Index: Sensitivity Analysis and Complex Mechanisms

Sensitivity Analysis and Complex Mechanisms

Routing Summary

This folder covers: (1) sensitivity analysis when unconfoundedness may fail (E-value, copula methods), (2) IV / principal stratification for settings where unconfoundedness is untenable, and (3) time-varying treatments with the g-formula and Bayesian g-computation. Contains 3 notes.

• Need to assess robustness to unmeasured confounders (E-value, Rosenbaum bounds, copula)? → Sensitivity Analysis in Observational Studies
• Need IV, compliance strata, CACE / LATE, Bayesian mixture model for IV? → Instrumental Variables and Principal Stratification
• Need sequential treatments, g-formula, Bayesian g-computation, MSM? → Time-Varying Treatments and G-computation

Concept Map

Concept	Note	Type	Depends On	Key Result
Cornfield inequality	Sensitivity Analysis in Observational Studies	theorem	Potential Outcomes Framework	Hidden confounder must match observed association to explain it away
E-value	Sensitivity Analysis in Observational Studies	definition	—	Model-free; min confounder strength to explain away effect
Copula sensitivity	Sensitivity Analysis in Observational Studies	definition	General Structure	Bayesian prior on copula params = sensitivity params
Compliance types	Instrumental Variables and Principal Stratification	definition	Potential Outcomes Framework	co/at/nt/df strata; $U_i=(W_i(0),W_i(1))$
CACE / LATE	Instrumental Variables and Principal Stratification	definition	Compliance types	${\tau }_{\text{co}}=\text{ITT}/\text{compliance rate}$
Bayesian IV	Instrumental Variables and Principal Stratification	concept	General Structure	Data augmentation over latent compliance stratum
Principal stratification	Instrumental Variables and Principal Stratification	concept	Compliance types	Generalization: any post-treatment variable defines strata
Sequential ignorability	Time-Varying Treatments and G-computation	definition	Potential Outcomes Framework	$Z_t\perp Y(\bar{z})\mid {\bar{Z}}_{t-1},{\bar{L}}_{t-1}$
G-formula	Time-Varying Treatments and G-computation	theorem	Sequential ignorability	Identification via iterating outcome regression across time
Bayesian g-computation	Time-Varying Treatments and G-computation	concept	General Structure	Fit Bayesian model per g-formula component; combine draws

Notes

• Sensitivity Analysis in Observational Studies — CONTAINS: Cornfield inequality (theorem), Rosenbaum & Rubin logistic model, E-value (definition), copula-based sensitivity analysis (definition), Rosenbaum’s Γ, comparison table
• Instrumental Variables and Principal Stratification — CONTAINS: compliance type definitions, IV validity assumptions, CACE/LATE definition, Bayesian IV posterior factorization, Example 7.1 (Gibbs sampler for one-sided non-compliance), principal stratification generalization
• Time-Varying Treatments and G-computation — CONTAINS: sequential ignorability (Assumption 7.2), g-formula (theorem), Bayesian g-computation algorithm, Example 7.3 (two-period Bayesian g-computation), g-null paradox, dynamic treatment regimes overview

Sources

• Li et al. - 2022 - Bayesian causal inference a critical review.pdf — §6–7, pp. 12–18

See Also

• Bayesian Inference — core Bayesian CI structure that these methods extend
• Copula Estimation — vault note on copulas used in sensitivity analysis