Alzheimer's disease (AD) is the most common form of dementia and is phenotypically heterogeneous. APOE is a triallelic gene which correlates with phenotypic heterogeneity in AD. In this work, we determined the effect of APOE alleles on the disease progression timeline of AD using a discriminative event-based model (DEBM). Since DEBM is a data-driven model, stratification into smaller disease subgroups would lead to more inaccurate models as compared to fitting the model on the entire dataset. Hence our secondary aim is to propose and evaluate novel approaches in which we split the different steps of DEBM into group-aspecific and group-specific parts, where the entire dataset is used to train the group-aspecific parts and only the data from a specific group is used to train the group-specific parts of the DEBM. We performed simulation experiments to benchmark the accuracy of the proposed approaches and to select the optimal approach. Subsequently, the chosen approach was applied to the baseline data of 417 cognitively normal, 235 mild cognitively impaired who convert to AD within 3 years, and 342 AD patients from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset to gain new insights into the effect of APOE carriership on the disease progression timeline of AD. The presented models could aid understanding of the disease, and in selecting homogeneous group of presymptomatic subjects at-risk of developing symptoms for clinical trials.