Nonparametric causal effects based on incremental propensity score interventions

Most work in causal inference considers deterministic interventions that set each unit's treatment to some fixed value. However, under positivity violations these interventions can lead to non-identification, inefficiency, and effects with little practical relevance. Further, corresponding effects in longitudinal studies are highly sensitive to the curse of dimensionality, resulting in widespread use of unrealistic parametric models. We propose a novel solution to these problems: incremental interventions that shift propensity score values rather than set treatments to fixed values. Incremental interventions have several crucial advantages. First, they avoid positivity assumptions entirely. Second, they require no parametric assumptions and yet still admit a simple characterization of longitudinal effects, independent of the number of timepoints. For example, they allow longitudinal effects to be visualized with a single curve instead of lists of coefficients. After characterizing these incremental interventions and giving identifying conditions for corresponding effects, we also develop general efficiency theory, propose efficient nonparametric estimators that can attain fast convergence rates even when incorporating flexible machine learning, and propose a bootstrap-based confidence band and simultaneous test of no treatment effect. Finally we explore finite-sample performance via simulation, and apply the methods to study time-varying sociological effects of incarceration on entry into marriage

Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview

We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared with related work by Robins and others: in particular, we show how Robins's 'G-computation' algorithm arises naturally from this decision-theoretic perspective. Careful attention is paid to the mathematical and substantive conditions required to justify the use of this formula. These conditions revolve around a property we term stability, which relates the probabilistic behaviours of observational and interventional regimes. We show how an assumption of 'sequential randomization' (or 'no unmeasured confounders'), or an alternative assumption of 'sequential irrelevance', can be used to infer stability. Probabilistic influence diagrams are used to simplify manipulations, and their power and limitations are discussed. We compare our approach with alternative formulations based on causal DAGs or potential response models. We aim to show that formulating the problem of assessing dynamic treatment strategies as a problem of decision analysis brings clarity, simplicity and generality.Comment: 49 pages, 15 figure

Assessing the Causal Effect of Policies: An Approach Based on Stochastic Interventions

Stochastic interventions are a powerful tool to define parameters that measure the causal effect of a realistic intervention that intends to alter the population distribution of an exposure. In this paper we follow the approach described in D\\u27iaz and van der Laan (2011) to define and estimate the effect of an intervention that is expected to cause a truncation in the population distribution of the exposure. The observed data parameter that identifies the causal parameter of interest is established, as well as its efficient influence function under the non parametric model. Inverse probability of treatment weighted (IPTW), augmented IPTW and targeted minimum loss based estimators (TMLE) are proposed, their consistency and efficiency properties are determined. An extension to longitudinal data structures is presented and its use is demonstrated with a real data example

Causal Mediation in a Survival Setting with Time-Dependent Mediators

The effect of an expsore on an outcome of interest is often mediated by intermediate variables. The goal of causal mediation analysis is to evaluate the role of these intermediate variables (mediators) in the causal effect of the exposure on the outcome. In this paper, we consider causal mediation of a baseline exposure on a survival (or time-to-event) outcome, when the mediator is time-dependent. The challenge in this setting lies in that the event process takes places jointly with the mediator process; in particular, the length of the mediator history depends on the survival time. As a result, we argue that the definition of natural effects in this setting should be based on only blocking those paths from treatment to mediators that are not through the survival history. We propose to use a stochastic interventions (SI) perspective, introduced by Didelez, Dawid, and Geneletti (2006), to formulate the causal mediation analysis problem in this setting. Under this formulation, the mediators are regarded as intervention variables, onto which a given counterfactual distribution is enforced. The natural direct and indirect effects can be defined analogously to the ideas in Pearl (2001). In particular, they also allow for a total effect decomposition and an interpretation of the natural direct effect as a weighted average of controlled direct effects. The statistical parameters that should arise are defined nonparametrically; therefore, they have meaningful interpretations, independent of the causal formulations and assumptions. We present a general semiparametric inference framework for these parameters. Using their efficient influence functions, we develop semiparametric efficient and robust targeted substitution-based (TMLE) and estimating-equation-based (A-IPTW) estimators. An IPTW estimator and g-computation estimator will also be presented

Causal etiology of the research of James M. Robins

This issue of Statistical Science draws its inspiration from the work of James M. Robins. Jon Wellner, the Editor at the time, asked the two of us to edit a special issue that would highlight the research topics studied by Robins and the breadth and depth of Robins' contributions. Between the two of us, we have collaborated closely with Jamie for nearly 40 years. We agreed to edit this issue because we recognized that we were among the few in a position to relate the trajectory of his research career to date.Fil: Richardson, Thomas S.. University of Washington; Estados UnidosFil: Rotnitzky, Andrea Gloria. Universidad Torcuato Di Tella. Departamento de Economía; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin