## Logrank test :

The logrank test is a statistical test used to compare the survival rates of two or more groups. This test is commonly used in medical research to evaluate the effectiveness of a new treatment or intervention on a particular condition or disease.

For example, a study may be conducted to evaluate the effectiveness of a new cancer drug on a group of patients with lung cancer. The researchers may compare the survival rates of the patients who received the drug with those who received a placebo or standard treatment. The logrank test would be used to determine whether the new drug significantly improved the survival rates of the patients with lung cancer.

Another example of the logrank test is in the evaluation of a new surgical technique for the treatment of a particular heart condition. The researchers may compare the survival rates of the patients who received the new surgical technique with those who received the standard surgical technique. The logrank test would be used to determine whether the new surgical technique significantly improved the survival rates of the patients with the heart condition.

To perform the logrank test, the researchers first need to determine the survival rates for each group being compared. This is typically done by collecting data on the length of time each individual in each group survived, and then calculating the proportion of individuals who survived to a specific time point (e.g. 1 year, 5 years, 10 years).

Next, the researchers will compare the observed survival rates for each group with the expected survival rates based on the assumption that there is no difference between the groups. This is done by calculating the chi-square statistic, which is a measure of the discrepancy between the observed and expected survival rates.

If the chi-square statistic is statistically significant (i.e. it is greater than the critical value for the chosen level of significance), this indicates that there is a significant difference in the survival rates between the groups being compared. In this case, the researchers can conclude that the new treatment or intervention had a significant effect on the survival rates of the patients with the condition or disease being studied.

Overall, the logrank test is a valuable tool for evaluating the effectiveness of new treatments or interventions in medical research. By comparing the survival rates of different groups, researchers can determine whether a new treatment or intervention significantly improves the chances of survival for individuals with a particular condition or disease.