Common Errors in Statistics (and How to Avoid Them), 4th Edition

TIME-TO-EVENT DATA (SURVIVAL ANALYSIS)

In survival studies and reliability analyses, we follow each subject and/or experiment unit until either some event occurs or the experiment is terminated; the latter observation is referred to as censored. The principal sources of error are the following:

• Lack of independence within a sample
• Lack of independence of censoring
• Too many censored values
• Wrong test employed

Lack of Independence within a Sample

Lack of independence within a sample is often caused by the existence of an implicit factor in the data. For example, if we are measuring survival times for cancer patients, diet may be correlated with survival times. If we do not collect data on the implicit factor(s) (diet in this case), and the implicit factor has an effect on survival times, then we no longer have a sample from a single population. Rather, we have a sample that is a mixture drawn from several populations, one for each level of the implicit factor, each with a different survival distribution.

Implicit factors can also affect censoring times, by affecting the probability that a subject will be withdrawn from the study or lost to follow-up. For example, younger subjects may tend to move away (and be lost to follow-up) more frequently than older subjects, so that age (an implicit factor) is correlated with censoring. If the sample under study contains many younger people, the results of the study may be substantially biased because of the different patterns of censoring. ...