Kaplan-Meier analysisKaplan-Meier analysis is part of:
Easy and user-friendly
Easy and user-friendly XLSTAT is flawlessly integrated with Microsoft Excel which is the most popular spreadsheet worldwide. This integration makes it one of the simplest available tools to work with as it utilizes the same philosophy as Microsoft Excel. The program is accessible in a dedicated XLSTAT tab. The analyses are grouped into functional menus. The dialog boxes are user-friendly and setting up an analysis is straightforward.
Data and results shared seamlessly
Data and results shared seamlessly One of the greatest advantages of XLSTAT is the way you can share data and results seamlessly. As the results are stored in Microsoft Excel, anyone can access them. There is no need for the receiver to have an XLSTAT license or any additional viewer which makes your team-work easier and more affordable. In addition, results are easily integrable into other Microsoft Office software such as PowerPoint, so that you can create striking presentation in minutes.
Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
Affordable XLSTAT is a complete and modular analytical solution that can suit any analytical business needs. It is very reasonably priced so that the return of your investment is almost immediate. Any XLSTAT license comes with top level support and assistance.
Accessible - Available in many languages
Accessible - Available in many languages We have ensured XLSTAT is accessible to everyone by making the program available in many languages, including Chinese, English, French, German, Italian, Japanese, Polish, Portuguese and Spanish.
Automatable and customizable
Automatable and customizable Most of the statistical functions available in XLSTAT can be called directly from the Visual Basic window of Microsoft Excel. They can be modified and integrated to more code to fit to the specificity of your domain. Adding tables and plots as well as modifying existing outputs becomes easy. Furthermore, XLSTAT includes some special tools on the dialog boxes to generate automatically the VBA code in order to reproduce your analysis using the VBA editor or to simply load pre-set settings. This effortless automation of routine analysis will be a huge time saver on your part.
What is Kaplan-Meier analysis
The Kaplan-Meier method, also called product-limit analysis, belongs to the descriptive methods of survival analysis, as does life table analysis. The life table analysis method was developed first, but the Kaplan-Meier method has been shown to be superior in many cases.
Kaplan-Meier analysis allows you to quickly obtain a population survival curve and essential statistics such as the median survival time. Kaplan-Meier analysis, which main result is the Kaplan-Meier table, is based on irregular time intervals, contrary to the life table analysis, where the time intervals are regular.
Use of Kaplan-Meier analysis
Kaplan-Meier analysis is used to analyze how a given population evolves with time. This technique is mostly applied to survival data and product quality data. There are three main reasons why a population of individuals or products may evolve: some individuals die (products fail), some other go out of the surveyed population because they get healed (repaired) or because their trace is lost (individuals move from location, the study is terminated, among other reasons). The first type of data is usually called "failure data", or "event data", while the second is called "censored data".
The Kaplan-Meier analysis allows you to compare populations, through their survival curves. For example, it can be of interest to compare the survival times of two samples of the same product produced in two different locations. Tests can be performed to check if the survival curves have arisen from identical survival functions. These results can later be used to model the survival curves and to predict probabilities of failure.
Censoring data for Kaplan-Meier analysis
Types of censoring for Kaplan-Meier analysis
There are several types of censoring of survival data:
- Left censoring: when an event is reported at time t=t(i), we know that the event occurred at t * t(i).
- Right censoring: when an event is reported at time t=t(i), we know that the event occurred at t * t(i), if it ever occurred.
- Interval censoring: when an event is reported at time t=t(i), we know that the event occurred during [t(i-1); t(i)].
- Exact censoring: when an event is reported at time t=t(i), we know that the event occurred exactly at t=t(i).
Independent censoring for Kaplan-Meier analysis
The Kaplan-Meier method requires that the observations are independent. Second, the censoring must be independent: if you consider two random individuals in the study at time t-1, if one of the individuals is censored at time t, and if the other survives, then both must have equal chances to survive at time t. There are four different types of independent censoring:
- Simple type I: all individuals are censored at the same time or equivalently individuals are followed during a fixed time interval.
- Progressive type I: all individuals are censored at the same date (for example, when the study terminates).
- Type II: the study is continued until n events have been recorded.
- Random: the time when a censoring occurs is independent of the survival time.
Results for the Kaplan-Meier analysis in XLSTAT
This table displays the various results obtained from the analysis, including:
- Interval start lime: lower bound of the time interval.
- At risk: number of individuals that were at risk.
- Events: number of events recorded.
- Censored: number of censored data recorded.
- Proportion failed: proportion of individuals who "failed" (the event did occur).
- Survival rate: proportion of individuals who "survived" (the event did not occur).
- Survival distribution function (SDF): Probability of an individual to survive until at least the time of interest. Also called cumulative survival distribution function, or survival curve.
- Survival distribution function standard error.
- Survival distribution function confidence interval.
Mean and Median residual lifetime
Mean and Median residual lifetime are computed and displayed into two tables.
- A first table displays the mean residual lifetime, the standard error, and a confidence range.
- A second table displays statistics (estimator, and confidence range) for the 3 quartiles including the median residual lifetime (50%). The median residual lifetime is one of the key results of the Kaplan-Meier analysis as it allows to evaluate the time remaining for half of the population to "fail".
Confidence interval for the Kaplan-Meier analysis function
Computing confidence intervals for the survival function can be done using three different methods:
- Greenwood’s method
- Exponential Greenwood’s method
- Log-transformed method
These three approaches give similar results, but the last ones will be preferred when samples are small.
Charts for Kaplan-Meier analysis
XLSTAT offers the following charts:
- Survival distribution function (SDF)
- -Log(SDF) corresponding to the –Log() of the survival distribution function (SDF).
- Log(-Log(SDF)) corresponding to the Log(–Log()) of the survival distribution function.
It is also possible to identify on the charts the times when censored data have been recorded.
Test of equality of the survival functions
It is possible to compute a test of equality of the survival functions with three different tests:
- the Log-rank test,
- the Wilcoxon test,
- and the Tarone Ware test.
These tests are based on a Chi-square distribution. The lower the corresponding p-value, the more significant the differences between the groups.