Estimating heterogeneous treatment effects in nonstationary time series with state-space models
Abstract
Randomized trials and observational studies, more often than not, run over a certain period
of time. The treatment effect evolves during this period which provides crucial insights into
the treatment response and the long-term effects. Many conventional methods for estimating
treatment effects are limited to the i.i.d. setting and are not suited for inferring the time
dynamics of the treatment effect. The time series encountered in these settings are highly
informative but often nonstationary due to the changing effects of treatment. This increases the
difficulty of the task, since stationarity, a common assumption in time series analysis, cannot
be reasonably assumed. Another challenge is the heterogeneity of the treatment effect when
the treatment affects units differently. The task of estimating heterogeneous treatment effects
from nonstationary and, in particular, interventional time series is highly relevant but remains
largely unexplored.
We propose Causal Transfer, a method which combines state-space model with imputation to
learn the effect of the treatment and how it evolves over time. Causal Transfer does not assume
the data to be stationary and can be applied to randomized trials and observational studies in
which treatment is confounded. Causal Transfer adjusts the effect for possible confounders and
transfers the learned effect to other time series and, thereby, estimates various forms of treatment
effects, such as the average treatment effect (ATE) or the conditional average treatment effect
(CATE). By learning the time dynamics of the effect, Causal Transfer can also predict the
treatment effect for unobserved future time points and determine the long-term consequences
of treatment.