  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, 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 has remained unexplored yet. We propose Causal Transfer, a method which
combines regression to adjust for confounding with time series modelling 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.
