Survival data need to be analyzed with specialized methods for two reasons:
1. The survival times usually have specialized nonnormal distributions, like the exponential, Weibull, and lognormal.
2. Some of the data could be censored.
Survival functions are calculated using the nonparametric Kaplan-Meier method for one or more groups of either complete or right-censored data. Complete data have no censored values. Right-censoring is when you do not know the exact survival time, but you know that it is greater than the specified value. Right-censoring occurs when the study ends without all the units failing, or when a patient has to leave the study before it is finished. The censored observations cannot be ignored without biasing the analysis. The elements of a survival model are:
• A time indicating how long until the unit (or patient) either experienced the event or was censored. Time is the model response (Y).
• A censoring indicator that denotes whether an observation experienced the event or was censored. JMP uses the convention that the code for a censored unit is 1 and the code for an uncensored event is zero.
• Explanatory variables (if a regression model is used.)
• Interval censoring is when a data point is somewhere on an interval between two values. If interval censoring is needed, then two Y variables hold the lower and upper limits bounding the event time.
Common terms used for reliability and survival data include lifetime, life, survival, failure-time, time-to-event, and duration.
The Survival platform computes product-limit (Kaplan-Meier) survival estimates for one or more groups. It can be used as a complete analysis or is useful as an exploratory analysis to gain information for more complex model fitting. The Kaplan-Meier Survival platform does the following:
• Shows a plot of the estimated survival function for each group. A plot for the whole sample is optional.
• Calculates and lists survival function estimates for each group and for the combined sample.
• Shows exponential, Weibull, and lognormal diagnostic failure plots to graphically check the appropriateness of using these distributions for further regression modeling. Parameter estimates are available on request.
• Computes the Log-Rank and generalized Wilcoxon Chi-square statistics to test homogeneity of the estimated survival function across groups.
• Analyzes competing causes, prompting for a cause of failure variable, and estimating a Weibull failure time distribution for censoring patterns corresponding to each cause.