On treating right-censoring events like treatments

TL;DR

The paper addresses how to handle right-censoring events in causal inference without requiring the elimination of all censoring to define estimands. It introduces a unified framework that distinguishes nuisance from non-nuisance right-censoring, formalizes two estimands $\Psi_1^g=E(Y_k^{g,\bar{\mathbf{c}}=0})$ and $\Psi_2^g=E(Y_k^{g})$, and derives identification results under models $\mathcal{M}_1$ and $\mathcal{M}_2$, clarifying when these estimands coincide. It connects the causal framework to classical survival analysis via conditional independent $\Delta_k$ and discusses identity slippages when censoring interacts with outcomes. The work guides practitioners in selecting appropriate estimands and applying g-formula or proxy-based methods, with sensitivity analyses and extensions to broader estimands. Overall, it provides a principled approach to incorporating right-censoring into causal estimands rather than treating it solely as missing data.

Abstract

In causal inference literature, potential outcomes are often indexed by the "elimination of all right-censoring events," leading to the perception that such a restriction is necessary for defining well-posed causal estimands. In this paper, we clarify that this restriction is not required: a well-defined estimand can be formulated without indexing on the elimination of such events. Achieving this requires a more precise classification of right-censoring events than has historically been considered, as the nature of these events has direct implications for identification of the target estimand. We provide a framework that distinguishes different types of right-censoring events from a causal perspective, and demonstrate how this framework relates to censoring definitions and assumptions in classical survival analysis literature. By bridging these perspectives, we provide a clearer understanding of how to handle right-censoring events and provide guidance for identifying causal estimands when right-censored events are present.

Figures (7)

• Figure 1: Directed Acyclic Graph (DAG) depicting the factual data. For simplicity, we define two observation-terminating event $\mathbf{C}_k = (C_{k1},C_{k2})$. Note that we omit other arrows (e.g., $\mathbf L_0$ to $Y_{k-1}$) to reduce clutter, as adding omitted edges from past to future variables does not affect our assumptions.
• Figure 2: Single World Intervention Graph (SWIG) depicting ($g,\overline{\mathbf{c}})$ potential variables (counterfactuals). For simplicity, we define two observation-terminating event $\mathbf{C}_k = (C_{k1},C_{k2})$. Note that we omit other arrows (e.g., $\mathbf L_0$ to $Y_{k-1}$) to reduce clutter, as adding omitted edges from past to future variables does not affect our assumptions.
• Figure 3: Single World Intervention Graph (SWIG) depicting $g$ potential variables (counterfactuals). For simplicity, we define two observation-terminating event $\mathbf{C}_k = (C_{k1},C_{k2})$. Note that we omit other arrows (e.g., $\mathbf L_0$ to $Y_{k-1}$) to reduce clutter, as adding omitted edges from past to future variables does not affect our assumptions.
• Figure 4: Directed Acyclic Graph (DAG) depicting the factual data, with right-censoring state added to Figure \ref{['fig:figure00']}. Bold arrows are used to emphasize deterministic relationships assumed herein.
• Figure 5: Classification of right-censoring events relative to the estimands considered herein.

Theorems & Definitions (8)

• Definition 1: Generalized definition of right-censoring event
• Definition 2: Nuisance and non-nuisance right-censoring events
• Proposition 1
• Definition 3: Model $\mathcal{M}_1$
• Proposition 2
• Definition 4: Model $\mathcal{M}_2$
• Proposition 3
• Remark 1