Table 1. Summary of Assumptions, Strengths, and Limitations of the Study Methods.

Treatment effect of interest	Method	Key assumption	Strength	Limitation
Effectiveness of percutaneous microaxial LVAD vs no percutaneous microaxial LVAD at time of PCI	Inverse probability of treatment weighting	No confounding by unmeasured variables The potential outcomes under the treatment actually received are equal to observed outcomes Within levels of the covariates, the probability of receiving each treatment is >0 and <1 The model for the probability of receiving treatment is correctly specified	If assumptions hold, a marginal treatment effect in the population meeting the study eligibility criteria is estimated	Unstable if observations have low probability of receiving the treatment they actually received Validity threatened by unmeasured confounders
Effectiveness of percutaneous microaxial LVAD vs no percutaneous microaxial LVAD, in patients whose treatment was influenced by cross-sectional institutional preferences	Instrumental variable analysis	The instrument is associated with treatment (relevance) The instrument is unconfounded (exchangeability or randomization) The instrument’s influence on the outcome is only through the treatment (exclusion restriction). Monotonicity in the relationship between the instrument and treatment Modifying the above assumptions leads to the identification of different treatment effects)	If assumptions hold, estimates average treatment effect in patients whose treatment is influenced by cross-sectional institutional preferences, even in the presence of unmeasured confounding of the treatment outcome association If the model for IV analyses includes covariates, the effect estimated is a weighted average of covariate-conditional effects	Finding a suitable instrument is challenging and not always possible (ie, violations of the first 3 assumptions may occur) When relying on monotonicity assumptions, the estimated treatment effect may have limited clinical relevance and may apply to a small subset of the overall population that is not identifiable at baseline When the model for IV analyses includes covariates additional model specification assumptions are needed
Effectiveness of the percutaneous microaxial LVAD initiation vs no percutaneous microaxial LVAD, in patients whose treatment was influenced by longitudinal changes in institutinoal practice patterns	Instrumented difference-in-differences analysis	The instrument is associated with changes in treatment use The instrument does not affect trends in the outcome except through treatment itself The instrument is unconfounded (with trends in the outcome) and does not modify the treatment effect A generalized version of monotonicity (as in IV analyses) for longitudinal settings The treatment effect is stable over time Modifying the above assumptions leads to the identification of different treatment effects)	Can account for temporal changes in the outcome due to factors beyond the treatment Can account for time-fixed differences between hospitals	Finding a suitable instrument is challenging and not always possible (ie, violations of the first 3 assumptions may occur) When relying on monotonicity assumptions, the estimated treatment effect may have limited clinical relevance The required assumptions are strong and there is limited experience in reasoning about them because the method is relatively novel
Effectiveness of percutaneous microaxial LVAD vs IABP vs no mechanical support within 2 d of PCI and 30-d outcomes	Grace period with analysis using cloning, censoring, and weighting	No unmeasured confounding by time-varying variables Duration of grace period determined by clinical understanding of treatment strategies appropriate for the condition	Eliminates baseline confounding Addresses mortality pretreatment initiation that could potentially lead to immortal time bias when using other analytical approaches Allows the estimation of outcome risk under each treatment strategy, including all events during the grace period	Validity threatened by unmeasured time-varying variables that affect the initiation of different treatments and the outcome The effectiveness of deferred treatment may not be clinically relevant, particularly in clinical settings with rapid changes in indications for treatment initiation

Abbreviations: IABP, intra-aortic balloon pump; IV, instrumental variable; LVAD, left ventricular assist device; PCI, percutaneous coronary intervention.