Title: Treatment-Response Models for Counterfactual Reasoning with Continuous-time, Continuous-valued Interventions,
Abstract: Treatment effects can be estimated from observational data as the difference
in potential outcomes. In this paper, we address the challenge of estimating
the potential outcome when treatment-dose levels can vary continuously over
time. Further, the outcome variable may not be measured at a regular frequency.
Our proposed solution represents the treatment response curves using linear
time-invariant dynamical systems---this provides a flexible means for modeling
response over time to highly variable dose curves. Moreover, for multivariate
data, the proposed method: uncovers shared structure in treatment response and
the baseline across multiple markers; and, flexibly models challenging
correlation structure both across and within signals over time. For this, we
build upon the framework of multiple-output Gaussian Processes. On simulated
and a challenging clinical dataset, we show significant gains in accuracy over
state-of-the-art models.