# In a time to event analysis, when is it appropriate to use parametric models to compute restricted means?

Restricted mean is gaining popularity as a substitute for the hazard ratios to compare survival times in time-to-event analysis, especially in observational studies where chances of violation of proportional hazards assumption are higher.

To compute restricted mean, we have two major approaches: 1. Using Kaplan-Meier estimate (non-parametric) 2. Using parametric models like Weibull, Gompertz, LogLog, etc.

Is there a guideline which says when to go for parametric estimates and when to go for non-parametric estimates for computing restricted mean?

The reason why nonparametric methods are most often used in survival analysis is censoring. Namely, that because of censoring it is more difficult to check the fit a specific parametric model. For example, residuals calculated for a parametric accelerated failure time (AFT) model will be censored because they are calculated based on the observed event times, and if you want to assess whether they follow a specific distribution, you will need to take censoring into account. However, as you also mentioned nonparametric models, like the Cox model, are not assumption-free.

Something in-between the two worlds is to choose a parametric but flexible model. For example, AFT models with a flexible error distribution.

• In case of restricted mean estimates, the choice of parametric or non-parametric estimates could actually be very dependent on what time you want to compute the restricted mean because of censoring. If the time at which restricted mean has to be computed is more close to the maximum follow-up time, the chances are that the number of people at risk at that time point will be much lower than the number of people at risk at the starting time point. In this case, would you rather go for a parametric estimate or non-parametric estimate? – j1897 Dec 5 '18 at 14:15