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Table 2 Description of analytic assumptions

From: Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening

Conditionsa Description of condition Empirically verifiable in a randomized trial? When the condition may be reasonable
Relevance (instrumental condition 1)b Randomization indicator is associated with treatment Yes Expected to hold in randomized trials, and is empirically verifiable
Exclusion restriction (instrumental condition 2)b Randomization indicator has no effect on the outcome except through treatment No Expected to hold in double-blinded placebo-controlled trials when double-blinding is successfully maintained and there is no placebo effect; may be approximately reasonable in other settings
Exchangeability (instrumental condition 3)b The effect of the randomization indicator on the outcome is not confounded No Expected to hold by design if no loss to follow-up or other forms of selection bias occur
Known feasible compliance type distribution (e.g., no “defiers”) Specify the proportion of patients that are “compliers,” “always-takers,” “never-takers,” or “defiers” No Compliance type distribution is identified in trials where non-adherence only occurs in one arm (e.g., when treatment is not available to the placebo arm); assuming zero or a minimal number of “defiers” may be reasonable in other settings
Limits on the unobserved compliance type counterfactual risksc Specify imposed limits on what could happen to the “never-takers” had they been treated and the “always-takers” had they not been treated No Subject-matter dependent; imposed limits may be more justifiable for rare outcomes
Additive effect homogeneity No additive effect modification by randomization arm among the treated and untreated No Subject-matter dependent and generally not expected to hold by design; may become more plausible in analyses conditional on measured patient characteristics
Multiplicative effect homogeneity No multiplicative effect modification by randomization arm among the treated and untreated No Subject-matter dependent and generally not expected to hold by design; may become more plausible in analyses conditional on measured patient characteristics
  1. aBounds for the per-protocol effect presented in the current study rely on (1) no assumptions (data only); (2) the instrumental conditions; (3) the instrumental conditions, a feasible known distribution of compliance types, and imposed limits on unobserved compliance type counterfactual risks; (4) the instrumental conditions and additive effect homogeneity; and (5) the instrumental conditions and multiplicative effect homogeneity
  2. bRelevance, exclusion restriction, and exchangeability are jointly referred to as the instrumental conditions
  3. cIn the NORCCAP trial, there are no “always-takers” by design and, therefore, we only discuss this assumption type in the context of the “never-takers”