Randomized trials and observational studies, more often than not, run over a certain period of time during which the treatment effect evolves. 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 fits state-space models to observational-interventional data in order 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), the sample average treatment effect (SATE), 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.
A related method which uses state-space models for causal effect estimation is Causal Impact @cite_12 . Causal Impact infers the counterfactual of a treated univariate time series, that is, its outcome under no interventions. For this purpose, it requires a control time series: a covariate which is predictive of the time series of interest but not affected by treatment itself. During the pre-period, Causal Impact learns the relationship between the response and the control time series by fitting a dynamic regression model. Causal Impact assumes that the learned relationship between the control and the response does not change due to treatment. By doing so, Causal Impact is able to predict the counterfactual of a treated time series for the treatment (or post-intervention) period from the model that was fitted to the pre-period. The treatment effect is estimated by subtracting the observed treated time series by the predicted untreated time series.
@cite_12
2078639378
An important problem in econometrics and marketing is to infer the causal impact that a designed market intervention has exerted on an outcome metric over time. In order to allocate a given budget optimally, for example, an advertiser must determine the incremental contributions that dierent advertising campaigns have made to web searches, product installs, or sales. This paper proposes to infer causal impact on the basis of a diusion-regressi on state-space model that predicts the counterfactual market response that would have occurred had no intervention taken place. In con- trast to classical dierence-in-dier ences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) exibly accommodate multiple sources of variation, including the time-varying inuence of contemporane- ous covariates, i.e., synthetic controls. Using a Markov chain Monte Carlo algorithm for posterior inference, we illustrate the statistical properties of our approach on synthetic data. We then demonstrate its practical utility by evaluating the eect of an online advertising campaign on search-related site visits. We discuss the strengths and limitations of our approach in improving the accuracy of causal at- tribution, power analyses, and principled budget allocation.