What is an event history model?

Think of it like this – you are interested in whether something happens, what predicts whether it happens and how long until it happens. Let’s take a common one, like, say, death.

An event history model could predict the duration from diagnosis of tuberculosis to death. In this model you have two groups, those who died during the study and those who were still alive at the end of the study. You could use a simple logistic regression model. I guess this says something about me that I use simple and logistic regression model adjacent to one another in the same sentence.

Logistic regression fails to use a critical piece of information, that is, how long the person survived.

Some terms to know thinking about event history analysis:
1. There are various types. Survival analysis is a special case of event history analysis. In this case, the curve eventually reaches zero – in the end, there are no survivors, everybody dies. Also, survival analysis does not have recidivism rate. You only die once. Related to this, it is a final point. You don’t die and then come back. I know every Christian from that original Mormon guy to Father Mike says you do, but it has never happened in the duration of any statistical study in which I have been involved. In mathematical terms, it would be said that the survivor function S(t) is a strictly decreasing function.

2. Some observations are censored. That does not mean they have been running around your study naked (although they could be, there is nothing to prevent a censored subject from going naked). Censored subjects have not experienced the event by the time the study ended or you lost track of them. (If you had kept their clothes, that might have prevented them from running off, but it is too late now. You should have thought of that sooner.) If your study is of the use of illegal drugs, some people will not have used drugs at all by the time the study ends. If your study lasts 700 days and Joseph goes out and does massive amounts of cocaine on day 700, while Mary is at church singing hymns all day for all 700 days of the study, it wouldn’t make any sense to consider Joe as having just one day less of cocaine-free lifestyle. In fact, it is very plausible that Mary will continue drug-free throughout the rest of her life for another 7,000 days or more, and, with behavior like this, she may even come back from the dead and live drug-free hymn-singing some more. You could drop Mary out of the study as “missing data” , since there is no data on when she began using illegal drugs. That’s an unsatisfactory solution also, though. Not only is she not really missing data but the data you do have is usually the outcome you are most interested in – the not-drug-taking, not-dead, not-incarcerated people.

3. Some event history models allow for multiple episodes of the event, whether your variable of interest might be drug use, incarceration, military intervention, or its don’t-try-this-at-home counterpart of domestic violence.

Comments

One Response to “Event History Lesson”

  1. James McDermott on May 13th, 2009 3:31 am

    Having mutated (wanted to say evolved or progressed but neither fitted) from medical statistician to businessman I am not often asked to describe survival analysis anymore….. if anyone does, I shall point to your description. Thank you.

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