Table 2.
Description of analytic assumptions
| 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 |
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
bRelevance, exclusion restriction, and exchangeability are jointly referred to as the instrumental conditions
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”