In intensive care, disputes sometimes arise when patients or surrogates strongly desire treatment, yet health professionals regard it as potentially inappropriate. While professional guidelines confirm that physicians are not always obliged to provide requested treatment, determining when treatment would be inappropriate is extremely challenging. One potential reason for refusing to provide a desired and potentially beneficial treatment is because (within the setting of limited resources) this would harm other patients. Elsewhere in public health systems, cost effectiveness analysis is sometimes used (...) to decide between different priorities for funding. In this paper, we explore whether cost-effectiveness could be used to determine the appropriateness of providing intensive care. We explore a set of treatment thresholds: the probability threshold (a minimum probability of survival for providing treatment), the cost threshold (a maximum cost of treatment), the duration threshold (the maximum duration of intensive care), and the quality threshold (a minimum quality of life). One common objection to cost-effectiveness analysis is that it might lead to rationing of life-saving treatment. The analysis in this paper might be used to inform debate about the implications of applying cost-effectiveness thresholds to clinical decisions around potentially inappropriate treatment. (shrink)