# Predicting survival time from log-hazard

I have estimated a Weibull regression model in BUGS/JAGS which gives me the log-hazard as a function of intercept (baseline hazard) and covariate effects.

The intercept is estimated as -9.826 and one of the covariates is estimated as 0.78. I can now compute the specific log-hazard for each individual in the dataset. However, I am interested in the expected survival time. Hence, I would like to predict each individual's survival time from their log-hazard.

I know that it is possible since, when estimating the same survival model in R, I can use predict(type="response") to get back to the survival times.

In my stats books and on the Internet, I can also find ways to express the survival probability but not the survival time. Is there a way?

## 1 Answer

I came up with the following idea: There is a link between the hazard estimates and the coefficients of an accelerated failure time parameterization of the Weibull regression model. Specifically, Beta_Hazard = - Beta_AFT / shape.

To get to the expected survival times, I would then first transform the regression coefficient to AFT estimates, and, in a second step, take the $$\exp()$$ of the linear predictor of the AFT model, which equals the survival time.

Can someone confirm that this works?

• Yes, that will be correct to do. – Dimitris Rizopoulos Nov 16 '18 at 20:22