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Optimal alpha spending for sequential analysis with binomial data

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  • Ivair R. Silva
  • Martin Kulldorff
  • W. Katherine Yih

Abstract

For sequential analysis hypothesis testing, various alpha spending functions have been proposed. Given a prespecified overall alpha level and power, we derive the optimal alpha spending function that minimizes the expected time to signal for continuous as well as group sequential analysis. If there is also a restriction on the maximum sample size or on the expected sample size, we do the same. Alternatively, for fixed overall alpha, power and expected time to signal, we derive the optimal alpha spending function that minimizes the expected sample size. The method constructs alpha spending functions that are uniformly better than any other method, such as the classical Wald, Pocock or O’Brien–Fleming methods. The results are based on exact calculations using linear programming. All numerical examples were run by using the R Sequential package.

Suggested Citation

  • Ivair R. Silva & Martin Kulldorff & W. Katherine Yih, 2020. "Optimal alpha spending for sequential analysis with binomial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 1141-1164, September.
    • Handle: RePEc:bla:jorssb:v:82:y:2020:i:4:p:1141-1164
    DOI: 10.1111/rssb.12379
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    References listed on IDEAS

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    1. I. R. Silva & M. Kulldorff, 2015. "Continuous versus group sequential analysis for post‐market drug and vaccine safety surveillance," Biometrics, The International Biometric Society, vol. 71(3), pages 851-858, September.
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