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Pragmatic trials are designed to address real-world questions about care options. This article addresses issues that may arise from per-protocol and intention-to-treat analyses of such trials, outlines alternative analytic approaches, and provides guidance on how to choose among them.

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification when there is the same number of moment functions as parameters of interest. We use these orthogonal moments and cross-fitting to construct debiased machine learning estimators of functions of high dimensional conditional quantiles and of dynamic discrete choice parameters with high dimensional state variables. We show that additional first steps needed for the orthogonal moment functions have no effect, globally, on average orthogonal moment functions. We give a general approach to estimating those additional first steps. We characterize double robustness and give a variety of new doubly robust moment functions. We give general and simple regularity conditions for asymptotic theory.

Methods from causal mediation analysis have generalized the traditional approach to direct and indirect elfects in the epidemiologic and social science literature by allowing for interaction and nonlinearities. However, the methods from the causal inference literature have themselves been subject to a major limitation, in that the so-called natural direct and indirect effects that are used are not identified from data whenever there is a mediator-outcome confounder that is also affected by the exposure. In this article, we describe three alternative approaches to effect decomposition that give quantities that can be interpreted as direct and indirect effects and that can be identified from data even in the presence of an exposure-induced mediator-outcome confounder. We describe a simple weighting-based estimation method for each of these three approaches, illustrated with data from perinatal epidemiology. The methods described here can shed insight into pathways and questions of mediation even when an exposure-induced mediator-outcome confounder is present.

The goal of this article is to construct doubly robust (DR) estimators in ignorable missing data and causal inference models. In a missing data model, an estimator is DR if it remains consistent when either (but not necessarily both) a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified. Because with observational data one can never be sure that either a missingness model or a complete data model is correct, perhaps the best that can be hoped for is to find a DR estimator. DR estimators, in contrast to standard likelihood‐based or (nonaugmented) inverse probability‐weighted estimators, give the analyst two chances, instead of only one, to make a valid inference. In a causal inference model, an estimator is DR if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified. Because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct, inference based on DR estimators should improve upon previous approaches. Indeed, we present the results of simulation studies which demonstrate that the finite sample performance of DR estimators is as impressive as theory would predict. The proposed method is applied to a cardiovascular clinical trial.

We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method employs U-statistics that are based on higher-order influence functions of the parameter of interest, which extend ordinary linear influence functions, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method often leads to a bias-variance trade-off, and results in estimators that converge at a slower than √n-rate. In a number of examples, the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at √n-rate, but we also consider efficient √n-estimation using novel nonlinear estimators. The general approach is applied in detail to the example of estimating a mean response when the response is not always observed.

We revisit the classic semi-parametric problem of inference on a low-dimensional parameter θ₀ in the presence of high-dimensional nuisance parameters η₀. We depart from the classical setting by allowing for η₀ to be so high-dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η₀, we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high-dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating η₀ cause a heavy bias in estimators of θ₀ that are obtained by naively plugging ML estimators of η₀ into estimating equations for θ₀. This bias results in the naive estimator failing to be N-½ consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ₀ can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate θ₀; (2) making use of cross-fitting, which provides an efficient form of data-splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an N-½-neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.

Objective Here we demonstrate via operative video the subtemporal extradural approach to a tumour in the cavernous sinus. Methods The extradural approach is performed here in a paediatric patient (a 15-year-old child) via a right extended pterional osteoplastic craniotomy with removal of the zygomatic arch. The operative microscope is introduced, and the dura is divided at the superior orbital fissure into endosteal and meningeal layers using a diamond knife. The middle cranial fossa floor is drilled flat to increase access, and the plane is further developed towards the cavernous sinus. The tumour is seen bulging from within the cavernous sinus, and the cavernous sinus is opened in the anteromedial triangle between cranial nerves Vi and Vii. After biopsy, the tumour is debulked with an ultrasonic aspirator. Doppler is used to identify the internal carotid artery and preserve it. The bone flap is replaced, and the wound is closed in layers in standard fashion. Results The patient recovered well and was discharged on post-operative day 3. Persistent sixth nerve palsy (present pre-operatively) was present; however, otherwise, there was good recovery from surgery. Good resection of tumour is demonstrated on post-operative MR imaging. Conclusions This approach is uncommon but important as it enables extradural access to the cavernous sinus, minimising the complications associated with an intradural approach such as cortical injury. In this video, we also demonstrate the fundamental anatomy using annotation and cadaveric images to enhance understanding required for the neurosurgeon to successfully complete this approach. The patient consented to the procedure in the standard fashion.

Background A 63-year-old presented with reduced left visual acuity and V1 sensation. Imaging demonstrated left sphenoid osseous meningioma narrowing superior orbital fissure with intracranial extension to superior temporal gyrus. Method Endoscopic transorbital approach utilising novel lateral orbit ‘sliding coach door’ osteotomy performed. Lateral canthal incision with lateral canthal ligament division mobilises and decompresses globe infero-medially. Osteotomy performed, tethered by temporalis. Osteotomy slides postero-laterally creating working space lateral to inferior and superior orbital fissures. Conclusion This technique requires reduced soft tissue dissection and facilitates reconstruction. Adequate working space enabled satisfactory resection with residual dural tail requiring future surveillance. Cosmesis was satisfactory.

A common problem in formulating models for the relative risk and risk difference is the variation dependence between these parameters and the baseline risk, which is a nuisance model. We address this problem by proposing the conditional log odds-product as a preferred nuisance model. This novel nuisance model facilitates maximum-likelihood estimation, but also permits doubly-robust estimation for the parameters of interest. Our approach is illustrated via simulations and a data analysis. An R package implementing the proposed methods is available on CRAN. Supplementary materials for this article are available online.

We consider estimation of the causal effect of a binary treatment on an outcome, conditionally on covariates, from observational studies or natural experiments in which there is a binary instrument for treatment. We describe a doubly robust, locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates V when randomization of the instrument is only true conditionally on a high dimensional vector of covariates X, possibly bigger than V. We discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on V that assumes no treatment–instrument interaction. We illustrate our methods with the estimation of the local average effect of participating in 401(k) retirement programmes on savings by using data from the US Census Bureau's 1991 Survey of Income and Program Participation.