Abstract: Alzheimer's disease (AD) has a poorly understood aetiology. Patients often have different rates and patterns of brain atrophy, and present at different stages along the natural history of their condition. This means that establishing the relationships between disease-related variables, and subsequently linking the clinical and radiological phenotypes of AD is difficult. Investigating this link is important because it could ultimately allow for a better understanding of the disease process, and this could enable tasks such as treatment effect estimates, disease progression modelling, and better precision medicine for AD patients. We extend a class of deep structural causal models (DSCMs) to the clinical and radiological phenotype of AD, and propose an aetiological model of relevant patient demographics, imaging and clinical biomarkers, and cognitive assessment/educational scores based on specific current hypotheses in the medical literature. The trained DSCM produces biologically plausible counterfactuals relating to the specified disease covariates, and reproduces ground-truth longitudinal changes in magnetic resonance images of AD. Such a model could enable the assessment of the effects of intervening on variables outside a randomized controlled trial setting. In addition, by being explicit about how causal relationships are encoded, the framework provides a principled approach to define and assess hypotheses of the aetiology of AD. Code to replicate the experiment can be found at: $\href{https://github.com/aay993/counterfactual_AD}{Counterfactual AD.}$