Difference between survival analysis and classification?

Question

Since the time variable can be treated as a normal feature in classification, why not using more powerful classification methods (such as, C4.5, SVM) to predict the occurrence of an event? Why lots of people still use the classic but old Cox model?

In case of the right-censoring data, since the time would change for an instances, so I think same object with different time values could be treated as two different instances in classification. Is this OK? Is there are some highly-cited paper on this topic? Thank you!

Answer 1

+1 for Michael Chernick, yet I'll add few words from a ML point of view.

Survival problem is specific -- it seems like a pure regression, but it adds a serious constrains (monotonicity between individual "sick/resistance factors" and output, autocorrelation of decision over time, asymmetry of error in case of censored data, etc.) -- and constrains mean information we can get for "free" instead of squeezing it from the data.

Thus, it is just beneficial to use survival-aware model for survival data -- Cox model may overtake plain SVMs and CARTs just because they would lose their accuracy advantage on recreating survival constrains. However, there actually are survival-aware ML methods -- survival CARTS in party, random survival forests, Cox model boosters... You can find some inspiration on CRAN Survival Task View.

Answer 2

I have a little trouble understanding your questions because they are not written well. But I will address what I think you are asking. If I misinterpret anything you can tell me and we can try again. 1. In classification can predicting the occurrence/non-occurrence of an event be enhanced by including time as a variable in the classification algorithm. Answer: Yes it could be very helpful.

1. Since the Cox proportional hazards model was original proposed in 1972 why is it used so much in survival analysis? Answer: The model is used because it is a powerful technique that is especially helpful in determination of hazard ratios. We don't stop using the t test because it was discovered by Gosset prior to 1920.

2. This question is one I have a hard time understanding. This is how I would rephrase it. But let me know if I have it wrong. Since in survival analysis we have to deal with right censoring, could we for the purpose of classifying events use the same subject twice with two different times as distinct pairs to use in training a classifier to predict events? Answer: I don't really like this idea because the classifier treats the data as though they are independent. But the two pairs you introduce this way could be highly correlated. There is some merit to the idea because the second time point does provide additional information that could help classification.

Survival analysis is not designed to predict events. It primarily is used to estimate a survival curve which measures the probability that an event has not occurred by time t taking all previous events and censored observations into account. Classification is used to predict a response given a set of variables (predictors). In the context of time to an event classification is used to predict when an event will occur for a new subject while survival analysis just tries to characterize how the probability of an outcome increases with time.

Regarding sources for information in survival analysis there is a wealth of excellent books. Look up the books by Jerald Lawless and the one by Kalbfleisch and Prentice for some good examples. The book by Therneau and Grambsch is excellent for learning the Cox model.