Construction of a continuous stopping boundary from an alpha spending function.
Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, alpha. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.
Betensky
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Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA. betensky@sdac.harvard.edu
D017088:AIDS-Related Opportunistic Infections / Q000517:prevention & control; D000319:Adrenergic beta-Antagonists / Q000627:therapeutic use; D001699:Biometry / Q000379:methods*; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D004311:Double-Blind Method; D006801:Humans; D009203:Myocardial Infarction / Q000188:drug therapy / Q000401:mortality; D011020:Pneumonia, Pneumocystis / Q000517:prevention & control; D011433:Propranolol / Q000627:therapeutic use; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data
D000319:Adrenergic beta-Antagonists; D011433:Propranolol