Survival Function, S(t): the probability that an individual will survive beyond time t What is the risk of the event at a particular point in time, among those who have survived until that point?Įach of these questions corresponds with a different type of function used in survival analysis: What proportion of individuals will have the event after a certain time?
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What proportion of individuals will remain free of the event after a certain time? Three different types of research questions that may be of interest for TTE data include: With TTE data, the research question can take several forms, which influences which survival function is the most relevant to the research question.
The choice of analytical tool should be guided by the research question of interest. Most survival analytic methods are designed for right-censored observations, but methods for interval and left-censored data are available. Interval-censored data occurs when the event is observed, but participants come in and out of observation, so the exact event time is unknown. Left-censored data occurs when the event is observed, but exact event time is unknown. If the events occur beyond the end of the study, then the data is right-censored. There are three main types of censoring, right, left, and interval. For most analytic approaches, censoring is assumed to be random or non-informative. Such censored interval times underestimate the true but unknown time to event. This phenomenon is called censoring and may arise in the following ways: the study participant has not yet experienced the relevant outcome, such as relapse or death, by the close of the study the study participant is lost to follow-up during the study period or, the study participant experiences a different event that makes further follow-up impossible. One of the challenges specific to survival analysis is that only some individuals will have experienced the event by the end of the study, and therefore survival times will be unknown for a subset of the study group. Some authors recommend that age rather than time on study be used as the time-scale as it may provide less biased estimates. Models with age as the time scale can be adjusted for calendar effects. Is there another option for time-scale other than time on study?Īge is another commonly used time-scale, where baseline age is the time origin and individuals exit at their event or censoring age.
For cohort studies, the time-scale is most commonly time on study. Other examples include birth and calendar year. This is often a natural choice if the outcome is related to that characteristic. Time origins can also be determined by a defining characteristic, such as onset of exposure or diagnosis. Examples include baseline time or baseline age. TTE data can employ a variety of time origins that are largely determined by study design, each having associated benefits and drawbacks. The time origin is the point at which follow-up time starts. Typically there is a single target event, but there are extensions of survival analyses that allow for multiple events or repeated events. Once these are well-defined, then the analysis becomes more straight-forward. It is important to have a clear definition of the target event, the time origin, the time scale, and to describe how participants will exit the study. There are 4 main methodological considerations in the analysis of time to event or survival data. What are important methodological considerations of time-to-event data? These techniques incorporate data from multiple time points across subjects and can be used to directly calculate rates, time ratios, and hazard ratios. Special techniques for TTE data, as will be discussed below, have been developed to utilize the partial information on each subject with censored data and provide unbiased survival estimates. In the presence of censoring, the true time to event is underestimated. Traditional regression methods also are not equipped to handle censoring, a special type of missing data that occurs in time-to-event analyses when subjects do not experience the event of interest during the follow-up time. Traditional methods of logistic and linear regression are not suited to be able to include both the event and time aspects as the outcome in the model.
Time-to-event (TTE) data is unique because the outcome of interest is not only whether or not an event occurred, but also when that event occurred. What is unique about time-to-event (TTE) data?
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This page briefly describes a series of questions that should be considered when analyzing time-to-event data and provides an annotated resource list for more information.