A sensitivity analysis approach to principal stratification with a continuous longitudinal intermediate outcome: Applications to a cohort stepped wedge trial

TL;DR

This paper extends principal stratification to settings with a continuous longitudinal intermediate outcome within closed-cohort SW-CRTs, addressing identification under untestable assumptions via a sensitivity-analysis framework. It adopts a Gaussian copula to model the joint distribution of potential mediators and a marginal structural model to relate outcomes to mediators, with sensitivity parameters that are calibrated from observed SW-CRT data and explored through Bayesian inference. The authors operationalize the approach with a Bayesian framework, using duration-specific mediator and outcome models, and integrate calibration uncertainty into PCE estimates for short- and long-term effects. Applied to a crowdsourcing HIV intervention study among MSM in China, the method yields generally positive PCEs across dissociative and associative strata with substantial uncertainty, and robustness to certain sensitivity parameters, illustrating the practical utility of PS with continuous intermediates in SW-CRTs.

Abstract

Causal inference in the presence of intermediate variables is a challenging problem in many applications. Principal stratification (PS) provides a framework to estimate principal causal effects (PCE) in such settings. However, existing PS methods primarily focus on settings with binary intermediate variables. We propose a novel approach to estimate PCE with continuous intermediate variables in the context of stepped wedge cluster randomized trials (SW-CRTs). Our method leverages the time-varying treatment assignment in SW-CRTs to calibrate sensitivity parameters and identify the PCE under realistic assumptions. We demonstrate the application of our approach using data from a cohort SW-CRT evaluating the effect of a crowdsourcing intervention on HIV testing uptake among men who have sex with men in China, with social norms as a continuous intermediate variable. The proposed methodology expands the scope of PS to accommodate continuous variables and provides a practical tool for causal inference in SW-CRTs.

Figures (4)

• Figure 1: Posterior summaries (mean and 95% credible intervals) of $\text{PCE}_{\text{D}}$ (Dissociative), $\text{PCE}_{\text{A}-}$ (Associative Negative), and $\text{PCE}_{\text{A}+}$ (Associative Positive) across time periods with $\delta=0.5$. Results are conditional on Province (Rows: GD, SD) and sorted by Duration (Columns: stPCE with $d=1$, ltPCE with $d=2$, ltPCE with $d=3$). This primary analysis uses the 'Calibrated' scenario for $\rho_{\bm c}$ and the baseline scaling factor $k=1.0$ for $\lambda_{\bm c}(\cdot)$.
• Figure 2: Sensitivity analysis of stPCE ($d=1$) to the correlation coefficient scenario for $\rho_{\bm c}$ with $\delta=0.5$ and $k=1.0$. Results are sorted by Stratum (Columns) and Province (Rows). Colored lines represent the different $\rho_{\bm c}$ scenarios.
• Figure 3: Scaling Factor Sensitivity Analysis of stPCE ($d=1$) to the scaling factor $k$ for $\lambda_{\bm c}(\cdot)$, with $\delta=0.5$ and calibrated $\rho_{\bm c}$. Results are sorted by Stratum (Columns) and Province (Rows). Colored lines represent the different scaling factors $k$.
• Figure 4: Sensitivity analysis of stPCE ($d=1$) to the indifference threshold $\delta$. Results are sorted by Stratum (Columns) and Province (Rows). Colored lines represent different $\delta$ values (0.5, 1.0, 1.5). The analysis uses the primary settings for $\rho_{\bm c}$ (calibrated) and $k=1.0$ for $\lambda_{\bm c}(\cdot)$.

Theorems & Definitions (1)

• Theorem 1: Identification