Patients are increasingly interested in becoming involved in the medical decisionmaking process. As a result, healthcare providers and researchers are concerned with finding new ways to integrate patients' preferences, by understanding their commitment to and the stability of those preferences. Preventive medicine, such as colorectal cancer screening, presents an opportunity for personalising the decision-making trajectory based on patients' preferences. In this paper, we propose a framework for a joint decision-making process, capable of integrating patients' changing preferences, as described by a stability analysis of those preferences and design scenarios for implementing the process in clinical practice. In this study, a secondary data analysis, we present scenarios that demonstrate how the stability analysis of an Analytic Network Process (ANP) model supports personalising the process of agreeing on an appropriate colorectal cancer screening option. We illustrate the framework using two patients whose preferences have different stabilities and for whom the healthcare provider has different rankings for the recommended alternatives. The results show the differences in additional medical information the healthcare provider might need to provide as part of the joint decision-making process in order to reach an agreement between the patient and the provider. A stability analysis of the patient's preferences provides the healthcare provider with a mapping of the preferred options. It also shows how the patient's most preferred alternative might change as the patient obtains additional relevant medical information. Knowing how the patient's priorities might change supports a personalisation of the medical decision-making process. We conclude that the healthcare provider can utilise the stability analysis of a patient's preferences to identify possible dialogue paths that would enable reaching a consensus about an appropriate screening option.