Survival analysis gets its name from the fact that it is often used to look at how long people will live, and to see what influences that. Do women live longer than men? Do people who take aspirin live longer than those who do not? and that sort of thing. But it can be time to any event. We could look at how long prisoners stay in jail, how long patients stay in the hospital, how long couples stay married, or any other variable that is a time.
When the dependent variable is continuous, we would ordinarily first think of linear regression , It’s a very good method when you want to look at the relationship between a continuous dependent variable and one or more independent variables.
But, like nearly all statistical techniques, it makes assumptions. And one of the assumptions that is so clear as to usually go unstated is that we know the value of the dependent variable; usually, this is not a problem. If we want to model, say, what people weigh, we can weigh them. But in one common type of analysis, we don’t always know the dependent variable – that’s when the dependent variable is time to an event. In that case, we need survival analysis.
The key reason that we need survival analysis is that these data are often censored. If, for example, we were looking at how long couples stay married, we could select some couples, and follow them over time. But some couples won’t get divorced before we finish our study. Similarly, some patients won’t die during our study, and so on.
Types of survival analysis
Although there are a wide variety of techniques for doing survival analysis, they fall into three famlies: Parametric, semi-parametric, and non-parametric. The difference is in what we wish to assume about the distribution of survival times. In parametric survival analysis, we assume that survival times come from some specific statistical distribution; in semiparametric survival analysis, we do not need to make this assumption, but we do make another assumption – usually the proportional hazards assumption. In nonparametric analysis, we avoid even that assumption. Since the exact nature of the survival function is hard to know, and is critical to the results, semiparametric survival analysis is much more commonly used than parametric. And semi-parametric offers more useful output than nonparametric analysis. By far the most common method is known as Cox proportional hazards regression.
Semiparametric methods, unlike parametric methods do not allow you to predict a survival time; rather, they just let you see differences between groups, or differences based on some other measure. For instance, Cox methods would not predict how long couples would stay together, but it could predict how much more quickly (say) couples with a large age difference got divorced than couples with similar ages. This is often of primary interest.
In addition, recent developments allow us to look at multiple events – for instance, we might model repeated patterns of being arrested over time, or getting a particular disease.