Clarifying identification and estimation of treatment effects in the Sequential Parallel Comparison Design

TL;DR

This paper challenges the conventional interpretation of Sequential Parallel Comparison Design (SPCD) estimators by embedding SPCD in a structural causal model with a latent placebo responder status. It shows that the stage 1 estimator targets the overall average treatment effect $\Delta_{\mathrm{all}}$, while the stage 2 estimator imperfectly targets $\Delta_{NR}$ due to misclassification of placebo responders, and the common weighted estimator combines these in a way that generally does not correspond to a clinically meaningful estimand. Through theoretical derivations and simulations, it demonstrates that placebo misclassification drives substantial bias in SPCD estimators unless unrealistic, unverifiable assumptions hold. The ADAPT-A example illustrates the mismatch between latent-baseline modeling and the actual SPCD implementation, underscoring the practical risk of misclassification. Overall, the authors advocate rethinking placebo-adjustment in SPCD and suggest modeling placebo response as a continuous latent variable or using alternative mixture-based approaches rather than relying on misclassified stage-2 re-randomization.

Abstract

Sequential parallel comparison design (SPCD) clinical trials aim to adjust active treatment effect estimates for placebo response to minimize the impact of placebo responders on the estimates. This is potentially accomplished using a two stage design by measuring treatment effects among all participants during the first stage, then classifying some placebo arm participants as placebo non-responders who will be re-randomized in the second stage. In this paper, we use causal inference tools to clarify under what assumptions treatment effects can be identified in SPCD trials and what effects the conventional estimators target at each stage of the SPCD trial. We further illustrate the highly influential impact of placebo response misclassification on the second stage estimate. We conclude that the conventional SPCD estimators do not target meaningful treatment effects.

Figures (4)

• Figure 1: A diagram of the SPCD design. At stage 1, $N$ participants are randomized to placebo $(A_1 = 0)$ or active treatment $(A_1=1).$ All participants are either latent true placebo responders $(L=1)$ or latent true placebo non-responders $(L=0),$ so each group is a mixture of placebo responders and non-responders. The placebo-treated participants are classified as placebo responders $(R=1)$ if their outcome is beyond a specified threshold and otherwise as placebo non-responders $(R=0).$ At stage 2, the placebo non-responders are randomized again and assigned to placebo $(A_2=0)$ or active treatment $(A_2=1).$ Classified placebo responders and those on active treatment from stage 1 continue on the originally assigned treatment without re-randomization.
• Figure 2: This causal DAG depicts the structural causal model underlying the SPCD with the addition of our latent placebo responder status $L.$
• Figure 3: The average negative predictive values $P(L = 0 | R = 0)$ for the threshold classifier used in the simulation study.
• Figure 4: Simulation under the null; $\Delta_{\mathrm{all}} = 0.$ Varying the average placebo effect (APE) $\Delta_{\mathrm{placebo}}$ and residual standard deviation $\sigma_\sigma$. The residual standard deviation is plotted along the x-axis. The y-axis in (a) is the estimated bias in estimating $\Delta_{\mathrm{all}}$ for each estimator. The y-axis in (b) is the estimated bias in estimating $\Delta_{NR}$ for each estimator. The lines and points are color-coded by the pre-set $\Delta_{\mathrm{placebo}}$.

Theorems & Definitions (10)

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