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Randomized trials and observational studies, more often than not, run over acertain period of time. The treatment effect evolves during this period whichprovides crucial insights into the treatment response and the long-termeffects. Many conventional methods for estimating treatment effects are limitedto the i.i.d. setting and are not suited for inferring the time dynamics of thetreatment effect. The time series encountered in these settings are highlyinformative but often nonstationary due to the changing effects of treatment.This increases the difficulty, since stationarity, a common assumption in timeseries analysis, cannot be reasonably assumed. Another challenge is theheterogeneity of the treatment effect when the treatment affects unitsdifferently. The task of estimating heterogeneous treatment effects fromnonstationary and, in particular, interventional time series is highly relevantbut has remained unexplored yet. We propose Causal Transfer, a method whichcombines regression to adjust for confounding with time series modelling tolearn the effect of the treatment and how it evolves over time. Causal Transferdoes not assume the data to be stationary and can be applied to randomizedtrials and observational studies in which treatment is confounded. CausalTransfer adjusts the effect for possible confounders and transfers the learnedeffect to other time series and, thereby, estimates various forms of treatmenteffects, such as the average treatment effect (ATE) or the conditional averagetreatment effect (CATE). By learning the time dynamics of the effect, CausalTransfer can also predict the treatment effect for unobserved future timepoints and determine the long-term consequences of treatment.

Estimating heterogeneous treatment effects in nonstationary time series with state-space models