The UK National Institute for Health and Clinical Excellence (NICE) has used its Single Technology Appraisal (STA) programme to assess several drugs for cancer. Typically, the evidence submitted by the manufacturer comes from one short-term randomized controlled trial (RCT) demonstrating improvement in overall survival and/or in delay of disease progression, and these are the pre-eminent drivers of cost effectiveness. We draw attention to key issues encountered in assessing the quality and rigour of the manufacturers' modelling of overall survival and disease progression. Our examples are two recent STAs: sorafenib (Nexavar®) for advanced hepatocellular carcinoma, and azacitidine (Vidaza®) for higher-risk myelodysplastic syndromes (MDS). The choice of parametric model had a large effect on the predicted treatment-dependent survival gain. Logarithmic models (log-Normal and log-logistic) delivered double the survival advantage that was derived from Weibull models. Both submissions selected the logarithmic fits for their base-case economic analyses and justified selection solely on Akaike Information Criterion (AIC) scores. AIC scores in the azacitidine submission failed to match the choice of the log-logistic over Weibull or exponential models, and the modelled survival in the intervention arm lacked face validity. AIC scores for sorafenib models favoured log-Normal fits; however, since there is no statistical method for comparing AIC scores, and differences may be trivial, it is generally advised that the plausibility of competing models should be tested against external data and explored in diagnostic plots. Function fitting to observed data should not be a mechanical process validated by a single crude indicator (AIC). Projective models should show clear plausibility for the patients concerned and should be consistent with other published information. Multiple rather than single parametric functions should be explored and tested with diagnostic plots. When trials have survival curves with long tails exhibiting few events then the robustness of extrapolations using information in such tails should be tested.