Survival analysis is described as an analysis of data that corresponds to the time from a well-defined origin until the occurrence of a given event. It has been applied in various disciplines such as medicine over a long time and statistics. There are three functions estimated by survival analysis ( Karabey & Tutkun, 2017; Moore, 2016). They include the survivorship function, density function, and hazard function.
The survivorship function is used to give the probability that an individual survives within a specified period ( 0, t ). it is denoted as S (t). Further, the hazard function, h (t ) is used to express as the risk of death or failure of a given event at time t ( Modhukur et al., 2018 ) . It is expressed as the probability that an individual will survive at time t , given that he or he has survived to that time ( Austin, 2017) . The density function f( t) characterizes the distribution of a survival random variable, t . Where, a random survival variable can either be continuous or discrete ( Farooq, & Karami, 2019 ). However, there are two types of survival data modelling; parametric and non-parametric. The parametric method assumes that the distribution of the survival data is known for unknown parameter, α. There are two ways of estimating the survival time for the non-parametric data, which is Kaplan Meir estimator and life tables Etikan, Abubakar & Alkassim, 2017 ). Second through the parametric method comprising of the cox model, PH model and accelerated failure time model.
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Additionally, censoring is a crucial aspect of survival analysis. Data is censored when a given point of interest is not observed for a specified individual. There are three types of censoring of the survival data; that is, the right, left, and interval censoring ( Klein et al., 2016 ). Right censoring happens after a person has been entered into the study, while the left censoring occurs before the experiment begins (Moore, 2016). Also, interval censoring occurs when the failure time is experienced within a specified time interval.
References
Austin, P. C. (2017). A tutorial on multilevel survival analysis: methods, models and applications. International Statistical Review , 85 (2), 185-203.
Etikan, I., Abubakar, S., & Alkassim, R. (2017). The kaplan meier estimate in survival analysis. Biometrics & Biostatistics International Journal , 5 (5).
Farooq, F. B., & Karami, M. J. H. (2019). Model Selection Strategy for Cox Proportional Hazards Model. The Dhaka University Journal of Science , 67 (2), 111-116.
Karabey, U., & Tutkun, N. A. (2017, July). Model selection criterion in survival analysis. In AIP Conference Proceedings (Vol. 1863, No. 1, p. 120003). AIP Publishing LLC.
Klein, J. P., Van Houwelingen, H. C., Ibrahim, J. G., & Scheike, T. H. (Eds.). (2016). Handbook of survival analysis . CRC Press.
Modhukur, V., Iljasenko, T., Metsalu, T., Lokk, K., Laisk-Podar, T., & Vilo, J. (2018). MethSurv: a web tool to perform multivariable survival analysis using DNA methylation data. Epigenomics , 10 (3), 277-288.
Moore, D. F. (2016). Applied survival analysis using R . Switzerland: Springer.
