\(\DeclareMathOperator{\expit}{expit}\) \(\DeclareMathOperator{\logit}{logit}\) \(\DeclareMathOperator*{\argmin}{\arg\!\min}\) \(\newcommand{\indep}{\perp\!\!\!\perp}\) \(\newcommand{\coloneqq}{\mathrel{=}}\) \(\newcommand{\R}{\mathbb{R}}\) \(\newcommand{\E}{\mathbb{E}}\) \(\newcommand{\M}{\mathcal{M}}\) \(\renewcommand{\P}{\mathbb{P}}\) \(\newcommand{\I}{\mathbb{I}}\) \(\newcommand{\1}{\mathbbm{1}}\)


“One enemy of robust science is our humanity – our appetite for being right, and our tendency to find patterns in noise, to see supporting evidence for what we already believe is true, and to ignore the facts that do not fit.”

Nature Editorial (Anonymous) (2015b)

Scientific research is at a unique point in its history. The need to improve rigor and reproducibility is greater than ever. Corroboration moves science forward, yet there is growing alarm that results cannot be reproduced or validated, suggesting that many discoveries may be false or less robust than initially claimed (Baker, 2016). A failure to meet this need will result in further declines in the rate of scientific progress, tarnishing of the reputation of the scientific enterprise as a whole, and erosion of the public’s trust in scientific findings (Munafò et al., 2017; Nature Editorial (Anonymous), 2015a).

“The key question we want to answer when seeing the results of any scientific study is whether we can trust the data analysis.”

Peng (2015)

Unfortunately, in its current state, the culture of statistical data analysis enables, rather than precludes, the manner in which human bias may affect the results of (ideally objective) data analytic efforts. A significant degree of human bias enters into statistical data analysis efforts in the form of improper model selection. All procedures for estimation and hypothesis testing are derived based on a choice of a statistical model; thus, obtaining valid estimates and statistical inference relies critically on the chosen model containing an accurate representation of the process that generated the data.

Consider, for example, a hypothetical study in which a treatment is assigned to a group of patients – was the treatment assigned randomly, or were characteristics of the individuals (i.e., “baseline covariates”) taken into account in making the treatment assignment decision? What’s more, in light of patient characteristics and heterogeneity in clinician decision-making, are patients assigned to the treatment arm uniformly receiving the same treatment? Any such knowledge can – indeed, must – be incorporated into the choice of statistical model. Alternatively, the data could arise from an observational study (or “quasi-experiment”), in which there is no (or very limited) control over the treatment assignment mechanism. In such cases, available knowledge about the data-generating process (DGP) is even more limited. In these situations, the statistical model should contain all possible distributions of the data. In practice, however, models are not selected based on scientific knowledge available about the DGP; instead, models are often selected based on (1) the philosophical leanings of the analyst, (2) the relative convenience of implementation of statistical methods admissible within the choice of model, and (3) the results of significance testing (i.e., p-values).

This practice of “cargo-cult statistics — the ritualistic miming of statistics rather than conscientious practice,” (Stark and Saltelli, 2018) is characterized by arbitrary modeling choices, even when these choices often result in different answers to the same research question. As opposed to its original purpose of safeguarding the scientific process – by providing formal techniques for evaluating the veracity of a claim using properly designed experiments and data collection procedures – Statistics is increasingly often used “to aid and abet weak science, a role it can perform well when used mechanically or ritual[istically]” (Stark and Saltelli, 2018). The current trend in deriving scientific discoveries by way of abusing statistical methods helps to explain the modern epidemic of false findings from which scientific research is suffering (van der Laan and Starmans, 2014).

“We suggest that the weak statistical understanding is probably due to inadequate”statistics lite” education. This approach does not build up appropriate mathematical fundamentals and does not provide scientifically rigorous introduction into statistics. Hence, students’ knowledge may remain imprecise, patchy, and prone to serious misunderstandings. What this approach achieves, however, is providing students with false confidence of being able to use inferential tools whereas they usually only interpret the p-value provided by black box statistical software. While this educational problem remains unaddressed, poor statistical practices will prevail regardless of what procedures and measures may be favored and/or banned by editorials.”

