Survival curves plot the results of experiments in which the outcome is the elapsed time until some one-time event of interest (giving the analysis its name, this one-time event is often death in clinical or animal studies). Often, you may want to compare the probability of survival as a function of time for two or more groups. Other pages in this guide provide more specific information regarding interpreting survival curves, and how to make comparisons between 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 these observations are not independent. For example, if the study pools data from two different hospitals, then the subjects may not be independent. It is possible in this situation that subjects from one hospital have different median survival times than subjects from another. Unexpected changes to the median survival time may occur by sampling of patients from one hospital vs the other. To analyze this sort of data, use Cox proportional hazards regression.
Typically, subjects in a study are enrolled over a period of months or years (the start date for any given subject in this sort of study may not be the same as the start date for another subject). However, in these studies, it is important that the enrollment 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 metastasis earlier? Even with no change in therapy or in the natural history of the disease, survival times will seem to increase. Here’s why: patients will die at the same age that they otherwise would, but are diagnosed sooner (at a younger age) using the new technology than they would have been using the older technology. For these patients, their elapsed observation time would subsequently be longer.
If the survival study is considering death as the event of interest, then there can be no ambiguity about which deaths to count. In a cancer trial, for example, how are deaths of subjects who died in car accidents considered? Some investigators count these as events of interest; others count them as censored subjects (since these individuals did not experience death from cancer prior to the end of the study). 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 to which study group each patient belongs.
If the studied event of interest is something other than death, it is crucial that the event be assessed consistently throughout the study.
Survival analyses are only valid when the survival times of censored patients are identical (on average) to the survival of subjects who remained in the study. This is sometimes referred to as data that are “Missing completely at random” (MCAR). If a large fraction of subjects are censored, the validity of this assumption is critical to the integrity of the results. Note that there is no reason to doubt this assumption for patients who are censored because they are still alive at the end of the study. However, when patients drop out of the study, you should ask whether the reason could have an effect on survival. For example, a survival curve could be misleading if many patients dropped out because they were too sick to come to the clinic, or because they stopped taking medication once they felt better.
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 enrolled subjects is not different from the average survival of the last few subjects. If the nature of the conditions leading to the event of interest (e.g. the disease being studied or the treatments being provided) change during the study, the results will be difficult to interpret.
The logrank test is only strictly valid when the assumption of proportional hazards holds true for the survival curves of the groups being compared. This means that the rate of the event of interest occurring for one group is a constant fraction of the rate of the event of interest occurring in the other group at all points in time. This assumption has proven to be reasonable in many situations. For example, it would not be reasonable if you were investigating death in one group employing a medical therapy with another group undergoing 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 higher in the medical therapy group. Since the hazard ratio is not consistent over time (i.e. the proportional hazards assumption is violated), these data should not be analyzed with the logrank test.
It is not valid to divide a single group of subjects (all considered equal during recruitment and study) into two groups based on whether or not they responded to treatment (tumor got smaller, lab tests got better, etc.). By definition, the responders must have survived long enough without the event of interest occuring in order to observe these different responses. And they may have survived longer anyway, regardless of any treatment received. When comparing groups, the groups must be defined before data collection begins.