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Stat Med. 2020 Feb 10;39(3):340-351. doi: 10.1002/sim.8405. Epub 2019 Nov 25.

Exact sequential analysis for multiple weighted binomial end points.

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Department of Statistics, Federal University of Ouro Preto, Brazil.
Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Harvard Medical School and Brigham and Women's Hospital, Boston, Massachusetts.


Sequential analysis is used in clinical trials and postmarket drug safety surveillance to prospectively monitor efficacy and safety to quickly detect benefits and problems, while taking the multiple testing of repeated analyses into account. When there are multiple outcomes, each one may be given a weight corresponding to its severity. This paper introduces an exact sequential analysis procedure for multiple weighted binomial end points; the analysis incorporates a drug's combined benefit and safety profile. It works with a variety of alpha spending functions for continuous, group, or mixed group-continuous sequential analysis. The binomial probabilities may vary over time and do not need to be known a priori. The new method was implemented in the free R Sequential package for both one- and two-tailed sequential analysis. An example is given examining myocardial infarction and major bleeding events in patients who initiated non-steroidal antiinflammatory drugs.


Type I error spending function; sequential testing; variable matching ratio


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