B2019
Title: Single time-series conditional causal effect
Authors: Ivana Malenica - Harvard University (United States) [presenting]
Mark van der Laan - Berkeley (United States)
Abstract: Causal estimands are defined in a single time-series setup with observational data. We consider a sequential setting, where at each time $t$, a data record $O(t)$ is observed, which consists of treatments $A(t)$, outcomes $Y(t)$, and time-varying covariates $W(t)$. We assume that the conditional distribution of $O(t)$ can be described by a function $Co(t)$ only depending on a fixed dimensional summary of the past. Intensive longitudinal data is collected on a single individual, where data recorded at $t$ carries information about a causal effect of treatment on the proximal outcome defined by $Co(t)$. Our approach allows the estimation of a broad class of estimands, including a class of summaries of the conditional causal parameters defined by the current context over time. The proposed target parameters are pathwise differentiable with an efficient influence function that is doubly robust. We propose a targeted maximum likelihood estimator (TMLE) of these causal parameters, and present results on the asymptotic consistency and normality of the TMLE. The limit distribution of the proposed estimator is characterized under a sequential Donsker condition, and expressed in terms of a notion of bracketing entropy adapted to martingale settings. Our methodology is inspired by financial and health care applications (e.g., chronic disease monitoring), where data is collected frequently over time, and holds immense promise for improving prevention and treatment allocation.
