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Computing assumption-lean bounds for per-protocol effects
Paul N Zivich1, Jessie K Edwards2,3, Valerie A Lucas2
1Department of Epidemiology, Gillings School of Global Public Health, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA. pzivich@unc.edu.
Background:
A common approach used to estimate per-protocol effects, or the effect of perfect adherence to a defined protocol on a specified outcome, is to artificially censor individuals when they deviate from the protocol. As adherence is not under control of the investigator, selection bias is a threat to the validity of per-protocol analyses.
Methods:
Here, we describe nonparametric bounds for the per-protocol effect. Importantly, these bounds describe the range of all possible per-protocol effects concordant with the observed data under the sole additional assumption-beyond those of a standard intent-to-treat analysis-that adherence was accurately measured. Further, these bounds naturally follow from an intuitive understanding of the "best" and "worst" cases among trial participants. Finally, the per-protocol bounds are straightforward to compute with standard statistical analysis software.
Results:
We describe and illustrate these bounds with two open-source data sets, one in the context of a binary outcome and the other with a survival outcome. These examples are accompanied by open-source code in several different software programs to aid implementation.
Conclusions:
Per-protocol bounds offer a simple and intuitive assessment of the per-protocol effect under relatively weak assumptions and offer insight into the strength of the assumptions like no selection bias.
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