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The correct method that uses average costs to demonstrate savings in healthcare interventions is cost-effective analysis. This analytical approach focuses on comparing the relative costs and outcomes (effects) of different courses of action, allowing for the assessment of the economic impact of healthcare interventions.

In a cost-effective analysis, average costs are calculated to compare specific interventions and their outcomes, typically measured in terms of quality-adjusted life years (QALYs) or other health-related metrics. The analysis helps decision-makers identify which interventions provide the most benefit for the least cost, leading to informed spending and resource allocation in healthcare.

Cost-benefit analysis, while similar, quantifies both costs and benefits in monetary terms, which may not directly demonstrate savings in the same average cost context. Efficacy studies primarily focus on the effectiveness of a treatment in controlled settings and do not typically involve cost comparisons. Product evaluations assess the functionality and performance of healthcare products rather than their economic savings.