# What researchers mean by... survival analysis

Researchers in work and health can use survival analysis—a branch of statistics that often predicts the timing of death—to calculate other things that are far more life affirming: return to work after an injury, for example.

Survival analysis is a branch of statistics that allows researchers to study lengths of time.

Historically, it was developed to study/predict time to death of patients with a disease or an illness, and it typically focused on the time between diagnosis (‘start’ time) and death (‘end’ time). As such, it is used to answer questions such as: What fraction of a population will survive past a certain time? How do particular circumstances (e.g. taking a new medication) or characteristics (e.g. age of patient) increase or decrease time to death?

However, survival analysis techniques do not always entail timelines leading to death. They can be used to study the probability of a wide range of time outcomes. For example, in the social sciences, researchers may study the “survival” of marriages, high school drop-out rates (time to drop-out), spells of unemployment and, as we will see, time to return to work following a workplace injury.

Survival times are data that measure follow-up time from a defined starting point to the occurrence of a given event or end point. However, if a study stops before all participants have reached the end point, survival analysis can accommodate this partial information; i.e. that these participants survived at least so long. For example, a researcher studying the effectiveness of a new treatment for a disease considered terminal would not want to exclude patients who survived the entire study period, because their survival reflects on the effectiveness of the treatment.

## Kaplan–Meier survival curve

Researchers have a number of methods for analyzing data in order to show the distribution of lengths of time taken to reach a certain end point. One of the more widely used methods is the Kaplan–Meier survival curve, named after its creators Edward Kaplan and Paul Meier.

To show how this curve conveys this information, let’s say you were studying return to work (RTW) among a group of injured workers with low back pain (LBP). Based on your findings, you might want to show what percentage of workers with LBP will return to work by certain points over time and how particular circumstances affect the timing of RTW.

The Kaplan-Meier curves (only available on hard copy of article) show workers who had no workplace RTW program (the lighter curve) and workers with an established RTW plan at work (the darker curve) and the number of days it took to return to work after a sick leave due to LBP. As shown in the graph, approximately 15 per cent of injured workers with an RTW program had not returned to work by 180 days, but an even greater percentage—20 per cent—had not yet returned to work by 180 days where there was no RTW program. This suggests that RTW programs are helpful in getting more injured workers back to work.

So survival analysis can do more than predict death. It can aid decision-making in a wide variety of situations, including work and health.

To see other columns, go to: www.iwh.on.ca/what-researchers-mean-by.

Source: At Work, Issue 69, Summer 2012: Institute for Work & Health, Toronto