I am trying to understand the meaning of the coefficients estimates of the output of flexsurv's flexsurvreg function. For example, let us assume I want to perform the survival analysis and fit of a Weibull model with respect to a covariate. I will call flexsurvreg in order to obtain the Weibull parameters and covariate coefficient of the best fit flexsurvreg can obtain through its standard method.

fit <- flexsurvreg(Surv(time, censored)~covariate, data=struct, dist="weibull")

fit$res.t then returns the estimates of coefficients in such a fashion for example:

              est
shape         3
scale         4
covariate    -0.3

From there on, I want to try to reconstruct the analytic expression of the hazard function. From my understanding, it should be built in this fashion (for a Weibull model):

$h(t) = \frac{\text{shape}}{\text{scale}} \left(\frac{t}{\text{scale}}\right)^{\text{shape}-1}\cdot \exp\left(\text{coefficient} \cdot (\text{covariate}-\mu)\right)$

with $\text{coefficient}$ being the covariate coefficient returned in the flexsurvreg output; $\text{covariate}$ being the covariate value for which I intend to construct the function and $\mu$ the mean value of the covariate over the fitting sample.

However, the plot of this function does not match the one that plot(fit, type="hazard", newdata=list(covariate=cov)) returns. Why is that? I would guess my analytic interpretation of the coefficient estimates is wrong. What is then the mathematical meaning of these estimates?