Survival analytics
Survival analytics originated from the famous article written by Sir David Cox in1972, Potentially applicable in proportional hazards modeling estimator that is now often called Cox modeling. It is basically a branch of statistics used in the analysis of the expected duration of time until a particular event occurs, such as estimation of the breakdown of machinery or attrition of employees in the human resource domain. One of the key features of survival analysis is based on the concept of data censoring. Data censoring refers to the situation in which we are interested in the time interval in which a particular event is most likely to occur. For example, researchers are conducting a study on a specific monkey activity. Suppose the researchers were not able to observe the activity due to some reason. In this situation, researchers could use survival analytics to anticipate the probability distribution of the event occurring as a function of time. The only information we have is whether the event took place before or after a certain point of time which then constitutes the lower bound on her survival time.
Censoring:
Censoring of data occurs when the information about the event time is not complete or missing. Another key aspect is that not every member of the population will experience the Event of Interest. For eg, the dataset will include machines that are not working as well as the machine which is working (which has not seen death). Their survival duration is longer than their time in the study. These entries are marked as “censored”. This enables us to calculate an approximate lifetime for items that have not yet experienced the event of interest. There are different types of Censorships done in Survival Analysis.
Right censoring occurs when a subject leaves the study before the event of interest occurs, or the study ends before the event of interest has occurred. Suppose a duration of a medical study is 10 years and some subjects left in between the study without experiencing the event of interest. This is considered as right censoring.
Left censoring is when the event of interest has already occurred before test conducting. The case of the monkey experiment is an example of left censoring.
Right truncation is done when the whole population of the study has already experienced the event of interest.
Left truncation occurs when the subjects have already been at risk before being considered for the study. Eg: Health Insurance of a person.
Sample R code for predictive maintenance using Survival Analytics:
Source:https://github.com/jeetbarot1998/Survival-Analysis-Using-R-programming/blob/main/Predictive%20mainenance.R
Survival function
Survival Function is the probability that the event of interest has not yet occurred at time “t”.
S(t)=P(T>t)
Hazard function
Hazard function is another attribute used in survival analysis defined as the probability of the subject experiencing the event of interest in a small interval of time. It is denoted by h(t) and mathematically given as:
Kaplan-Meier Estimate
It is used to get a big picture and an average view of the population diversity. It gives the segmented measure of subjects who survived for a certain amount of time “t”. It is defined as
Survival Time
Survival Time is the duration between the starting time from a predefined point to the occurrence of the event of interest.
Nelson Aalen Fitter
Nelson Aalen Fitter is very similar to Kaplan-Meier Estimate
and gives the average view of the population. Unlike Kaplan-Meier it is a non-parametric model.
Cox Proportional Hazard Regression Model
The Cox Proportional Hazards Regression Analysis Model was introduced by Cox and it takes the effect of multiple attributes into consideration at a time. It also observes the relationship and interconnections between these variables and aims to identify relationships among them. It is somewhat similar to multiple linear regression.
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