Kaplan-Meier Survival Analysis
Supported Worksheet Layout
To perform a Kaplan-Meier analysis, each survival data set must include:
- A time variable that represents the time to the event (death, failure, recurrent failure, etc.)
- A status variable that must contain both the event code and censor code, and can additionally contain a 3rd code representing the subjects at risk beyond completion of the study.
- In order to split the data (e.g., subdividing subjects, conditions, treatments, etc.), the data also should contain a grouping variable.
When a grouping variable is used to split the data, the auto-generated legend differentiating the survival
curves will be based on categories of the grouping variable
(see the example below).
The survival curves in the right-hand side image below were generated in Aabel using raw survival data. The left-hand side image shows a fraction of data used in the analysis, displaying the worksheet layout.
Subjects Remaining at Risk Beyond Completion of the Study
If the Kaplan-Meier curve is plotted without taking into account the number of subjects remaining at risk beyond completion of the study, the shape of the curve will be unaffected, but the survival probability values will be affected.
- Some raw data include the subjects at risk beyond completion of the study as additional rows in the data table (these added rows are tagged with a status code different from the event or censor code). Others may not include the subjects at risk beyond completion of the study. If your data is of the latter type, but you know the number of subjects at time zero, Aabel provides a flexible means of including the information in the analysis.
- While performing Kaplan-Meier analysis, Aabel splits, cross-tabulates, and summarizes the raw survival data, and stores the summarized data in auto-appended columns in the source worksheet as it displays the survival curves on the viewer page. The generated curves are hot-linked to the summarized data.
- Life table computation results include time (in years, months, etc.), number at the start of each time interval, censor (withdrawn during each time interval), at risk, observed number of events (death, recurrence, etc.), probability of event (death, recurrence, etc.) at time x, probability of surviving the time x, and cumulative probability of surviving the time x.
- When we have generated two or more survival curves, the logrank test report is used to determine whether the differences in survival between groups, treatments, etc., are more than we would expect by chance alone.
Life Table Computation Results:
Logrank Computation Results:
Logrank Significance Test
Survival curves compare the cumulative probability of survival at any specific time. When we have generated two or more survival curves, the logrank test is used to determine whether the differences in survival between groups, treatments, etc., are more than we would expect by chance alone.
- When comparing 3+ survival curves, the logrank tests for differences are pair-wise by default (i.e., the test for each pair is performed independent of other groups). You can also compare pairs while taking into account all groups.
- The logrank test results include the hazard Ratio (i.e., the risk factor for one group, treatment, etc.
compared to another group, treatment. etc.), the logrank chi-square and p values.
The survival curves and log rank test results shown below were generated in Aabel using the published data of Bland, M. (2000): gallstone-free survival after the dissolution of single and multiple gallstones.
Comparying Kaplan-Meier Survival Curves From Different Data Sets
A chart instance from raw survival data analysis allows displaying survival curves from single or multiple groups belonging to one data set; you may want to compare survival curves from multiple groups belonging to different data sets. Aabel allow this by:
- Providing means for pivoting & summarizing raw survival data for each data set (a data transformation method)
- Allowing to plot the curves from the summarized data belonging to different data sets
Below, is shown an example of Kaplan-Meier survival curves from two data sets, each having two groups. You can optionally display the censor observations on the curves.