Counter-Example(s):****See:**Time-Series Analysis, Temporal Co-occurrence Analysis, Cox Regression, Censored Data, Systems Reliability, Reliability Theory, Systems Reliability, Reliability Theory.

## References

### 2020

- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/survival_analysis Retrieved:2020-3-13.
**Survival analysis**is a branch of statistics for analyzing the expected duration of time until one or more events happen, such as death in biological organisms and failure in mechanical systems. This topic is called**reliability theory**or**reliability analysis**in engineering,**duration analysis**or**duration modelling**in economics, and**event history analysis**in sociology. Survival analysis attempts to answer questions such as: what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival?To answer such questions, it is necessary to define "lifetime". In the case of biological survival, death is unambiguous, but for mechanical reliability, failure may not be well-defined, for there may well be mechanical systems in which failure is partial, a matter of degree, or not otherwise localized in time. Even in biological problems, some events (for example, heart attack or other organ failure) may have the same ambiguity. The theory outlined below assumes well-defined events at specific times; other cases may be better treated by models which explicitly account for ambiguous events.

More generally, survival analysis involves the modelling of time to event data; in this context, death or failure is considered an "event" in the survival analysis literature – traditionally only a single event occurs for each subject, after which the organism or mechanism is dead or broken.

*Recurring event*or*repeated event*models relax that assumption. The study of recurring events is relevant in systems reliability, and in many areas of social sciences and medical research.

### 2018

- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Survival_analysis#Definitions_of_common_terms_in_survival_analysis Retrieved:2018-3-5.
- The following terms are commonly used in survival analyses:
- Event: Death, disease occurrence, disease recurrence, recovery, or other experience of interest
- Time: The time from the beginning of an observation period (such as surgery or beginning treatment) to (i) an event, or (ii) end of the study, or (iii) loss of contact or withdrawal from the study.
- Censoring / Censored observation: If a subject does not have an event during the observation time, they are described as censored. The subject is censored in the sense that nothing is observed or known about that subject after the time of censoring. A censored subject may or may not have an event after the end of observation time.
- Survival function S(t): The probability that a subject survives longer than time t.

- The following terms are commonly used in survival analyses:

### 2011

- (Hosmer Jr. et al., 2011) ⇒ David W. Hosmer Jr, Stanley Lemeshow, and Susanne May. (2011). “Applied Survival Analysis: Regression modeling of time to event data, 2nd edition." Wiley-Interscience, ISBN 1118211588
- QUOTE: ... analyses using time-to-event methods have increase considerably in all areas of scientific inquiry mainly as a result of model-building methods available in modern statistical software packages. ... This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. ... Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data.
Features of the Second Edition include:

- Expanded coverage of interactions and the covariate-adjusted survival functions
- The use of the Worchester Heart Attack Study as the main modeling data set for illustrating discussed concepts and techniques
- New discussion of variable selection with multivariable fractional polynomials
- Further exploration of time-varying covariates, complex with examples
- Additional treatment of the exponential, Weibull, and log-logistic parametric regression models
- Increased emphasis on interpreting and using results as well as utilizing multiple imputation methods to analyze data with missing values
- New examples and exercises at the end of each chapter

- Analyses throughout the text are performed using Stata® Version 9, and an accompanying FTP site contains the data sets used in the book. Applied Survival Analysis, Second Edition is an ideal book for graduate-level courses in biostatistics, statistics, and epidemiologic methods. It also serves as a valuable reference for practitioners and researchers in any health-related field or for professionals in insurance and government.

- QUOTE: ... analyses using time-to-event methods have increase considerably in all areas of scientific inquiry mainly as a result of model-building methods available in modern statistical software packages. ... This book places a unique emphasis on the practical and contemporary applications of regression modeling rather than the mathematical theory. ... Key topics covered include: variable selection, identification of the scale of continuous covariates, the role of interactions in the model, assessment of fit and model assumptions, regression diagnostics, recurrent event models, frailty models, additive models, competing risk models, and missing data.