Background Treatment of progression independent of relapse activity (PIRA) is a relevant unmet need in multiple sclerosis (MS), being only modestly affected by disease-modifying treatments (DMTs) which target predominantly adaptive immunity in the periphery. As chemotherapy administered during autologous haematopoietic stem cell transplantation (AHSCT) is bioavailable within the central nervous system (CNS), the hypothesis that AHSCT could affect long-term PIRA was explored in aggressive relapsing-remitting (RR)-MS.Methods Retrospective propensity-score matched study including RR-MS patients who received BEAM/ATG AHSCT or started natalizumab (NTZ, ie, controls) at our centre in Florence in the period 2007-2018. Main outcome: cumulative proportion of patients with PIRA during NTZ treatment epoch (ie, censoring controls at NTZ discontinuation) and whole follow-up (NTZ-other[o]DMTs, that is, including switch from NTZ to alternative DMTs).Results Thirty RR-MS were included in each group; median follow-up duration was 106 (6-209) months. NTZ was discontinued by 29/30 patients, who subsequently started alternative DMTs. Cumulative proportion of patients with PIRA did not differ between the two groups during the NTZ treatment epoch (p=0.990), but it was lower in AHSCT-treated compared with NTZ-oDMTs treated patients over the whole follow-up, being 10% vs 21% at year 5, and 10% versus 49% at year 10, respectively (p=0.020). AHSCT was superior to NTZ on relapses and NEDA-3, and to NTZ-oDMTs on all the secondary outcomes analysed. Baseline age and Expanded Disability Status Scale independently predicted PIRA in the whole cohort.Conclusion Timely treatment with AHSCT or DMTs targeting inflammation in both the peripheral and CNS compartments might prevent long-term PIRA in aggressive RR-MS.

In the seminal paper from 1960, Thistlethwaite and Campbell (1960) introduce the key ideas underlying regression discontinuity (RD) designs, which, even if initially almost completely ignored, have then acted as a fuse of a blowing number of studies applying and extending RD designs starting from the late nineties.Building on the original idea by Thistlethwaite and Campbell (1960), RD designs have been often described as designs that lead to locally randomized experiments for units with a realized value of a so-called forcing variable falling around a pre-fixed threshold.We embrace this perspective, and in this discussion we offer our view on how the original proposal by Thistlethwaite and Campbell (1960) should be formalized.We introduce an explicit local overlap assumption for a subpopulation around the threshold, for which we re-formulate the Stable Unit Treatment Value Assumption (SUTVA), and provide a formal definition of the hypothetical experiment underlying RD designs, by invoking a local randomization assumption.A distinguishing feature of this approach is that it embeds RD designs in a framework that is fully consistent with the potential outcome approach to causal inference.We discuss how to select suitable subpopulation(s) around the threshold with adjustment for multiple comparisons, and how to draw inference for the causal estimands of interest in this framework.We illustrate our approach in a study concerning the effects of University grants on students' dropout.

In semicompeting risks problems, nonterminal time-to-event outcomes such as time to hospital readmission are subject to truncation by death. These settings are often modeled with illness-death models for the hazards of the terminal and nonterminal events, but evaluating causal treatment effects with hazard models is problematic due to conditioning on survival (a post-treatment outcome) that is embedded in the definition of a hazard. Extending an existing survivor average causal effect (SACE) estimand, we frame the evaluation of treatment effects in the context of semicompeting risks with principal stratification and introduce two new causal estimands: the time-varying survivor average causal effect (TV-SACE) and the restricted mean survivor average causal effect (RM-SACE). These principal causal effects are defined among units that would survive regardless of assigned treatment. We adopt a Bayesian estimation procedure that parameterizes illness-death models for both treatment arms. We outline a frailty specification that can accommodate within-person correlation between nonterminal and terminal event times, and we discuss potential avenues for adding model flexibility. The method is demonstrated in the context of hospital readmission among late-stage pancreatic cancer patients.

