# MLE of Weibull hazard and lognormal frailty in R

Consider a Gaussian random variable log(U), with mean mu and variance sigma^2. How can the parameter estimates of the corresponding log-normal frailty model (i.e the frailty random variable is U which follows a log-normal distribution) be obtained? The hazard distribution can assumed to be Weibull.

The parfm package (in R) assumes log(U) has a mean of zero.

$$\mu$$ is fixed (to zero) to ensure identifiability of the parameters in the frailty model, similar to the zero-mean constraint for the random effects in the linear mixed model.
In other terms, $$\mu$$ plays the same role as the scale parameter of the Weibull baseline hazard.