## Survival analysis

Survival analysis is a statistical analysis that is mostly done by medical practitioners. It analyses the time it takes for events such as death, heart attack, or failure of a mechanical system to occur. The questions in such an analysis can include how does a particular substance increase the chances of survival? Will the subject in question make it past a particular time? Survival analysis is a broad topic that will take an enormous amount of time to grasp the concepts. In this article, we will focus on the basics. You will learn the key terms in survival analysis that should prepare you to deal with the complexities of the topic.

**A case example.**

The analysis and the terms will become vivid if we suggest to you a case example of a survival analysis study. With an example, you will be able to relate to the concepts proposed here for further studies.

Let's take an example of medical research that was conducted to investigate the survival rate of cancer patients admitted to a specific hospital. Such a study is conducted to show how a particular drug or treatment influences the survival rates of the patients. In this case, let's take the example of chemotherapy. Therefore, our research question is the effect of chemotherapy treatment on cancer patients. let's start with our definition of terms.

**An Event**

An Event is an experience of interest for the study. In most cancer studies, the event of interest can be death or relapse.

**Time**

Generally, time is a period within which the subject under study was observed. In survival analysis, the beginning of the analysis is always defined. However, not all subjects enter the study at the same time. Survival analysis accounts for the total time for which each subject remains in the study.

**Censorship**

There are cases where the subject under study might not remain until the desired effect is achieved. This is very common in survival analysis. Let's take the example of an event, i.e., death. There are patients who survive after chemotherapy treatment. At times, others may leave the study out of their own volition. For such subjects, we cannot know what happened to them after leaving the study. They could experience the event or do not leave the study.

### Survival function

In survival analysis, the survival function often denoted as S(t) is defined as the probability that death for our example hasn't occurred. In simpler terms, a subject will not die before time t. This function ranges from 0 to 1, and it's a decreasing function.

#### Hazard function

This function is the exact opposite of the survival function. It's the probability that the subject under study will die before time t.

#### Kaplan-Meier plots

They are used to visualize the survival probabilities. They provide a graphical description of the survival function. The curve takes a step shape, given the discrete nature of survival data. On the y-axis are the survival probabilities and on the x-axis the total number of subjects. The curve decreases from the left side to the right side depicting the non-decreasing nature of survival probabilities.

#### Log-rank test

Let's assume that we were testing the effects of chemotherapy treatment to cancer patients against the effect of applying no treatment. To analyze the two categories (chemotherapy and non-treatment), we would need to use the log-rank test. It's a non-parametric test ideal for comparing two survival curves. The advantage of using the log-rank test is that it's easy to calculate and has few assumptions.

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