We study causal inference in settings characterized by interference with a bipartite structure. There are two distinct sets of units: intervention units to which an intervention can be applied and outcome units on which the outcome of interest can be measured. Outcome units may be affected by interventions on some, but not all, intervention units, as captured by a bipartite graph. Examples of this setting can be found in analyses of the impact of pollution abatement in plants on health outcomes for individuals, or the effect of transportation network expansions on regional economic activity. We introduce and discuss a variety of old and new causal estimands for these bipartite settings. We do not impose restrictions on the functional form of the exposure mapping and the potential outcomes, thus allowing for heterogeneity, non-linearity, non-additivity, and potential interactions in treatment effects. We propose unbiased weighting estimators for these estimands from a design-based perspective, based on the knowledge of the bipartite network under general experimental designs. We derive their variance and prove consistency for increasing number of outcome units. Using the Chinese high-speed rail construction study, analyzed in Borusyak and Hull [2023], we discuss non-trivial positivity violations that depend on the estimands, the adopted experimental design, and the structure of the bipartite graph.

In many causal studies, outcomes are censored by death, in the sense that they are neither observed nor defined for units who die. In such studies, the focus is usually on the stratum of always survivors up to a single fixed time s. Building on a recent strand of the literature, we propose an extended framework for the analysis of longitudinal studies, where units can die at different time points, and the main endpoints are observed and well defined only up to the death time. We develop a Bayesian longitudinal principal stratification framework, where units are cross classified according to the longitudinal death status. Under this framework, the focus is on causal effects for the principal strata of units that would be alive up to a time point s irrespective of their treatment assignment, where these strata may vary as a function of s. We can get precious insights into the effects of treatment by inspecting the distribution of baseline characteristics within each longitudinal principal stratum, and by investigating the time trend of both principal stratum membership and survivor-average causal effects. We illustrate our approach for the analysis of a longitudinal observational study aimed to assess, under the assumption of strong ignorability of treatment assignment, the causal effects of a policy promoting start ups on firms survival and hiring policy, where firms hiring status is censored by death.

We study whether access to standardized test scores improves the quality of teachers' secondary school track recommendations, using Dutch data and a metric based on Principal Stratification in a quasi-randomized setting. Allowing teachers to revise their recommendations when test results exceed expectations increases the share of students successfully placed in more demanding tracks by at least 6

Clinical trials often allow patients in the control arm to switch to the treatment arm if their physical conditions are worse than certain tolerance levels. For instance, treatment switching arises in the Concorde clinical trial, which aims to assess causal effects on the time-to-disease progression or death of immediate versus deferred treatment with zidovudine among patients with asymptomatic HIV infection. The Intention-To-Treat analysis does not measure the effect of the actual receipt of the treatment and ignores the information on treatment switching. Other existing methods reconstruct the outcome a patient would have had if they had not switched under strong assumptions. Departing from the literature, we re-define the problem of treatment switching using principal stratification and focus on causal effects for patients belonging to subpopulations defined by the switching behavior under control. We use a Bayesian approach to inference, taking into account that (i) switching happens in continuous time; (ii) switching time is not defined for patients who never switch in a particular experiment; and (iii) survival time and switching time are subject to censoring. We apply this framework to analyze the synthetic data based on the Concorde study.

In clinical trials, patients may discontinue treatments prematurely, breaking the initial randomization. In our motivating study, a randomized controlled trial in oncology, patients assigned the investigational treatment may discontinue it due to adverse events. The ICH E9(R1) Addendum provides guidelines for handling such "intercurrent events." The right strategy to adopt depends on the questions of interest. We propose adopting a principal stratum strategy and decomposing the overall intention-to-treat effect into principal causal effects for groups of patients defined by their potential discontinuation behaviour. We first show how to implement a principal stratum strategy to assess causal effects on a survival outcome in the presence of continuous-time treatment discontinuation, its advantages, and the conclusions that can be drawn. Our strategy allows us to properly handle the time-to-event intermediate variable, which is not defined for patients who would not discontinue, and to account for the fact that the discontinuation time and the primary endpoint are subject to censoring. We employ a flexible model-based Bayesian approach to tackle these complexities, providing easily interpretable results. We apply this Bayesian principal stratification framework to analyze synthetic data of the motivating oncology trial. Supported by a simulation study, we shed light on the role of covariates in this framework. Beyond making structural and parametric assumptions more credible, they lead to more precise inference. Also, they can be used to characterize patients' discontinuation behavior, which could help inform clinical practice and future protocols.

