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(lambda), for all lambda may be obtained by forming a confidence interval based on student's t statistic, and letting the willingness-to-pay value, lambda, 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(lambda) for some value of lambda. 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(lambda) if and only if a T(2) based confidence ellipsoid does not cover the true mean c-e vector.