favour a model with heavier tails than normal. The lack of flexibility in the tails and the presence of extreme observations affect the estimation of the shape parameter $\gamma_{\varepsilon}$ in the LTP Normal model by pulling out this estimator in the opposite direction. This emphasises the importance of assessing the type of flexibility required for properly modelling the data.

           Model                LTP $t$       LTP Normal       Log-$t$       Log-normal
  ------------------------ ----------------- ------------ ----------------- ------------
         Intercept               7.704          7.518           7.539          7.731
            Age                 -0.026          -0.026         -0.027          -0.025
        log(Albumin)             1.552          1.529           1.554          1.472
       log(Bilirubin)           -0.587          -0.620         -0.595          -0.606
           Edema                -0.762          -0.710         -0.706          -0.840
        log(Protime)            -2.464          -2.189         -2.313          -2.371
   $\sigma_{\varepsilon}$        0.773          0.908           0.770          0.973
   $\gamma_{\varepsilon}$       -0.133          0.190             –              –
   $\delta_{\varepsilon}$        4.446            –             5.602            –
            AIC             [**635.019**]{}    642.318     [**633.702**]{}    642.222

  : PBC data: Maximum likelihood estimates, AIC (best values in bold).[]{data-label="table:PBCMLE"}

Example 3: NCCTG Lung Cancer Data {#Lung}
---------------------------------

In this section, we revisit the popular NCCTG Lung Cancer Data. This data set contains the survival times of $n=227$ patients (the total number of patients is 228 but we have removed one patient with a missing covariate, for the sake of simplicity) with advanced lung cancer from the North Central Cancer Treatment Group. The goal of this study was 