Partial identification of principal causal effects under violations of principal ignorability

TL;DR

This paper analyzes partial identification of principal causal effects under violations of principal ignorability in both binary and continuous intermediate settings. It shows that even with simple parametric models, point identification of key association parameters (notably the correlation $ ho$ between $(S(0),S(1))$) is generally infeasible unless PI is violated and the outcome model is known; otherwise, partial identification regions remain wide. The authors derive explicit partial identification regions, discuss conditions under which these regions shrink, and propose weaker alternative assumptions (Same Sign, Dominant Observed Effect) to sharpen inference without full identifiability. They extend the analysis to semiparametric and Bayesian nonparametric frameworks and illustrate the implications through simulations and an ACTG trial dataset, highlighting practical gains in inference when the proposed weaker assumptions are employed. Overall, the work clarifies the identifiability landscape for principal causal effects under violations of PI and provides actionable modeling strategies for informative inference under less restrictive assumptions.

Abstract

Principal stratification is a general framework for studying causal mechanisms involving post-treatment variables. When estimating principal causal effects, the principal ignorability assumption is commonly invoked, which we study in detail in this manuscript. Our first key contribution is studying a commonly used strategy of using parametric models to jointly model the outcome and principal strata without requiring the principal ignorability assumption. We show that even if the joint distribution of principal strata is known, this strategy necessarily leads to only partial identification of causal effects, even under very simple and correctly specified outcome models. While principal ignorability leads to point identification in this setting, we discuss alternative, weaker assumptions and show how they can lead to informative partial identification regions. An additional contribution is that we provide theoretical support to strategies used in the literature for identifying association parameters that govern the joint distribution of principal strata. We prove that this is possible, but only if the principal ignorability assumption is violated. Additionally, due to partial identifiability of causal effects even when these association parameters are known, we show that these association parameters are only identifiable under strong parametric constraints. Lastly, we extend these results to more flexible semiparametric and nonparametric Bayesian models.

Figures (6)

• Figure 1: The posterior distributions of $\rho$ corresponding to $n=$300, 600, 1200 under three different amounts of constraints on the model parameters.
• Figure 2: The first row shows PCEs and corresponding 95% credible intervals for the principal strata defined by $S(0)=S(1) = s$ with varying $s$. The second row corresponds to the principal strata with $S(0)=340$ and increasing $S(1)$. Note that $S(0)$ and $S(1)$ are scaled by $10^2$ in the plot. From left to right, the columns correspond to different assumptions: no constraints, dominant effect, and same sign, respectively. The dashed line in the CI plots implies that the CI is truncated, and the arrow indicates which side is truncated.
• Figure 3: Trace plots of $\beta_{01}$ with and without the positive sign constraint.
• Figure 4: Trace plots of $\beta_{10}$ with and without the positive sign constraint.
• Figure 5: Trace plots of $p_{11}$ with and without the positive sign constraint.

Theorems & Definitions (16)

• Theorem 1
• Theorem 2: Asymptotic approximation of posterior variance
• Proposition 1
• Proposition 2
• Proposition 3
• Definition 1
• Theorem 3
• proof
• proof
• proof