Learning Objectives
After completing this module, the student will be able to:
<span>Identify applications with time to event outcomesConstruct a life table using the actuarial approachConstruct a life table using the Kaplan-Meier approachPerform and interpret the log rank testCompute and interpret a hazard ratioInterpret coefficients in Cox proportional hazards regression analysis</span>
Time to Event Variables
There are unique features of time to event variables. First, times to event are always positive and their distributions are often skewed. For example, in a study assessing time to relapse in high risk patients, the majority of events (relapses) may occur early in the follow up with very few occurring later. On the other hand, in a study of time to death in a community based sample, the majority of events (deaths) may occur later in the follow up. Standard statistical procedures that assume normality of distributions do not apply. Nonparametric procedures could be invoked except for the fact that there are additional issues. Specifically, complete data (actual time to event data) is not always available on each participant in a study. In many studies, participants are enrolled over a period of time (months or years) and the study ends on a specific calendar date. Thus, participants who enroll later are followed for a shorter period than participants who enroll early. Some participants may drop out of the study before the end of the follow-up period (e.g., move away, become disinterested) and others may die during the follow-up period (assuming the outcome of interest is not death).
In each of these instances, we have incomplete follow-up information. True survival time (sometimes called failure time) is not known because the study ends or because a participant drops out of the study before experiencing the event. What we know is that the participants survival time is greater than their last observed follow-up time. These times are called censored times.
Censoring
There are several different types of censoring. The most common is called right censoring and occurs when a participant does not have the event of interest during the study and thus their last observed follow-up time is less than their time to event. This can occur when a participant drops out before the study ends or when a participant is event free at the end of the observation period.
In the first instance, the participants observed time is less than the length of the follow-up and in the second, the participant's observed time is equal to the length of the follow-up period. These issues are illustrated in the following examples.
Example:
A small prospective study is run and follows ten participants for the development of myocardial infarction (MI, or heart attack) over a period of 10 years. Participants are recruited into the study over a period of two years and are followed for up to 10 years. The graphic below indicates when they enrolled and what subsequently happened to them during the observation period.
During the study period, three participants suffer myocardial infarction (MI), one dies, two drop out of the study (for unknown reasons), and four complete the 10-year follow-up without suffering MI. The figure below shows the same data, but shows survival time starting at a common time zero (i.e., as if all participants enrolled in the study at the same time).
