Cox regression models the association between time-to-event outcomes and covariates. However, variations in the nature and definition of the outcome requires modification of the standard Cox-model. This is motivated by study of the Fibrosis-4 Index (FIB-4) association with risk of severe liver outcomes in primary care patients with and without previously diagnosed chronic-liver-disease. FIB-4 non-invasively assesses fibrosis-risk for patients with non-alcoholic fatty-liver-disease using readily available inputs. A retrospective cohort of adult patients with these inputs (Age, AST, Platelets, ALT) results is formed from electronic health records (2007-2018) and their longitudinal FIB-4 scores are calculated. Patients with a liver disease diagnosis or outcome prior to their FIB-4 score are excluded. FIB-4 fibrosis-risk is categorized as low, indeterminate, and high risk. Time from first FIB-4 to severe liver outcome is used as an outcome. We demonstrate novel applications of modified Cox-models accounting for variations in definition of the outcome and censoring mechanisms.