Survival Analysis In Machine Learning

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Survival Analysis

Survival analysis, also known as time-to-event analysis or reliability analysis, is a branch of statistics that focuses on the time it takes for an event of interest to occur. It's commonly used in a variety of fields, including medicine (to measure patient survival time), marketing (to predict customer churn), and engineering (to predict failure of machinery).

Survival analysis corresponds to a set of statistical approaches used to investigate the time it takes for an event of interest to occur.Survival analysis is used in a variety of field such as:

Cancer studies for patients survival time analyses,
Sociology for “event-history analysis”,
and in engineering for “failure-time analysis”.

Survival analysis Techniques

Survival analysis encompasses several statistical approaches to deal with time-to-event data. Here are some common techniques used in survival analysis:

Kaplan-Meier Estimate: This is a non-parametric statistic used to estimate the survival function from lifetime data. It provides a survival probability estimate at each time point when an event occurs and is widely used in clinical trials and studies.
Cox Proportional Hazards Model: This is a semi-parametric model most commonly used in medical research for identifying the risk factors of an event. The model allows estimating the effect of several risk factors on survival.
Nelson-Aalen Estimate: This is a non-parametric estimator used to estimate the cumulative hazard function in survival analysis.
Log-Rank Test: This is a hypothesis test to compare the survival distributions of two or more groups. It's especially useful in analyzing survival data for clinical trials.
Parametric Survival Models: These models (like Weibull, exponential, log-normal, etc.) assume a particular statistical distribution for the survival times. They can be more efficient than the Cox model if the chosen distribution closely matches the true survival times.
Life Table Analysis: Also known as actuarial analysis, life tables summarize survival data and estimate probabilities of surviving in different intervals.
Competing Risks Analysis: When an individual is at risk of more than one event, competing risks analysis allows for accurate estimates of event-specific survival probabilities.
Time-Dependent Covariates Models: These models allow the effect of covariates (risk factors) to change over time.
Machine Learning Models for Survival Analysis: More recently, advanced machine learning techniques such as random survival forests, neural networks for survival analysis, and gradient boosting for survival outcomes have been applied.

Each technique has its strengths and weaknesses, and the best one to use depends on the specifics of the data and the research question being addressed.

Survival analysis in R

Install and load required R package

We’ll use two R packages:

survival for computing survival analyses
survminer for summarizing and visualizing the results of survival analysis
Install the packages

install.packages(c("survival", "survminer"))

Load the packages

library("survival")
library("survminer")