Also known as “time to event” analysis, survival analysis is a statistical technique used to approximate the lifespan of a given population. Its purpose is to estimate how much time an individual has before he/she experiences an event of interest. Usually, the time approximated is the period between birth and death events. This method was initially developed and used by data analysts and medical researchers to determine the lifespan of a given population. Over the years, however, survival analysis has been applied in many other events like estimating the lifetime of an equipment, how long an employee will stay in a company, the lifespan of a product, etc. The birth event, for instance, can be considered the time an employee joins a company and the death event the time the employee leaves the company.
When performing a survival analysis, it is important to note that not every member or subject of the population being studied will experience the expected event of interests throughout the study period. For instance, there is equipment that will still be functioning, employees who will still be working for the organization, or products that will still be doing well in the market during the study or observation period. We have no idea when these subjects will experience the event during the period of observation. All we know is that they have not experienced the event yet. Since their survival time is longer than their duration in the observation, their survival time is therefore categorized as “censored”. This basically designates that the survival time of these objects was cut off. Censorship allows researchers to measure the lifetime of a population that has not gone through the event of interest yet.
There are several types of censoring performed in survival analysis. These include:
- Right censoring: This occurs when the subject being observed enters the study at the start and leaves before experiencing the event of interest. It could be either that the subject lived longer than the period of observation or was not part of the research and hence terminated early without the event of interest occurring. That is, the subjects aborted the study and could not be observed any longer.
- Left censoring: The left censoring occurs when the event of birth was not observed. The purpose of this analysis is to study subjects that have already experienced the event of interest to see whether the event will occur again.
- Interval censoring: This occurs when the time between observations, i.e. the follow up period is not continuous. It can be weekly, monthly, annually, etc.
- Left truncation: Also known as late entry, left truncation happens when the subjects being observed enter the study after the event of interest has already occurred.
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Types of survival analysis tools
Survival analysis is not just a single technique. It involves intricate models, graphs, and tests, all used to study different data and provide solutions to different situations. Below are three common types of survival analysis tools:
- Kaplan-Meier curve: This is used to approximate the likelihood of survival at each point of time. The Kaplan-Meier curve is purely descriptive and has very few assumptions. It is usually the very first graph in survival analysis. To conduct survival analysis using the Kaplan-Meier curve, three assumptions must be met:
- The censored subjects must have similar survival prospects to those who continue being studied.
- The survival probability must be similar in all the subjects regardless of when they joined the study.
- The event of interest must occur at the stipulated time.
- Log-rank test: This is used when studying two or more groups at a time. It is similar to one way analysis of variance and just like the Kaplan-Meier curve, it has very few assumptions. The log-rank test is also very easy to calculate, and in many instances, it could be the only test you will need.
- Cox proportion hazards regression: The Cox model is the first thing that comes to mind when someone mentions survival analysis. It is the most revolutionary model in data analysis, perhaps because it is semi-parametric, meaning, it is not fully parametric and not fully non-parametric. This creates a great deal of flexibility, one of the most essential elements in survival analysis.
Other tools used in survival analysis include:
- Parametric models
- Frailty models
- Competing risk models
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