Statistical Models Answer the Fundamental Clinical Question and Provide Clinical Trial Estimands – Statistical Thinking

Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies

Presents a discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation. The objective was to specify the benefits of randomization in estimating causal effects of treatments. It is concluded that randomization should be employed whenever possible but that the use of carefully controlled nonrandomized data to estimate causal effects is a reasonable and necessary procedure in many cases.

Recursive partitioning for heterogeneous causal effects

In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without “sparsity” assumptions. We propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7–22%.

mediation: R Package for Causal Mediation Analysis

In this paper, we describe the R package mediation for conducting causal mediation analysis in applied empirical research. In many scientific disciplines, the goal of researchers is not only estimating causal effects of a treatment but also understanding the process in which the treatment causally affects the outcome. Causal mediation analysis is frequently used to assess potential causal mechanisms. The mediation package implements a comprehensive suite of statistical tools for conducting such an analysis. The package is organized into two distinct approaches. Using the model-based approach, researchers can estimate causal mediation effects and conduct sensitivity analysis under the standard research design. Furthermore, the design-based approach provides several analysis tools that are applicable under different experimental designs. This approach requires weaker assumptions than the model-based approach. We also implement a statistical method for dealing with multiple (causally dependent) mediators, which are often encountered in practice. Finally, the package also offers a methodology for assessing causal mediation in the presence of treatment noncompliance, a common problem in randomized trials.

Reducing Bias in Observational Studies Using Subclassification on the Propensity Score

The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates. Subclassification on an estimated propensity score is illustrated, using observational data on treatments for coronary artery disease. Five subclasses defined by the estimated propensity score are constructed that balance 74 covariates, and thereby provide estimates of treatment effects using direct adjustment. These subclasses are applied within subpopulations, and model-based adjustments are then used to provide estimates of treatment effects within these subpopulations. Two appendixes address theoretical issues related to the application: the effectiveness of subclassification on the propensity score in removing bias, and balancing properties of propensity scores with incomplete data.

A Nonparametric Approach to Practical Identifiability of Nonlinear Mixed Effects Models

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread adoption of this individual-based fitting, it is becoming increasingly common to take a hierarchical approach to parameter estimation, where modellers characterize the population parameter distributions, rather than considering each individual independently. This hierarchical parameter estimation is standard in pharmacometric modelling. However, many of the existing techniques for parameter identifiability do not immediately translate from the individual-based fitting to the hierarchical setting. In this work, we propose a nonparametric approach to study practical identifiability within a hierarchical parameter estimation framework. We focus on the commonly used nonlinear mixed effects framework and investigate two well-studied examples from the pharmacometrics and viral dynamics literature to illustrate the potential utility of our approach.

The central role of the propensity score in observational studies for causal effects

Abstract. The propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates. Both large and

Causality

Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interest to students and professionals in a wide variety of fields. Dr Judea Pearl has received the 2011 Rumelhart Prize for his leading research in Artificial Intelligence (AI) and systems from The Cognitive Science Society.

Machine Learning Who to Nudge: Causal vs Predictive Targeting in a Field Experiment on Student Financial Aid Renewal

In many settings, interventions may be more effective for some individuals than others, so that targeting interventions may be beneficial. We analyze the value of targeting in the context of a large-scale field experiment with over 53,000 college students, where the goal was to use "nudges" to encourage students to renew their financial-aid applications before a non-binding deadline. We begin with baseline approaches to targeting. First, we target based on a causal forest that estimates heterogeneous treatment effects and then assigns students to treatment according to those estimated to have the highest treatment effects. Next, we evaluate two alternative targeting policies, one targeting students with low predicted probability of renewing financial aid in the absence of the treatment, the other targeting those with high probability. The predicted baseline outcome is not the ideal criterion for targeting, nor is it a priori clear whether to prioritize low, high, or intermediate predicted probability. Nonetheless, targeting on low baseline outcomes is common in practice, for example because the relationship between individual characteristics and treatment effects is often difficult or impossible to estimate with historical data. We propose hybrid approaches that incorporate the strengths of both predictive approaches (accurate estimation) and causal approaches (correct criterion); we show that targeting intermediate baseline outcomes is most effective in our specific application, while targeting based on low baseline outcomes is detrimental. In one year of the experiment, nudging all students improved early filing by an average of 6.4 percentage points over a baseline average of 37% filing, and we estimate that targeting half of the students using our preferred policy attains around 75% of this benefit.

