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Given survival analysis relates to an analysis/prediction of time to an event, I was wondering if it was possible to be used to predict eathquakes. If so, how would one go about carrying out that analysis on say one particular region say Japan or California?

So I guess a question related to that say...for example if we took a univariate time-series based dataset looking at the tremors over time in Japan, could this be converted in a manner that would applicable to be useable for survival analysis... this is assuming that potentially prior small tremors might be indicative of a much larger earthquake to come.

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There is no reason I can see that it couldn't be used, but I am guessing that the model would get quite complex with the spatial and temporal nesting. I'm also pretty sure it's been studied. – Peter Flom Sep 5 '12 at 23:52
@Peter Flom, I guess that was what I was driving at...given univariate time-series data, how/what is the process that one goes through to split up that data to make it usable...also I did look for some papers that related to this, but couldn't find much, any links would be much appreciated. – h.l.m Sep 5 '12 at 23:54
It's not a field I know much about. But a little Googling found this which looks like it has a lot of relevant info. – Peter Flom Sep 6 '12 at 0:17
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I don't think survival analysis is mentioned in the link Peter found. If you accumulate time between earthquakes at a certain region that could be used as the basis for a survival curve. But what is missing is the total number of earthquakes that will eventually occur. That prevents us from determining the magnitude of the steps down in say a Kaplan-Meier curve. Also even if we are given a survival curve how would we use that for prediction.Perhaps we could use median survival time as the prediction for the next event. But that doesn't seem to be a good way to forecast. – Michael Chernick Sep 6 '12 at 0:44
Point process theory would seem to be more applicable. – Michael Chernick Sep 6 '12 at 0:44
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2 Answers

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No.

Survival analysis is used to summarize the survival times (or times to any event that can only happen once) of a bunch of people. And, of course, the survival curve of two groups (or two treatments) can be compared. So a survival curve can show that certain percentage of a certain group of people have died within a certain time after a defined starting period. Say that 30% of men between 50 and 60 years old with a certain kind of tumor being treated with a certain protocol will have died within five years.

The key point is that the event - death in this case - can only happen once to each person, and we are tracking lots of people. I don't see how the earthquake example fits this mindset.

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Is survival analysis not used also in the context of probability of reoccurrence of cancer in cancer patients? Would this not be an example of an event happening more than once and survival analysis still being used? – h.l.m Sep 11 '12 at 21:45
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Survival analysis can be used for events that occur more than once. It is called recurrent events. – jkd Oct 12 '12 at 17:45
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Yes, survival analysis may be used to model earthquake data, but perhaps not in the way you originally envisioned.

Specifically you can trade out time-to-death (survival) for another interval variable, and it need not be time-based. It could be a set of financial thresholds, losses on an insurance policy, or perhaps the max magnitude of an earthquake experienced for a particular region (the studied unit in this example) between 2000-2010.

For n = 100 measurement regions, grouped by richter scale band:
9.0+: 1
8.0-8.9: 2
7.0-7.9: 6
6.0-6.9: 9
etc……
<2.0: 40

From there all of the standard statistics apply: Kaplan-Meier estimator, Nelson-Aelan hazard rate, their variance approximations, cumulative survival rates, conditional 'survival' analyses, etc. And assuming you have appropriate covariates then Cox regression as well.

Not sure this is the best case to use or a great example. But such survival analysis techniques are sometimes employed in insurance, particularly for cases where there's notable truncation, censoring, or grouping of the data you have to work with (though given the ease of capturing data these days this is less of an issue).

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