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Is there anything you should be looking out for in your data before fitting a Cox hazard model? 

For example, with other kinds of models, like linear regression, you should check if your response is normally distributed. I'm wondering if it's the same for Cox proportional hazard models - if any variables need to follow a particular distribution or if there are any other important assumptions. 

If so, what are common ways of finding and dealing with problems in this kind of data? 

Thanks! 

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The Cox regression model is a semi-parametric model in the sense that you do not need to specify a functional form of the baseline hazard rate. So you do not need to assume that any variables follow a particular distribution therefore your response does not need to follow any particular distribution (you can however fit a fully parametric proportional hazards model by assuming that the survival times follow a specific distribution and then checking to see how well that distribution fits the data). The main thing you need to look out for in the data is any truncation or censoring of observations. 

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