Statistical methods are given for producing a cost-effectiveness frontier for an arbitrary number of programs. In the deterministic case, the net health benefit (NHB) decision rule is optimal; the rule funds the program with the largest positive NHB at each l, the amount a decision-maker is willing to pay (WTP) for an additional unit of effectiveness. For bivariate normally distributed cost and effectiveness variables and a specified l, a statistical procedure, based on the method of constrained multiple comparisons with the best (CMCB), determines the program with the largest NHB. A one-tailed t test is used to determine if the NHB is positive. To obtain a statistical frontier for any value of l, the region in which each program has the largest NHB is delineated by pivoting a CMCB confidence interval. A one-sided version of Fieller's theorem is used to determine the region where the NHB of each program is positive. At each l, the pointwise error rate is bounded by a prespecified a. Upper bounds on the familywise error rate, the probability of an error at any value of l, are given.
A Mathematica program lists and plots the deterministic frontier as l, the WTP parameter varies. The deterministic frontier is also plotted in the effectiveness – cost plane. Results of the step determining the region where each program is best are displayed in a table and the statistical frontier is listed and plotted. Bounds on the familywise error rates are given in a table. To download a zipped file containing the instructions and 2 Mathematica files, click below:
Mathematica (download file)
Laska E, Meisner M, Siegel C, Wanderling, J. Statistical Cost-Effectiveness Analysis of Two Treatments Based on Net Health Benefits. Statistics in Medicine, 2001;20:1279-1302.
Laska E, Meisner M, Siegel C, Wanderling, J (2001). Statistical Determination of a Cost-Effectiveness Frontier Based on Net Health Benefits. Health Economics, 11(3):249-264.
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Updated: 09/23/02
