Incremental causal effects: an introduction and review

Summary There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pretreatment variables. The unconfoundedness assumption is often more plausible if a large number of pretreatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect estimation. We develop a method for debiasing penalized regression adjustments to allow sparse regression methods like the lasso to be used for √n-consistent inference of average treatment effects in high dimensional linear models. Given linearity, we do not need to assume that the treatment propensities are estimable, or that the average treatment effect is a sparse contrast of the outcome model parameters. Rather, in addition to standard assumptions used to make lasso regression on the outcome model consistent und …

In this section we first describe a new class of stochastic dynamic intervention, which we call incremental propensity score interventions, and give some motivation and examples. We go on to show that these interventions are nonparametrically identified without requiring any positivity restrictions on the propensity scores (e.g., the propensity scores do not need to be bounded away from zero and one). Then we describe the efficiency theory for estimating mean outcomes under these interventions, based on a new result for general stochastic interventions that depend on the observational treatment distribution.

We consider estimation of average treatment effects given observational data with high-dimensional pretreatment variables. Existing methods for this problem typically assume some form of sparsity for the regression functions. In this work, we introduce a debiased inverse propensity score weighting (DIPW) scheme for average treatment effect estimation that delivers $\sqrt{n}$-consistent estimates when the propensity score follows a sparse logistic regression model; the outcome regression functions are permitted to be arbitrarily complex. We further demonstrate how confidence intervals centred on our estimates may be constructed. Our theoretical results quantify the price to pay for permitting the regression functions to be unestimable, which shows up as an inflation of the variance of the estimator compared to the semiparametric efficient variance by a constant factor, under mild conditions. We also show that when outcome regressions can be estimated faster than a slow $1/\sqrt{ \log n} …

The methodological development of this paper is motivated by the need to address the following scientific question: does the issuance of heat alerts prevent adverse health effects? Our goal is to address this question within a causal inference framework in the context of time series data. A key challenge is that causal inference methods require the overlap assumption to hold: each unit (i.e., a day) must have a positive probability of receiving the treatment (i.e., issuing a heat alert on that day). In our motivating example, the overlap assumption is often violated: the probability of issuing a heat alert on a cooler day is zero. To overcome this challenge, we propose a stochastic intervention for time series data which is implemented via an incremental time-varying propensity score (ItvPS). The ItvPS intervention is executed by multiplying the probability of issuing a heat alert on day $t$ -- conditional on past information up to day $t$ -- by an odds ratio $δ_t$. First, we introduce …

In this section we first describe a new class of stochastic dynamic intervention, which we call incremental propensity score interventions, and give some motivation and examples. We go on to show that these interventions are nonparametrically identified without requiring any positivity restrictions on the propensity scores (e.g., the propensity scores do not need to be bounded away from zero and one). Then we describe the efficiency theory for estimating mean outcomes under these interventions, based on a new result for general stochastic interventions that depend on the observational treatment distribution.