# What to do in case of nonsensical (negative survival time) predictions?

I have a rather small dataset of clinical variables and survival times. I've tried running linear regression on these in a cross-validated fashion. I note that in some cases, the regression will give a negative prediction. As these are survival times, this is nonsense.

I am wondering if there is a generally accepted fix for this type of situation (set negative predictions to zero?)

I had considered using a categorical predictor of some kind, but my dataset is too small to populate a meaningful number of categories.

Thanks for any pointers or suggestions.

A OLS model assumes your data is normally distributed around the estimates, and negative values not impossible. You would probably get better estimates from a model that uses an alternative distribution, such as a Poisson or Gamma distribution.

The R survival package has methods for estimating these sort of models. SAS also has various survival estimation methods, such as LIFEREG. Or you could just fit a generalized linear model instead of an OLS with a Poisson or Gamma distribution (in R using glm() with an appropriate family, or in SAS using PROC GENMOD).

• Ain't the OLS assumptions about the errors, and not the data? – Dimitriy V. Masterov Feb 14 '14 at 3:22
• Thank you for the suggestions. I am fairly new to the topic and have a tendency to get "stuck" in my thinking when trying to solve a problem. I've been doing some runs with other distributions and now I think I grasp the whole area much better. – PickledZebra Feb 15 '14 at 1:50

Why would you fit a model (linear regression) that can go negative, when you know that negatives are impossible in your problem?

At the least, one should try to fit a model that doesn't contradict basic knowledge.

So if survival time is the response, fit a model that is unable to be negative (is restricted in some way to be non-negative). Exactly what kind of model may be suitable depends on your particular circumstances.

One thing that definitely impacts a choice of approach - since this is survival time, do you have any censoring?

If censoring isn't an issue, it may be that some kind of GLM might work (e.g. Gamma with log-link or inverse link), or it may be that a more typical parametric survival model may do better (e.g. a Weibull model). It may even be that a simple nonlinear least squares model would be reasonable, or perhaps even a linear regression on suitably transformed data. There are many other choices, but not enough information in your question to really suggest one in particular.

• I appreciate the suggestions and will investigate. I was attempting to use the simplest approach in my understanding. – PickledZebra Feb 14 '14 at 3:27