Survival curves plot the results of experiments where the outcome is time until death. Usually you wish to compare the survival of two or more groups. Read elsewhere to learn about interpreting survival curves, and comparing two (or more than two) survival curves.
Factors that influence survival should either affect all subjects in a group or just one subject. If the survival of several subjects is linked, then you don't have independent observations. For example, if the study pools data from two hospitals, the subjects are not independent, as it is possible that subjects from one hospital have different average survival times than subjects from another. You could alter the median survival curve by choosing more subjects from one hospital and fewer from the other. To analyze these data, use Cox proportional hazards regression, which Prism cannot perform.
Typically, subjects are enrolled over a period of months or years. In these studies, it is important that the starting criteria don't change during the enrollment period. Imagine a cancer survival curve starting from the date that the first metastasis was detected. What would happen if improved diagnostic technology detected metastases earlier? Even with no change in therapy or in the natural history of the disease, survival time will apparently increase. Here's why: Patients die at the same age they otherwise would, but are diagnosed when they are younger, and so live longer with the diagnosis. (That is why airlines have improved their “on-time departure” rates. They used to close the doors at the scheduled departure time. Now they close the doors ten minutes before the “scheduled departure time”. This means that the doors can close ten minutes later than planned, yet still be "on time". It's not surprising that “on-time departure” rates have improved.)
If the curve is plotting time to death, then there can be ambiguity about which deaths to count. In a cancer trial, for example, what happens to subjects who die in a car accident? Some investigators count these as deaths; others count them as censored subjects. Both approaches can be justified, but the approach should be decided before the study begins. If there is any ambiguity about which deaths to count, the decision should be made by someone who doesn't know which patient is in which treatment group.
If the curve plots time to an event other than death, it is crucial that the event be assessed consistently throughout the study.
The survival analysis is only valid when the survival times of censored patients are identical (on average) to the survival of subjects who stayed with the study. If a large fraction of subjects are censored, the validity of this assumption is critical to the integrity of the results. There is no reason to doubt that assumption for patients still alive at the end of the study. When patients drop out of the study, you should ask whether the reason could affect survival. A survival curve would be misleading, for example, if many patients quit the study because they were too sick to come to clinic, or because they stopped taking medication because they felt well.
Many survival studies enroll subjects over a period of several years. The analysis is only meaningful if you can assume that the average survival of the first few patients is not different than the average survival of the last few subjects. If the nature of the disease or the treatment changes during the study, the results will be difficult to interpret.
The logrank test is only strictly valid when the survival curves have proportional hazards. This means that the rate of dying in one group is a constant fraction of the rate of dying in the other group. This assumption has proven to be reasonable for many situations. It would not be reasonable, for example, if you are comparing a medical therapy with a risky surgical therapy. At early times, the death rate might be much higher in the surgical group. At later times, the death rate might be greater in the medical group. Since the hazard ratio is not consistent over time (the assumption of proportional hazards is not reasonable), these data should not be analyzed with a logrank test.
It is not valid to divide a single group of patients (all treated the same) into two groups based on whether or not they responded to treatment (tumor got smaller, lab tests got better). By definition, the responders must have lived long enough to see the response. And they may have lived longer anyway, regardless of treatment. When you compare groups, the groups must be defined before data collection begins.