Survival Analysis
Survival Analysis
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, semiparametric, and nonparametric. 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 semiparametric 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.
Featured Posts

[latexpage] In regression models of various kinds (e.g.

Today, we think of probability as an intensively mathematical subject. But the mathematics took a long to...

Question: How do I calculate a ttest for proportion in a small sample of 8 to do hypothesis testing? My...

I'll bootstrap from here to eternity 'Cause that's my statistics fraternity The idea is quite old But it...

Cluster analysis is a set of methods for finding subjects (people, corporations, drugs, whatever) that "go...

Are you writing a dissertation? Congratulations! You've gotten through undergraduate education, graduate...

One problem with academic research publications is known as the "filedrawer" problem. If you do research on a...

Question: How does a good statistician contrast with a good mathematician? How do the fundamental skills of...

Many times, researchers will categorize continuous variables. For example, birth weight of human infants is...

When dealing with ordinal data, many methods require you to assign a number or score to each level of a...

This is a talk developed by David Cassell and me, and given at NESUG and SGF and WUSS

One question that sometimes arises in doing statistical analysis is whether to use a sophisticated method that...