Causal Survival Analysis in Platform Trials with Non-Concurrent Controls

TL;DR

This work develops an estimand-first causal survival framework targeting the treatment-specific counterfactual survival curve in the concurrent population and the corresponding functionals including the concurrent restricted mean survival time (RMST).

Abstract

Platform trials allow treatment arms to enter and exit over time while maintaining a shared control arm, yielding concurrent and non-concurrent controls (NCC). Pooling NCC is often motivated as a strategy to improve statistical efficiency, but it is unclear which estimand is targeted, what assumptions justify identification and estimation, and when precision gains are achievable; these questions are further complicated by time-to-event/survival data. Motivated by the Adaptive COVID-19 Treatment Trial (ACTT) platform trial with time to recovery as the primary endpoint, we develop an estimand-first causal survival framework targeting the treatment-specific counterfactual survival curve in the concurrent population and the corresponding functionals including the concurrent restricted mean survival time (RMST). We give nonparametric identification results and formalize conditions that justify pooling using NCC. We study covariate-adjusted outcome-regression (OR) and doubly robust (DR) estimators for the concurrent RMST, comparing concurrent-only versions to pooled-control versions. Pooling improves precision for OR estimators only when the pooling assumption holds and parametric hazard models are correctly specified; otherwise, pooling can induce bias. Moreover, in certain settings, pooling NCC yields no efficiency gain for the DR estimator. Overall, the most robust route to improve precision is to target concurrent causal survival estimands and use a covariate-adjusted DR estimation that uses only concurrent controls. An ACTT application corroborates these results.

Figures (10)

• Figure 1: Bias squared, mean squared error, variance and coverage of the 95% confidence interval of the estimators listed in Table \ref{['methods']} under correct model specification. The DR estimators have substantial overlap in variance and mean squared error.
• Figure 2: Ratio of the estimated standard errors DR-oc/DR-ac and OR-oc/OR-ac across model misspecifications considering $V_{\tilde{a}}$ as a deterministic function of E (top row) and $V_{\tilde{a}}$ as a stochastic function of E (bottom row). A ratio greater than 1 indicates a gain in efficiency.
• Figure 3: Estimated proportion of patients recovered in the combined treatment group, Remdesivir plus Baricitinib compared to the control group Remdesivir alone stratified by disease severity measured at baseline. The estimates were computed using an application of the delta method and DR_oc.
• Figure 4: Bias squared, mean squared error, variance and coverage of the 95% confidence interval of the estimators listed in Table \ref{['methods']} under incorrect model specification. The DR estimators have substantial overlap in variance.
• Figure 5: Bias squared, mean squared error, variance and coverage of the 95% confidence interval of the estimators listed in Table \ref{['methods']} under correct model specification for a discrete time horizon of $\tau=4$. The DR estimators have substantial overlap in variance and mean squared error.

Theorems & Definitions (7)

• Definition 4.1: Concurrent treatment-specific counterfactual survival curve
• Proposition 1: Product representation
• Theorem 1: Nonparametric identification of $\theta(a,t)$
• Remark 1: Pooling controls for the hazard
• Definition 4.2: Difference in restricted mean survival time ($\mathsf{dRMST}$)
• Theorem 2: Efficient influence function of $\mathsf{dRMST}$
• Remark 2: Pooling concurrent and nonconcurrent controls for the censoring mechanism