Szucs and Ioannidis (2017)

Our team at the University of California, Berkeley is uniquely positioned to provide such an education. Spearheaded by Professor Mark van der Laan, and now spreading rapidly through his students and colleagues who have greatly enriched the field, the aptly named “Targeted Learning” paradigm emphasizes a focus upon (i.e., “targeting of”) the scientific question motivating a given study or dataset. The philosophy of Targeted Learning runs counter to the current cultural problem of “convenience statistics,” which opens the door to biased estimation, misleading data analytic results, and erroneous discoveries. Targeted Learning (TL) embraces the fundamentals that formalized the field of Statistics, notably including the dual notions that a statistical model must represent real knowledge about the data-generating experiment and that a target parameter (a particular feature of the data-generating probability distribution) represents what we seek to learn from the data (van der Laan and Starmans, 2014). In this way, TL defines a ground truth and establishes a principled standard for inference, thereby curtailing opportunities for our all-too-human biases (e.g., hindsight bias, confirmation bias, and outcome bias) to infiltrate our efforts at objective data analysis.

“The key for effective classical [statistical] inference is to have well-defined questions and an analysis plan that tests those questions.”

Nosek et al. (2018)

Inspired loosely by R.A. Fisher’s influential classic Statistical Methods for Research Workers (Fisher, 1946), this handbook aims to provide practical training for students, researchers, industry professionals, and academicians in the sciences (broadly considered – whether biological, physical, economic, or social), medicine and public health, statistics, and numerous other allied disciplines, equipping them with the necessary knowledge and skills to utilize the methodological developments of TL. The Targeted Learning paradigm encompasses a principled set of techniques, united by a single philosophy, for developing answers to queries with confidence, utilizing advances in causal inference, state-of-the-art non/semi-parametric statistical theory, and machine learning — so that each and every data analysis is realistic, reflecting appropriately what is known (and unknown) about the process that generated the data, while remaining fully compatible with the guiding principles of computational reproducibility.

Just as the conscientious use of modern statistical methodology is necessary to ensure that scientific practice thrives — robust, well-tested software plays a critical role in allowing practitioners to access the published results of a given scientific investigation. We concur with the view put forth by Buckheit and Donoho (1995) that “an article…in a scientific publication is not the scholarship itself, it is merely advertising of the scholarship. The actual scholarship is the complete software development environment and the complete set of instructions which generated the figures,” making the availability and adoption of robust statistical software key to enhancing the transparency that is an inherent (and assumed) aspect of the scientific process.

For a statistical methodology to be readily accessible in practice, it is crucial that it is accompanied by user-friendly software (Pullenayegum et al., 2016; Stromberg et al., 2004). The tlverse software ecosystem, composed of a set of packages for the R language and environment for statistical computing (R Core Team, 2021), was developed to fulfill this need for the TL methodological framework. Not only does this suite of software tools facilitate computationally reproducible and efficient analyses, it is also a tool for TL education. Rather than focusing on implementing a specific estimator or a small set of related estimators, the design paradigm of the tlverse ecosystem focuses on exposing the statistical framework of Targeted Learning itself: all software packages in the tlverse ecosystem directly model the key objects defined in the mathematical and theoretical framework of Targeted Learning. What’s more, the tlverse software packages share a core set of design principles centered on extensibility, allowing for them to be used in conjunction with each other and used cohesively as building blocks for formulating sophisticated statistical analyses. For an introduction to the TL framework, we recommend Coyle et al. (2021)’s recent review paper.

In this handbook, the reader will embark on a journey through the tlverse ecosystem. Guided by R programming exercises, case studies, and intuition-building explanations, readers will learn to use this toolbox for applying the TL statistical methodology, which will translate to real-world causal analyses. Some preliminaries are required prior to this learning endeavor – for this, we provide a list of recommended learning resources.