Randomized Controlled Trials without Data Retention

Amidst rising appreciation for privacy and data usage rights, researchers have increasingly acknowledged the principle of data minimization, which holds that the accessibility, collection, and retention of subjects' data should be kept to the bare amount needed to answer focused research questions. Applying this principle to randomized controlled trials (RCTs), this paper presents algorithms for making accurate inferences from RCTs under stringent data retention and anonymization policies. In particular, we show how to use recursive algorithms to construct running estimates of treatment effects in RCTs, which allow individualized records to be deleted or anonymized shortly after collection. Devoting special attention to non-i.i.d. data, we further show how to draw robust inferences from RCTs by combining recursive algorithms with bootstrap and federated strategies.

The C-Word: Scientific Euphemisms Do Not Improve Causal Inference From Observational Data

Causal inference is a core task of science. However, authors and editors often refrain from explicitly acknowledging the causal goal of research projects; they refer to causal effect estimates as associational estimates. This commentary argues that using the term “causal” is necessary to improve the quality of observational research. Specifically, being explicit about the causal objective of a study reduces ambiguity in the scientific question, errors in the data analysis, and excesses in the interpretation of the results.

Choosing informative priors in Bayesian regression models: a simulation study and tutorial using Stan and R

BackgroundBayesian regression models provide a robust framework for complex data analysis, which is particularly advantageous in scenarios with small sample sizes, common in psychology or medical research. However, specifying appropriate prior distributions that incorporate existing knowledge to regularize model parameters remains a challenge for many researchers. This can lead to unstable or implausible estimates. This study aims to demonstrate the impact of different prior distributions on regression models and to provide a practical guide for choosing and justifying informative priors to produce more stable and credible results.MethodsThe study involved two parts. First, a simulation study was conducted to systematically assess the sensitivity of Bayesian linear regression models to prior specification. We systematically varied the sample size, prior location, and prior scale to observe their impact on posterior estimates for a known true effect size. Second, a case–control study using real-world patient data (N = 526) demonstrated the practical application of choosing informative priors. Bayesian logistic regression models were used to analyze the relationship between severe dementia and fall incidence, comparing results from priors based on existing literature (“believer”), conservative priors (“agnostic”), and priors assuming an opposite effect (“skeptical”).ResultsThe simulation study showed that strongly informative priors had a substantial influence on posterior estimates, particularly for smaller sample sizes. As the sample size increased, the influence of the data increased, and the estimates converged toward the true effect. In the case–control study, a standard frequentist logistic regression produced an odds ratio of 8.87 with a very wide and unstable confidence interval (1.66–165.19), likely due to data sparsity. In contrast, a Bayesian model using a moderately informative “believer” prior derived from existing research yielded a more stable and plausible odds ratio of 4.01 with a substantially narrower credible interval (1.99–8.78).ConclusionCareful and transparent specification of informative priors is a critical tool in Bayesian analysis, especially when data are sparse. By incorporating justified evidence-based assumptions, researchers can regularize models to prevent implausible outcomes and produce more stable, interpretable, and credible results. This approach enhances the robustness of statistical inference in fields where small sample sizes are a frequent challenge.

Can Revealed Preferences Clarify LLM Alignment and Steering?

LLMs are increasingly used to make or support high-stakes decisions under uncertainty, where alignment depends not only on factual accuracy but on how models weigh tradeoffs between different outcomes. We present an empirical pipeline for estimating the implied preferences that an LLM's observed choices optimize: we elicit the model's probability distribution over unknowns along with the choice it would make for the decision task and then fit a discrete choice model to recover the cost function that best rationalizes the model's decisions. We show how this revealed-preference description allows rigorous evaluation of whether models behave in a consistently goal-directed way, whether they can verbalize a description of their objectives which matches their revealed decision policy, and whether prompting can reliably steer those policies to implement a user-specified cost function. We apply this evaluation across four medical diagnosis domains and multiple frontier and open-source models. We find that while many models have a nontrivial degree of internal coherence, they also have significant weaknesses in faithfully reporting or adopting preferences in response to user direction.

