A positivity threshold is often applied to markers or predicted risks to guide disease management. These rules are often decided exclusively by clinical experts despite being sensitive to the preferences of patients and general public as ultimate stakeholders. We propose an analytical framework for quantifying the net benefit of an evidence-based positivity threshold based on combining preference-sensitive (e.g., how individuals weight benefits and harms of treatment) and preference-agnostic (e.g., the magnitude of benefit and the risk of harm) parameters. We propose parsimonious choice experiments to elicit preference-sensitive parameters from stakeholders, and evidence synthesis to quantify the value of preference-agnostic parameters. We apply this framework to maintenance azithromycin therapy for chronic obstructive pulmonary disease (COPD) using a discrete choice experiment (DCE) to estimate preference weights for attribute level associated with treatment. We identify the positivity threshold on 12-month moderate or severe exacerbation risk that would maximize the net benefit of treatment in terms of severe exacerbations avoided. In the case study, the prevention of moderate and severe exacerbations (benefits) and the risk of hearing loss and gastrointestinal symptoms (harms) emerged as important attributes. 477 respondents completed the DCE survey. Relative to each percent risk of severe exacerbation, preference weights for each percent risk of moderate exacerbation, hearing loss, and gastrointestinal symptoms were 0.395 (95%CI 0.338-0.456), 1.180 (95%CI 1.071-1.201) and 0.253 (95%CI 0.207-0.299), respectively. The optimal threshold that maximized net benefit was to treat patients with a 12-month risk of moderate or severe exacerbations ≥12%. The proposed methodology can be applied to many contexts where the objective is to devise positivity thresholds that need to incorporate stakeholder preferences. Applying this framework to COPD pharmacotherapy resulted in a stakeholder-informed treatment threshold that was substantially lower than the implicit thresholds in contemporary guidelines.