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When modelling survival data one usually starts with a Kaplan-Meier curve and uses then Cox regression for machine learning. I am wondering if I could use also more sophisticated methods as models such as neural networks or support vector regressors etc to model the survival data?

Let's say I am interested in predicting survival for 1 year; can I simply remove all data censored from people in the first year and use that as the dataset? This includes people that did not die at all, died after a year and were censored after a year as 'positive' examples and treat all people which died within a year as a negative example. Is this an ok method? I am aware I do throw out valuable information on people censored in the first year but can I make this assuption to make NNs and SVRs work?

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I don't see any reason why not, but then you aren't really modeling survival data. You've changed the question. You could make the question binary: Survival for 1 year (yes/no) and then use any method suitable for binary data.

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