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Sharp symbolic nonparametric bounds for measures of benefit in observational and imperfect randomized studies with ordinal outcomes

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  • Erin E Gabriel
  • Michael C Sachs
  • Andreas Kryger Jensen

Abstract

The probability of benefit can be a valuable and meaningful measure of treatment effect. Particularly for an ordinal outcome, it can have an intuitive interpretation. Unfortunately, this measure, and variations of it, are not identifiable even in randomized trials with perfect compliance. There is, for this reason, a long literature on nonparametric bounds for unidentifiable measures of benefit. These have primarily focused on perfect randomized trial settings and one or two specific estimands. We expand these bounds to observational settings with unmeasured confounders and imperfect randomized trials for all three estimands considered in the literature: the probability of benefit, the probability of no harm and the relative treatment effect.

Suggested Citation

  • Erin E Gabriel & Michael C Sachs & Andreas Kryger Jensen, 2024. "Sharp symbolic nonparametric bounds for measures of benefit in observational and imperfect randomized studies with ordinal outcomes," Biometrika, Biometrika Trust, vol. 111(4), pages 1429-1436.
    • Handle: RePEc:oup:biomet:v:111:y:2024:i:4:p:1429-1436.
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    File URL: http://hdl.handle.net/10.1093/biomet/asae020
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