[Paper Review] Sequential causal inference in a single world of connected units

Aurélien Bibaut, Maya L. Petersen+3 more|arXiv (Cornell University)|Jan 18, 2021

Statistical Methods in Clinical Trials29 references4 citations

TL;DR

This paper develops a framework for sequential causal inference in networks of connected, dependent units over time, enabling adaptive trial design and inference under temporal and network dependence. It introduces a novel estimation method with uniform-in-time convergence and almost-sure equicontinuity, allowing optimal treatment allocation and adaptive stopping rules that achieve asymptotically efficient inference despite a single, dependent observation stream.

ABSTRACT

We consider adaptive designs for a trial involving N individuals that we follow along T time steps. We allow for the variables of one individual to depend on its past and on the past of other individuals. Our goal is to learn a mean outcome, averaged across the N individuals, that we would observe, if we started from some given initial state, and we carried out a given sequence of counterfactual interventions for $τ$ time steps. We show how to identify a statistical parameter that equals this mean counterfactual outcome, and how to perform inference for this parameter, while adaptively learning an oracle design defined as a parameter of the true data generating distribution. Oracle designs of interest include the design that maximizes the efficiency for a statistical parameter of interest, or designs that mix the optimal treatment rule with a certain exploration distribution. We also show how to design adaptive stopping rules for sequential hypothesis testing. This setting presents unique technical challenges. Unlike in usual statistical settings where the data consists of several independent observations, here, due to network and temporal dependence, the data reduces to one single observation with dependent components. In particular, this precludes the use of sample splitting techniques. We therefore had to develop a new equicontinuity result and guarantees for estimators fitted on dependent data. We were motivated to work on this problem by the following two questions. (1) In the context of a sequential adaptive trial with K treatment arms, how to design a procedure to identify in as few rounds as possible the treatment arm with best final outcome? (2) In the context of sequential randomized disease testing at the scale of a city, how to estimate and infer the value of an optimal testing and isolation strategy?

Motivation & Objective

• To enable causal inference in sequential trials with temporal and network dependence among N units.
• To design adaptive treatment rules that learn the optimal intervention with minimal regret or exploration time.
• To construct adaptive stopping rules for sequential hypothesis testing under dependent data.
• To achieve asymptotically efficient inference despite the absence of independent samples due to dependence.
• To develop a statistical model that supports uniform-in-time convergence and almost-sure equicontinuity for estimators on dependent data.

Proposed method

• Uses a single-world intervention framework to define counterfactual outcomes under sequences of interventions.
• Introduces a nonparametric model for nuisance parameters that supports uniform-in-time convergence and equicontinuity.
• Employs targeted maximum likelihood estimation (TMLE) with uniform-in-time concentration bounds to ensure valid inference.
• Derives asymptotic variance expressions for estimators under different designs to guide adaptive design selection.
• Uses plug-in estimation of asymptotic variances to select the most efficient design at each time step.
• Applies concentration inequalities instead of limit theorems to control type I error in sequential testing under dependence.

Experimental results

Research questions

• RQ1 How can we design adaptive trials to identify the optimal treatment arm with minimal rounds in a networked, temporally dependent system?
• RQ2 How can we estimate and infer the value of an optimal testing and isolation strategy in a city-scale sequential disease testing trial?
• RQ3 What statistical guarantees can be provided for estimators when data consists of a single, dependent observation stream due to temporal and network dependence?
• RQ4 How can we construct adaptive stopping rules for sequential hypothesis testing under such dependence?
• RQ5 Can we achieve asymptotically efficient inference without sample splitting, given the lack of independent observations?

Key findings

• The proposed method achieves uniform-in-time convergence of nuisance estimators and almost-sure equicontinuity, enabling valid inference under temporal and network dependence.
• The adaptive design, based on minimizing estimated asymptotic variance, converges almost surely to the optimal design, ensuring the TMLE achieves the minimal possible asymptotic variance.
• The framework supports adaptive stopping rules for sequential testing by leveraging concentration inequalities that control type I error under dependence.
• The effective sample size is proportional to T×N, even though only one observation stream exists, due to the homogeneity assumption across individuals and time.
• The Neyman allocation design is conjectured to be optimal for two-arm trials at τ=1, with higher efficiency than uniform designs.
• The method avoids sample splitting by relying on concentration bounds and uniform convergence, which is critical in settings with dependent data.