ArticleTrials2026
Computing assumption-lean bounds for per-protocol effects.
Article in Trials, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
What it found
Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.
The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.
Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.
Who cites it
0 citing papers in PubMed.
No citing paper in PubMed yet.
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
6 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
backgroundA 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.
methodsHere, 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.
resultsWe 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.
conclusionsPer-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.
Indexed as
Identifiers
42919425What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.