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.
Marginal integration @cite_17 is another related method for causal effect estimation. The main difference is that the regression function in Equation is nonparametric and estimated with kernel regression before integrating out the adjustment set. Marginal integration can consistently estimate the ATE with optimal one-dimensional nonparametric convergence rate @math for continuous treatment variables @cite_17 . The price to be paid for such a general result is that it requires strict stationarity for the estimation of the smooth regression function and is, therefore, restricted to observational time series. The theoretical guarantees hold for estimands which are functions of @math for some @math in the support of @math , such as the ATE. In principle, marginal integration can be extended to estimate sample average treatment effects or heterogenous effects. The theoretical guarantees, however, may not carry over as the estimation of the latter is severely exposed to the curse of dimensionality. Marginal integration is capable of predicting future effects but only up to the maximum time distance present in the data and assuming stationarity. It does not support the estimation of prediction intervals.
@cite_17
2963139802 2930033329 2138290169 2064903582
Causal inference from observational data is an ambitious but highly relevant task, with diverse applications ranging from natural to social sciences. Within the scope of nonparametric time series, causal inference defined through interventions is largely unexplored, although time order simplifies the problem substantially. A marginal integration scheme is considered for inferring causal effects from observational time series data, MINT-T (marginal integration in time series), which is an adaptation for time series of a previously proposed method for the case of independent data. This approach for stationary stochastic processes is fully nonparametric and, assuming no instantaneous effects consistently recovers the total causal effect of a single intervention with optimal one-dimensional nonparametric convergence rate n−2 5 assuming regularity conditions and twice differentiability of a certain corresponding regression function. Therefore, MINT-T remains largely unaffected by the curse of dimensionality as long as smoothness conditions hold in higher dimensions and it is feasible for a large class of stationary time series, including nonlinear and multivariate processes. For the case with instantaneous effects, we provide a procedure which guards against false positive causal statements. We consider inference about a scalar parameter under a non-parametric model based on a one-step estimator computed as a plug in estimator plus the empirical mean of an estimator of the parameter's influence function. We focus on a class of parameters that have influence function which depends on two infinite dimensional nuisance functions and such that the bias of the one-step estimator of the parameter of interest is the expectation of the product of the estimation errors of the two nuisance functions. Our class includes many important treatment effect contrasts of interest in causal inference and econometrics, such as ATE, ATT, an integrated causal contrast with a continuous treatment, and the mean of an outcome missing not at random. We propose estimators of the target parameter that entertain approximately sparse regression models for the nuisance functions allowing for the number of potential confounders to be even larger than the sample size. By employing sample splitting, cross-fitting and @math -regularized regression estimators of the nuisance functions based on objective functions whose directional derivatives agree with those of the parameter's influence function, we obtain estimators of the target parameter with two desirable robustness properties: (1) they are rate doubly-robust in that they are root-n consistent and asymptotically normal when both nuisance functions follow approximately sparse models, even if one function has a very non-sparse regression coefficient, so long as the other has a sufficiently sparse regression coefficient, and (2) they are model doubly-robust in that they are root-n consistent and asymptotically normal even if one of the nuisance functions does not follow an approximately sparse model so long as the other nuisance function follows an approximately sparse model with a sufficiently sparse regression coefficient. Abstract We outline a framework for causal inference in settings where assignment to a binary treatment is ignorable, but compliance with the assignment is not perfect so that the receipt of treatment is nonignorable. To address the problems associated with comparing subjects by the ignorable assignment—an “intention-to-treat analysis”—we make use of instrumental variables, which have long been used by economists in the context of regression models with constant treatment effects. We show that the instrumental variables (IV) estimand can be embedded within the Rubin Causal Model (RCM) and that under some simple and easily interpretable assumptions, the IV estimand is the average causal effect for a subgroup of units, the compliers. Without these assumptions, the IV estimand is simply the ratio of intention-to-treat causal estimands with no interpretation as an average causal effect. The advantages of embedding the IV approach in the RCM are that it clarifies the nature of critical assumptions needed for a... Researchers have long struggled to identify causal effects in nonexperimental settings. Many recently proposed strategies assume ignorability of the treatment assignment mechanism and require fitting two models—one for the assignment mechanism and one for the response surface. This article proposes a strategy that instead focuses on very flexibly modeling just the response surface using a Bayesian nonparametric modeling procedure, Bayesian Additive Regression Trees (BART). BART has several advantages: it is far simpler to use than many recent competitors, requires less guesswork in model fitting, handles a large number of predictors, yields coherent uncertainty intervals, and fluidly handles continuous treatment variables and missing data for the outcome variable. BART also naturally identifies heterogeneous treatment effects. BART produces more accurate estimates of average treatment effects compared to propensity score matching, propensity-weighted estimators, and regression adjustment in the nonlinear ...