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 Alzheimers Disease Neuroimaging Initiative (ADNI) dataset to gain new insights into the effect of APOE carriership on the disease progression timeline of AD. In the ε4 carrier group, the model predicted with high confidence that CSF Amyloidβ42 and the cognitive score of Alzheimer's Disease Assessment Scale (ADAS) are early biomarkers. Hippocampus was the earliest volumetric biomarker to become abnormal, closely followed by the CSF Phosphorylated Tau181 (PTAU) biomarker. In the homozygous ε3 carrier group, the model predicted a similar ordering among CSF biomarkers. However, the volume of the fusiform gyrus was identified as one of the earliest volumetric biomarker. While the findings in the ε4 carrier and the homozygous ε3 carrier groups fit the current understanding of progression of AD, the finding in the ε2 carrier group did not. The model predicted, with relatively low confidence, CSF Neurogranin as one of the earliest biomarkers along with cognitive score of Mini-Mental State Examination (MMSE). Amyloid β42 was found to become abnormal after PTAU. 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.