Targeted learning in data science. Causal inference for complex longitudinal studies
The book consists of eight parts structured as a thorough overview of different aspects of targeted learning. The first part is built as an introduction to targeted learning in data science and comprises of four chapters leading to the definition of LTMLE. In the first chapter, the authors overview the main research questions in data science covering both the traditional approaches and newer methods. Next, the statistical estimation problem is presented in detail; the chapter concludes with a roadmap/pipeline for approaching targeted learning. In the second chapter, the authors describe methods for defining the structural causal model. The third chapter overviews methods for sequential super-learning. Starting with a description of ensemble learning, the authors continue with a definition of the estimation problem and remarks on computation. In the fourth chapter, the LTMLE is introduced using HIV treatment example. The different steps such as the definition of the estimation problem, the identification of the efficient influence curve, of the loss function and fluctuation submodel, as well as the analysis of the asymptotic efficiency are presented in detail. In the second part, the authors explore additional core topics including the one step TMLE (in Chapter 5, with a focus on the least favourable submodel), the highly adaptive Lasso (HAL, in Chapter 6, with characteristics introduced mainly through applications such as the prediction simulation and data analysis and simulation for missing data), a combination of two i.e. generally efficient HAL-TMLE (in Chapter 7), the HAL estimator of the efficient influence curve (in Chapter 8, with the details on the rate of convergence and the effect of using a subset from the truth data distribution), an approach for inferring data-adaptive target parameters (in Chapter 9, with details on the CV-TMLE and specific software for data-adaptive VIMs, varipact) and C-TMLE for continuous tuning (in Chapter 10, concentrated on the targeted tuning of the nuisance parameter). In the third part, the authors discuss randomised trials. In the eleventh chapter, based on a vaccine example, the targeted estimation of cumulative sieve effects is introduced. The initial estimates, the submodels and loss function, and the TMLE algorithm and its statistical properties in this context are examined in detail. In the twelfth chapter, the sample average treatment effect is presented on causal models. The TMLE on population and sample effects, and potential extensions to pair-matched trails are also presented. In the thirteenth chapter, the authors discuss the data-adaptive estimation in cluster randomised trials, with or without matching and assess the collaborative estimation of the exposure mechanism. The fourth part is built on the handling of observational data. In the fourteenth chapter, the authors present the stochastic treatment regimes. Following an overview of notations, the optimality theory and the asymptotic distribution of TMLE are discussed in detail. The next chapter is dedicated to applying the LTMLE on clustering; using the PROBIT study as starting point, two parameterizations of the g-formula and the LTMLE for a saturated marginal structural model are presented. The sixteenth chapter overviews the comparative effectiveness of adaptive treatment strategies, with details on the action mechanism \(g_0^\theta\) and outcome regressions \(Q_0^\theta\). This part concludes with a chapter on mediation analysis with time-varying mediators and exposures, where the natural direct and indirect effects are discussed in detail. The fifth part overviews approaches for on-line learning and commences with a chapter on online super-learning (Chapter 18) for which the statistical formulation of the estimation problem is presented first, followed by the description of the oracle inequality for online cross-validation selector (and the special case for iid observations). The nineteenth chapter presents online targeted learning for time series with a focus on Monte Carlo approximation of the efficient influence curve using nesting assumptions and the special representation of the efficient influence curve for binary variables. Also discussed is the online TMLE and the online one step estimator. The sixth part comprises of two chapters focused on data from networks. In the twentieth chapter, the authors discuss the causal inference in longitudinal network-dependent data and present the estimation problem in detail, including the effects of counterfactuals and stochastic interventions, the dimension reduction and the exchangeability assumptions. In the twenty-first chapter, the single time point interventions are assessed, including simulations in R that underline various aspects of the analysis. The seventh part commences with a chapter on the optimal dynamic treatment rules for which the statistical inference for the average of sample split specific mean counterfactual outcomes is discussed under data adaptively determined dynamic treatments. Also included in this part are a chapter on optimal individualized treatments under limited resources (the canonical gradient of the optimal resource constraint value and the inference of \(\Psi (P_0)\) are presented in detail) and a chapter on targeting a simple statistical bandit problem using TMLE. The eighth part of the book is dedicated to special topic including the CV-TMLE for nonpathwise differentiable target parameters (in Chapter 25), higher order targeted loss-based estimation, in Chapter 26 (in which the higher order TMLEs are presented in detail), a sensitivity analysis (Chapter 27), targeted bootstrapping and the inference of treatment specific mean and of the variance of the influence curve (in Chapter 28), targeted learning using adaptive survey sampling (in Chapter 29) and the predicament of truth and philosophy of science, from a statistical angle in the concluding chapter (Chapter 30). The book recommends itself as a thorough overview of TMLE approaches with a variety of examples and case studies, all presented in detail, in a text-book like manner, making this work accessible to a wide audience from undergraduates to established researchers. Some statistical/mathematical/computational background is required, but the amount of details, simulations, examples, concluding ``further reading'' sections and references offer a solid starting point for understanding the concepts which are presented and for future research.
longitudinal targeted maximum likelihood estimator (LTMLE)
targeted maximum likelihood estimation (TMLE)
canonical one-dimensional submodel for a multidimensional target parameter
targeted estimation of cumulative effects
scientific article; zbMATH DE number 6891537