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📊 '''Survival analysis''' is a branch of statistical methodology that models the time until a specific event occurs — and in insurance, those events span policyholder death, contract lapse, disability onset, claim closure, and equipment failure, among many others. Originally developed in biomedical research to study patient lifetimes, the technique has become a cornerstone of [[Definition:Actuarial science | actuarial science]], where understanding the probability and timing of future events is essential for [[Definition:Pricing | pricing]] products, setting [[Definition:Reserves | reserves]], and managing [[Definition:Longevity risk | longevity]] and [[Definition:Mortality risk | mortality]] exposures. Its power lies in its ability to handle "censored" data — observations where the event of interest has not yet occurred by the end of the study period — a situation that is pervasive in insurance portfolios where many policies remain in force at any given valuation date.

⚙️ Actuaries and data scientists working in insurance employ several survival analysis techniques depending on the complexity of the problem. The Kaplan-Meier estimator provides a non-parametric view of survival probabilities over time and is commonly used to analyze policyholder [[Definition:Persistency | persistency]] and [[Definition:Lapse rate | lapse rates]]. The Cox proportional hazards model allows analysts to assess how covariates — such as age, policy size, distribution channel, or health status — influence the hazard rate without specifying the underlying survival distribution, making it widely used for [[Definition:Experience study | experience studies]] and [[Definition:Predictive modeling | predictive modeling]] in [[Definition:Life insurance | life]] and [[Definition:Health insurance | health insurance]]. Parametric models (Weibull, Gompertz, and others) are fitted when a specific distributional form is appropriate, as in [[Definition:Mortality table | mortality table]] construction. Modern applications increasingly integrate [[Definition:Machine learning | machine learning]] extensions, such as random survival forests, to capture non-linear relationships in large policyholder datasets.

🎯 Survival analysis directly informs some of the most consequential decisions insurers make. Accurate modeling of mortality and [[Definition:Morbidity | morbidity]] survival curves drives the pricing of [[Definition:Term life insurance | term life]], [[Definition:Annuity | annuity]], and [[Definition:Long-term care insurance | long-term care]] products, while lapse survival models shape assumptions embedded in [[Definition:Embedded value | embedded value]] calculations and [[Definition:IFRS 17 | IFRS 17]] liability measurements. In [[Definition:General insurance | general insurance]], survival models applied to claims runoff patterns help reserving actuaries estimate how quickly open claims will settle and at what cost — feeding directly into [[Definition:Loss development | loss development]] triangles and [[Definition:Incurred but not reported (IBNR) | IBNR]] estimates. Regulators across jurisdictions expect insurers to justify the statistical methods underlying their assumptions, and survival analysis provides a rigorous, transparent framework that satisfies those expectations whether under [[Definition:Solvency II | Solvency II]], [[Definition:Risk-based capital (RBC) | RBC]], or other supervisory regimes.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Actuarial science]]
* [[Definition:Mortality table]]
* [[Definition:Lapse risk]]
* [[Definition:Predictive modeling]]
* [[Definition:Experience study]]
* [[Definition:Loss development]]
{{Div col end}}

Definition:Survival analysis - Revision history

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