to compare the descriptive information from a questionnaire applied to a group of patients against the information obtained by the patient’s physician, in terms of prognostic power [@L94]. We fit an AFT model with three covariates “age” (in years),“sex” (Male=1 Female=2), “ph.ecog” (ECOG performance score, 0=good–5=dead) as well as an intercept, with different choices for the distribution of the errors in (\[AFTModel\]). Table \[table:LungMLE\] shows the MLEs associated to each of these models together with the AIC values. The AIC favours the model with LTP logistic errors, closely followed by the model with LTP SAS errors. One explanation for this is that the estimators of the LTP SAS model indicate tails heavier than normal ($\hat\delta=0.6674$), which is a tail behaviour naturally captured by the LTP logistic distribution without additional shape parameters that control the tail. The 95% confidence intervals for $\gamma$ and $\delta$ in the LTP SAS model are $(-0.05,0.60)$ and $(0.46,0.86)$, respectively, while the corresponding confidence interval for the parameter $\gamma$ in the LTP logistic model is $(0.16, 0.62)$.

     Model     LTP SAS    LTP Normal   Log-normal     LTP logistic     Log-logistic
  ----------- ---------- ------------ ------------ ------------------ --------------
   Intercept    6.2077      6.9505       6.4940          6.5538           5.9500
      Age      -0.0068     -0.0149      -0.0191         -0.0100          -0.0082
      Sex       0.4614      0.4259       