Causal inference for complex longitudinal data: the continuous case

We extend Robins theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments In particular we establish versions of the key results of the discrete theory the gcomputation formula and a collection of powerful characterizations of the gnull hypothesis of no treatment eect This is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the pas

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Estimating treatment importance in multidrug-resistant tuberculosis using Targeted Learning : an observational individual patient data network meta-analysis

Persons with multidrug‐resistant tuberculosis (MDR‐TB) have a disease resulting from a strain of tuberculosis (TB) that does not respond to at least isoniazid and rifampicin, the two most effective anti‐TB drugs. MDR‐TB is always treated with multiple antimicrobial agents. Our data consist of individual patient data from 31 international observational studies with varying prescription practices, access to medications, and distributions of antibiotic resistance. In this study, we develop identifiability criteria for the estimation of a global treatment importance metric in the context where not all medications are observed in all studies. With stronger causal assumptions, this treatment importance metric can be interpreted as the effect of adding a medication to the existing treatments. We then use this metric to rank 15 observed antimicrobial agents in terms of their estimated add‐on value. Using the concept of transportability, we propose an implementation of targeted maximum likelihood estimation, a doubly robust and locally efficient plug‐in estimator, to estimate the treatment importance metric. A clustered sandwich estimator is adopted to compute variance estimates and produce confidence intervals. Simulation studies are conducted to assess the performance of our estimator, verify the double robustness property, and assess the appropriateness of the variance estimation approach

Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point identification of the ATE under IV assumptions, express the identification results in a common notation and terminology, and propose a taxonomy that is based on sets of identifying assumptions. We further demonstrate and provide software for the application of these methods to estimate bounds. Supplementary materials for this article are available online

Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Minimax estimation of a functional on a structured high-dimensional model

Analysis and Stochastic

Local domestication of lactic acid bacteria via cassava beer fermentation

Cassava beer, or chicha, is typically consumed daily by the indigenous Shuar people of the Ecuadorian Amazon. This traditional beverage made from cassava tuber (Manihot esculenta) is thought to improve nutritional quality and flavor while extending shelf life in a tropical climate. Bacteria responsible for chicha fermentation could be a source of microbes for the human microbiome, but little is known regarding the microbiology of chicha. We investigated bacterial community composition of chicha batches using Illumina high-throughput sequencing. Fermented chicha samples were collected from seven Shuar households in two neighboring villages in the Morona-Santiago region of Ecuador, and the composition of the bacterial communities within each chicha sample was determined by sequencing a region of the 16S ribosomal gene. Members of the genus Lactobacillus dominated all samples. Significantly greater phylogenetic similarity was observed among chicha samples taken within a village than those from different villages. Community composition varied among chicha samples, even those separated by short geographic distances, suggesting that ecological and/or evolutionary processes, including human-mediated factors, may be responsible for creating locally distinct ferments. Our results add to evidence from other fermentation systems suggesting that traditional fermentation may be a form of domestication, providing endemic beneficial inocula for consumers, but additional research is needed to identify the mechanisms and extent of microbial dispersal

Bose-Einstein condensate collapse: a comparison between theory and experiment

We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed at JILA with Bose-Einstein condensates of Rb-85, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. Besides the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally. Quantum field effects, such as fragmentation, that might account for these discrepancies are discussed.Comment: 4 pages, 2 figure