A connection between survival multistate models and causal inference for external treatment interruptions

Abstract

Recently, treatment interruptions such as a clinical hold in randomized clinical trials have been investigated by using a multistate model approach. The phase III clinical trial START (Stimulating Targeted Antigenic Response To non-small-cell cancer) with primary endpoint overall survival was temporarily placed on hold for enrollment and treatment by the US Food and Drug Administration (FDA). Multistate models provide a flexible framework to account for treatment interruptions induced by a time-dependent external covariate. Extending previous work, we propose a censoring and a filtering approach both aimed at estimating the initial treatment effect on overall survival in the hypothetical situation of no clinical hold. A special focus is on creating a link to causal inference. We show that calculating the matrix of transition probabilities in the multistate model after application of censoring (or filtering) yields the desired causal interpretation. Assumptions in support of the identification of a causal effect by censoring (or filtering) are discussed. Thus, we provide the basis to apply causal censoring (or filtering) in more general settings such as the COVID-19 pandemic. A simulation study demonstrates that both causal censoring and filtering perform favorably compared to a naïve method ignoring the external impact.

Keywords: Aalen-Johansen estimator; back-door criterion; g-computation; structural accelerated failure time model.

Figure 1.

Multistate model with progression of disease (PD) as intermediate state.

Figure 2.

DAG for CH situation at fixed t. Note: The DAG describes causal relations for patients still alive at time t. DAG: directed acyclic graph; CH: clinical hold.

Figure 3.

Multistate model with progression of disease (PD) as intermediate state for the control group.

Figure 4.

Multistate model $(X_t{)}_{t\ge 0}$ with PD and CH as intermediate states for the treatment group. PD: progression of disease; CH: clinical hold.

Figure 5.

Multistate model $(Z_t{)}_{t\ge 0}$ illustrating “censoring by CH.” Note the 2 → 1 rather than 1→ 2 transition. Solid lines represent observed transitions. Note that state 1 is an absorbing state under causal censoring by clinical hold (CH).

Figure 6.

Multistate model ( $X_t{)}_{t\ge 0}$ illustrating “censoring and filtering by treatment interruption.” Solid lines represent observed transitions.

Figure 7.

Comparison of simulation results of naïve, causal censoring and causal filtering approach. Simulation scenario I: $\exp ({\beta }_{02})=0.6$, $\exp ({\beta }_{12})=1.0$, $\exp ({\beta }_{42})=0.6$.

Figure 8.

Comparison of simulation results of naïve, causal censoring and causal filtering approach. Simulation Scenario II: $\exp ({\beta }_{02})=0.5$, $\exp ({\beta }_{12})=1.1$, $\exp ({\beta }_{42})=0.5$.

Figure 9.

Comparison of simulation results of naïve, causal censoring and causal filtering approach. Simulation Scenario IV: $\exp ({\beta }_{02})=0.6$, $\exp ({\beta }_{12})=1.0$, $\exp ({\beta }_{42})=0.9$.

Figure 10.

Comparison of simulation results of naïve, causal censoring and causal filtering approach. Simulation Scenario V.