A **log rank test** is the most common way to compare survival curves between two groups.

This test uses the following hypotheses:

**H _{0}:** There is no difference in survival between the two groups.

**H _{A}:** There

*is*a difference in survival between the two groups.

If the p-value of the test is less than some significance level (e.g. α = .05), then we can reject the null hypothesis and conclude that there is sufficient evidence to say there is a difference in survival between the two groups.

To perform a log rank test in R, we can use the **survdiff()** function from the **survival** package, which uses the following syntax:

**survdiff(Surv(time, status) ~ predictors, data)**

This function returns a Chi-Squared test statistic and a corresponding p-value.

The following example shows how to use this function to perform a log rank test in R.

**Example: Log Rank Test in R**

For this example, we’ll use the **ovarian** dataset from the **survival** package. This dataset contains the following information about 26 patients:

- Survival time (in months) after being diagnosed with ovarian cancer
- Whether or not survival time was censored
- Type of treatment received (rx =1 or rx = 2)

The following code shows how to view the first six rows of this dataset:

library(survival) #view first six rows of dataset head(ovarian) futime fustat age resid.ds rx ecog.ps 1 59 1 72.3315 2 1 1 2 115 1 74.4932 2 1 1 3 156 1 66.4658 2 1 2 4 421 0 53.3644 2 2 1 5 431 1 50.3397 2 1 1 6 448 0 56.4301 1 1 2

The following code shows how to perform a log rank test to determine if there is a difference in survival between patients who received different treatments:

#perform log rank test survdiff(Surv(futime, fustat) ~ rx, data=ovarian) Call: survdiff(formula = Surv(futime, fustat) ~ rx, data = ovarian) N Observed Expected (O-E)^2/E (O-E)^2/V rx=1 13 7 5.23 0.596 1.06 rx=2 13 5 6.77 0.461 1.06 Chisq= 1.1 on 1 degrees of freedom, p= 0.3

The Chi-Squared test statistic is **1.1** with 1 degree of freedom and the corresponding p-value is **0.3**. Since this p-value is not less than .05, we fail to reject the null hypothesis.

In other words, we don’t have sufficient evidence to say that there is a statistically significant difference in survival between the two treatments.

We can also plot the survival curves for each group using the following syntax:

#plot survival curves for each treatment group plot(survfit(Surv(futime, fustat) ~ rx, data = ovarian), xlab = "Time", ylab = "Overall survival probability")

We can see that the survival curves are slightly different, but the log rank test told us that the difference is not statistically significant.