An Exercise to understand Survival Analysis

Following data are related to time in days at which first claim happened in various cases under a health insurance product.

157, 300, 289, 91, 235, 28, 188, 119, 273, 78, 37, 349, 235, 96, 157, 314, 178, 62, 235, 192.

We are interested in knowing the pattern in probability of first claim happening after certain number of days.

(Apply your own concept and try finding the pattern. To draw any conclusion related to probability in this case, we need larger volume of data. But doing this exercise manually will help in understanding the concept.)

1. In how many cases, there is no claim till 150 days?
2. What is the probabilty that there will not be any claim till 150 days?
3. What is the range of days for which the probability in Q2 above remains same?
4. Identify similar ranges in which probabilty doesn't chamge.
5. Draw the probability Vs. time graph. This graph is called Survival Graph and represents the survival function.
6. Develop a method to draw such graphs from any given set of similar data.
7. There may be many cases in which claim did not happen during the study period or the case got withdrawn. Data related to such cases are called censored data. Think about how to include them in similar analysis.