Recently, there has been much interest in using the cost-effectiveness acceptability curve (CEAC) to measure the statistical evidence of cost-effectiveness. The CEAC has two well established but fundamentally different interpretations: one frequentist and one Bayesian. As an alternative, we suggest characterizing the statistical evidence about cost-effectiveness using the likelihood function (the key element of both approaches). Its interpretation is neither dependent on the sample space nor on the prior distribution. Moreover, the probability of observing misleading evidence is low and controllable, so this approach is justifiable in the traditional sense of frequentist long-run behaviour. We propose a new graphic for displaying the evidence about cost-effectiveness and explore the strengths of likelihood methods using data from an economic evaluation of a Program in Assertive Community Treatment (PACT).