Robust Estimation of Data-Dependent Causal Effects based on Observing a Single Time-Series

TL;DR

This paper develops a robust statistical framework for estimating causal effects from a single time-series, enabling valid inference in sequential experiments without extra assumptions, using double robust methods and TMLE.

Contribution

It introduces a general class of estimators for causal effects in single time-series data, with a TMLE approach and asymptotic guarantees, extending causal inference to sequentially randomized experiments.

Findings

Proposes a double robust estimator for causal effects in single time-series.

Establishes asymptotic normality and consistency of the TMLE.

Extends framework to adaptive treatment rules within a single unit.

Abstract

Consider the case that one observes a single time-series, where at each time t one observes a data record O(t) involving treatment nodes A(t), possible covariates L(t) and an outcome node Y(t). The data record at time t carries information for an (potentially causal) effect of the treatment A(t) on the outcome Y(t), in the context defined by a fixed dimensional summary measure Co(t). We are concerned with defining causal effects that can be consistently estimated, with valid inference, for sequentially randomized experiments without further assumptions. More generally, we consider the case when the (possibly causal) effects can be estimated in a double robust manner, analogue to double robust estimation of effects in the i.i.d. causal inference literature. We propose a general class of averages of conditional (context-specific) causal parameters that can be estimated in a double robust manner, therefore fully utilizing the sequential randomization. We propose a targeted maximum likelihood estimator (TMLE) of these causal parameters, and present a general theorem establishing the asymptotic consistency and normality of the TMLE. We extend our general framework to a number of typically studied causal target parameters, including a sequentially adaptive design within a single unit that learns the optimal treatment rule for the unit over time. Our work opens up robust statistical inference for causal questions based on observing a single time-series on a particular unit.