Survival distributions, Kaplan-Meier estimation

Comparison of Kaplan-Meier survival estimates is often called for in clinical trial analysis. With survival analysis, you are trying to determine which treatment group displays a better time-to-event distribution than another. Part of this analysis is the production of Kaplan-Meier estimates plots that show the probability of a given event over time for each treatment group. In the following example you see that New Drug displays better survival estimates over time than either Old Drug or Placebo. ... 

Sometimes, these data are presented in a shorter table that displays only those time points at which an individual had an event or was censored, and thus the only values of time for which the probability of survival changes. It is more common, however, to see analyses of this type displayed graphically. The Kaplan-Meier estimate of the survival distribution is displayed for both groups in Figure 8.3. The survival curves displayed in the figure are termed "step functions" because of their appearance. We return to the interpretation of Figure 8.3 after we have fully specified the survival distribution function. 

Figure 8.3 Kaplan-Meier estimate of the survival distribution for adverse event A...

The Kaplan-Meier estimate is a nonparametric method that requires no distributional assumptions. The only assumption required is that the observations are independent. In the case of this example, the observations are event times (or censoring times) for each individual. Observations on unique study participants can be considered independent. The confidence interval approach described here is consistent with the stated preference for estimation and description of risks associated with new treatments. A method for testing the equality of survival distributions is discussed in Chapter 11. 

The distributions of immune function parameters were compared across treatment groups via t-test. Kaplan Meier estimates were used to summarize overall survival (OS) and event free survival (EPS). Survival was calculated from PBSC infusion until death or date of last contact. EPS is defined as the absence of death, relapse, disease progression and de novo secondary cancer. Cox regression models were fitted for the outcomes of OS and EPS. P values associated with regression models were derived from the Wald test. The last possible day of contact was Pebruary 21,2006. 

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