# Survival Analysis or Not?

I am conducting an analysis where the outcome is time to an event in minutes, with no censoring of the event, and in this situation the event always occurs. The distribution of the outcome variable is skewed right, but a log-transformation makes it roughly normally distributed. An intervention was implemented to decrease the time to the outcome event, and the main research questions revolve around the impact of the intervention on the outcome, and how the intervention affected the association of other covariates with the outcome.

My question - Is survival analysis the appropriate method to use here, or would it be better to start with a linear regression on the log-transformed outcome variable and go that route? Does the choice of method depend on the research question? Or is one type of method more appropriate in this situation than the other regardless of question?

• Time to event is often modeled as having an exponential distribution: en.wikipedia.org/wiki/Exponential_distribution
– Dan
Jun 22, 2018 at 13:45
• As there is no censoring, survival analysis is unnecessary here. You can try an ordinary regression. Also, the distributional assumption of normality in linear regression is about the residuals (f(Y|X)), not about the marginal distribution of the outcome f(Y). So first fit your model and see if the non-normality persists. Jun 22, 2018 at 14:46
• Note that the exponential distribution assumes a constant hazard. There are many possible survival models out there to characterize the function of the hazard with respect to time. Here is a good starting point for survival analysis in general. data.princeton.edu/wws509/notes/c7.pdf Jun 22, 2018 at 18:49

Survival Analysis does not require that your data be censored. Though not having censored data certainty does give you substantially more options regarding your choice of models.

The main factors that you should use to determine whether survival analysis is appropriate are:

1. Does the "time" component fit the distribution you want to use? Which from what you said, it looks like it does.

2. Does the proportional hazard assumption hold? If it does not, there are alternatives, though they are more complex to model and interpret. For instance, I often use the Royston and Parmar model (Royston & Parmar, 2002), which uses restricted cubic splines to estimate the survival distribution.

So given the information you provided, I would not recommend against the use of a survival model. Though for me to make a specific recommendation, I would need more information.

References

Royston, P., & Parmar, M. K. (2002). Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modeling and estimation of treatment effects. Statistics in medicine, 21(15), 2175-2197.

I agree that if there is no censoring, it is probably not really necessary to use the survival analysis. However, I would point out that the goal of your work is very important. If you just want to make a predictive model, then it actually does not matter which method you use as long as it gives you good (it is up to you how you define it) results.

If you want to make the model more descriptive and understand which variables and how they effect the dependent variable, I would go as simple as possible so that it is easily interpretable. The final model, in this case, should reflect on your hypothesis how actually the data generating process (DGP) works . Well, you can try OLS, GLM or some f.e. non-linear method, but you need to decide, which one would make the most sense for your DGP.

Stripped down to its mathematical technicalities, survival analysis is essentially just the analysis of continuous non-negative random variables, and certain common compositions of these random variables (e.g., looking at minimums or maximums of these random variables). While survival analysis can accommodate censored data, it is not necessary for censoring to occur to fall within the scope of survival analysis. Survival analysis generally focuses on aspects of continuous non-negative random variables that are most using in contexts involving times-to-failure of objects (e.g., hazard rates, etc.), but it also interfaces with other areas of statistics when they use continuous non-negative random variables.

The problem you have described is a regression problem where your response variable is a continuous non-negative random variable. You want to know the effect of a binary intervention on your time response variable (both its direct effect and its interaction effect with other covariates). While the response variable is amenable to methods in survival analysis, this is primarily a regression problem and it would use standard methods for regression with a non-negative response variable (e.g., log-linear regression).