In clinical trials, especially in cancer clinical trials, at least one of the outcome variables may be date data, which needs to be analyzed. For example, in most of the cancer clinical trials, the end point may be the progression free survival (PFS) or Overall Survival (OS). Here we need to analyse the data based on two dates, viz., start date of the study drug and occurrence of the event of interest such as progression of the disease or death in case of PFS calculation and the start date of the study drug and date of death in case of OS calculation. For certain subjects, the event of interest might not have happened during the study period or some subjects might have been withdrawn from the study due to severe side effects or some subjects might have been migrated to some other place. However, we have the partial information about their survival till last observation recorded during their follow up period. This information is useful and can be incorporated in the survival analyze.  Such information is called censored observation. Since the censored observations are also expected in the date data, we cannot use ordinary analysis procedures, but we need to use special procedure such as Kaplan – Meier procedure by including censored observations. Usually in clinical trials we have at least two groups to be compared to see whether there is any significant difference in survival times among the study groups. For this purpose, log rank test is used to compare the survival times between two groups. In this paper we are trying to explain briefly about the analysis procedures by using some dummy data for illustration purpose and also explained about SAS procedures as well.

The log rank test is used to test the null hypothesis of no difference in survival times between two or more independent groups. The test compares the entire survival experience between groups and can be thought of as a test of whether the survival curves are identical or not. This test is a nonparametric procedure which makes no assumptions about the distribution of survival times. It is easy to apply and is usually more powerful than an analysis based on proportions. It compares survival across the whole spectrum of time, not just at one or two points.

Log rank test is used to compare two or more groups statistically when data is time dependent. Log rank test is related to the chi-square test statistic and compares observed to expected number of events at each time point over the follow-up period. For example, to test the survival probabilities of cancer patients between age groups less than or equal to 25 years vs. above 25 years. The null hypothesis is that there is no difference in survival times between these two age groups. In other words, there is no significant difference between these two groups in the probability of death at any point during the study period.

Below is the survival data for 40 subjects to compare their survival times between two treatment groups.

The SAS procedure LIFETEST is used to perform the log-rank test. The TIME statement designates the variable, days, whose values are the survival times, followed by the variable, Status, which identifies the censored observations. In this case, value of 0 for Status indicate a censored value (i.e., *Status (0)). The STRATA statement identifies the grouping or stratification variable, in this case, Treatment. The ODS GRAPHICS statement and PLOTS= option with the LIFETEST procedure are included to request survival plots and a plot of the negative log of the event times.

ods graphics on;

      proc lifetest data=Exposed plots=(s);

      time Days*Status(0);

      strata Treatment;

   run;

   ods graphics off;

SAS output is given below:

Note:   The marked survival times are censored observations.

Note:   The marked survival times are censored observations.

Log-rank test showed that there is significant difference in survival pattern between two study groups (P= 0.0175).  Thus Log-rank test is a simple procedure to compare the survival times between two or more groups in clinical trials.

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