The familywise error rate of a simultaneous confidence band for the incremental net health benefit

Interest in the use of net health benefit in cost‐effectiveness analysis derives from its optimality property for decision‐making. A description of the results of an economic evaluation of health care interventions is incomplete if it does not include point and interval estimates of this outcome measure. A simultaneous confidence band for the incremental net health benefit, INHB( λ ), for all λ may be obtained by forming a confidence interval based on student's t statistic, and letting the willingness‐to‐pay value, λ , run over all values. The familywise error rate (FWER) of the simultaneous confidence band is the probability that the confidence interval does not cover the true INHB( λ ) for some value of λ . We show that the FWER equals P ( T 2 > t 2 ), where T 2 follows Hotelling's central distribution and that the simultaneous confidence band does not cover the true INHB( λ ) if and only if a T 2 based confidence ellipsoid does not cover the true mean c – e vector. Copyright © 2002 John Wiley & Sons, Ltd.