Collaborative Causal Inference with Fair Incentives

Collaborative causal inference (CCI) aims to improve the estimation of the causal effect of treatment variables by utilizing data aggregated from multiple self-interested parties. Since their source data are valuable proprietary assets that can be costly or tedious to obtain, every party has to be incentivized to be willing to contribute to the collaboration, such as with a guaranteed fair and sufficiently valuable reward (than performing causal inference on its own). This paper presents a reward scheme designed using the unique statistical properties that are required by causal inference to guarantee certain desirable incentive criteria (e.g., fairness, benefit) for the parties based on their contributions. To achieve this, we propose a data valuation function to value parties’ data for CCI based on the distributional closeness of its resulting treatment effect estimate to that utilizing the aggregated data from all parties. Then, we show how to value the parties’ rewards fairly based on a modified variant of the Shapley value arising from our proposed data valuation for CCI. Finally, the Shapley fair rewards to the parties are realized in the form of improved, stochastically perturbed treatment effect estimates. We empirically demonstrate the effectiveness of our reward scheme using simulated and real-world datasets.

Picking on the Same Person: Does Algorithmic Monoculture lead to Outcome Homogenization?

As the scope of machine learning broadens, we observe a recurring theme of algorithmic monoculture: the same systems, or systems that share components (e.g. datasets, models), are deployed by multiple decision-makers. While sharing offers advantages like amortizing effort, it also has risks. We introduce and formalize one such risk, outcome homogenization: the extent to which particular individuals or groups experience the same outcomes across different deployments. If the same individuals or groups exclusively experience undesirable outcomes, this may institutionalize systemic exclusion and reinscribe social hierarchy. We relate algorithmic monoculture and outcome homogenization by proposing the component sharing hypothesis: if algorithmic systems are increasingly built on the same data or models, then they will increasingly homogenize outcomes. We test this hypothesis on algorithmic fairness benchmarks, demonstrating that increased data-sharing reliably exacerbates homogenization and individual-level effects generally exceed group-level effects. Further, given the current regime in AI of foundation models, i.e. pretrained models that can be adapted to myriad downstream tasks, we test whether model-sharing homogenizes outcomes across tasks. We observe mixed results: we find that for both vision and language settings, the specific methods for adapting a foundation model significantly influence the degree of outcome homogenization. We also identify societal challenges that inhibit the measurement, diagnosis, and rectification of outcome homogenization in deployed machine learning systems.

Promises and Perils of Pre-analysis Plans

The purpose of this paper is to help think through the advantages and costs of rigorous pre-specification of statistical analysis plans in economics. A pre-analysis plan pre-specifies in a precise way the analysis to be run before examining the data. A researcher can specify variables, data cleaning procedures, regression specifications, and so on. If the regressions are pre-specified in advance and researchers are required to report all the results they pre-specify, data-mining problems are greatly reduced. I begin by laying out the basics of what a statistical analysis plan actually contains so those researchers unfamiliar with it can better understand how it is done. In so doing, I have drawn both on standards used in clinical trials, which are clearly specified by the Food and Drug Administration, as well as my own practical experience from writing these plans in economics contexts. I then lay out some of the advantages of pre-specified analysis plans, both for the scientific community as a whole and also for the researcher. I also explore some of the limitations and costs of such plans. I then review a few pieces of evidence that suggest that, in many contexts, the benefits of using pre-specified analysis plans may not be as high as one might have expected initially. For the most part, I will focus on the relatively narrow issue of pre-analysis for randomized controlled trials.

A Statistical Interrogation of “The Case for Causality, Part 1” by Rausch and Haidt – Matthew B. Jané

I don’t know anything about the literature on social media and mental health so my focus on this post is to interrogate the statistical approach taken by the article written by Zach Rausch and Jonathon Haidt (link here) and to some extent the original meta-analysis by Ferguson.