# What are papers about simulating survival data to compare merits and disadvantages of various survival analysis methods?

What are papers about simulating survival data to compare merits and disadvantages of various survival analysis methods?

In particular, is there any survival analysis method better for really small sample sizes, a full-likelihood approach, penalized-quasilikelihood, power analysis, type-1 error, short series length?

## 1 Answer

This document nicely outlines how the distribution of (log) survival event times can be expressed in terms of distributions such as extreme-value distributions of various flavors, normal or logistic distributions, etc. So if you want to simulate survival data under a particular type of survival model, choose the parameter values needed for the distribution, sample from the corresponding distribution, and follow the formulas for translating back to event times.

For example, for a log-normal survival model, you have:

$$\log T = \alpha + \sigma W,$$

where $$W$$ represents the variability provided by a standard normal distribution. You choose values for $$\alpha$$ and $$\sigma$$, sample repeatedly from a standard normal distribution ($$W$$), then use the above formula to calculate simulated event times $$T$$.

If your underlying problem is limited numbers of events, however, I don't think that simulation will help much. To avoid overfitting and poor generalizability you need about 15 events for each predictor that you are evaluating in a survival model. It's not completely clear just what you mean by applying some of the approaches you list to survival data, but only penalization in some form can overcome that limit with much hope of reliability. This answer has some general suggestions and a link to a paper specifically on "Too Many Covariates and Too Few Cases." For further background on regression analysis in general and survival analysis in particular, the resources provided by Frank Harrell are quite valuable.