During the COVID-19 pandemic, some studies suggested that transmission events could originate from schools. This study aimed to evaluate early-warning methods for identifying asymptomatic COVID-19 cases by implementing screening programs in schools. This study was conducted between September 2021 and May 2023, employing a rotation-screening plan for COVID-19 detection on a sample of students aged 14 to 19 years attending secondary schools in the regions of Tuscany, Veneto, Apulia and Friuli-Venezia Giulia. The schools were divided into two groups: experimental and control, with a ratio of 1:2. Two types of molecular salivary tests for SARS-CoV-2 were used to conduct the screening. This study included 16 experimental schools and 32 control schools. Out of 2527 subjects, 11,475 swabs were administrated, with 9177 tests deemed valid for analysis (a 20% loss of tests). Among these, 89 subjects (3.5%) tested positive. In control schools, 1895 subjects (6.5%) tested positive for SARS-CoV-2. This study recorded peaks in infections during the winter and autumn months, consistent with patterns observed in the general population. Beginning in September 2022, a shift occurred, with 2.6% of positive cases reported in the case schools compared to 0.3% in the control schools. Initially, most cases of COVID-19 were detected in the control schools; however, as the pandemic emergency phase concluded, cases were primarily identified through active screening in experimental schools. Although student participation in the active screening campaign was low during the project’s extension phase, this approach was efficacious in the early identification of positive cases.

The Brazil Bolsa Familia (BF) program is a conditional cash transfer program aimed to reduce short-term poverty by direct cash transfers and to fight long-term poverty by increasing human capital among poor Brazilian people. Eligibility for Bolsa Familia benefits depends on a cutoff rule, which classifies the BF study as a regression discontinuity (RD) design. Extracting causal information from RD studies is challenging. Following Li et al (2015) and Branson and Mealli (2019), we formally describe the BF RD design as a local randomized experiment within the potential outcome approach. Under this framework, causal effects can be identified and estimated on a subpopulation where a local overlap assumption, a local SUTVA and a local ignorability assumption hold. We first discuss the potential advantages of this framework over local regression methods based on continuity assumptions, which concern the definition of the causal estimands, the design and the analysis of the study, and the interpretation and generalizability of the results. A critical issue of this local randomization approach is how to choose subpopulations for which we can draw valid causal inference. We propose a Bayesian model-based finite mixture approach to clustering to classify observations into subpopulations where the RD assumptions hold and do not hold. This approach has important advantages: a) it allows to account for the uncertainty in the subpopulation membership, which is typically neglected; b) it does not impose any constraint on the shape of the subpopulation; c) it is scalable to high-dimensional settings; e) it allows to target alternative causal estimands than the average treatment effect (ATE); and f) it is robust to a certain degree of manipulation/selection of the running variable. We apply our proposed approach to assess causal effects of the Bolsa Familia program on leprosy incidence in 2009.

Safety evaluation of new therapies is an essential aspect of clinical trials, primarily quantifying the incidence of adverse events (AEs) and comparing it to a standard treatment. Despite its importance, safety analysis of adverse events is often rather simplistic: AEs probabilities are estimated without explicitly defining the target causal comparison and neglecting assumptions on the censoring mechanisms, leading to differential follow-up times. In this work, we make a first proposal addressing the evaluation of drugs' safety in the estimand strategy framework under the Principal Stratification approach. We define principal estimands and estimate them under the assumption of principal ignorability leveraging a fully Bayesian model.

Evaluating air quality interventions is confronted with the challenge of interference since interventions at a particular pollution source likely impact air quality and health at distant locations and air quality and health at any given location are likely impacted by interventions at many sources. The structure of interference in this context is dictated by complex atmospheric processes governing how pollution emitted from a particular source is transformed and transported across space, and can be cast with a bipartite structure reflecting the two distinct types of units: 1) interventional units on which treatments are applied or withheld to change pollution emissions; and 2) outcome units on which outcomes of primary interest are measured. We propose new estimands for bipartite causal inference with interference that construe two components of treatment: a "key-associated" (or "individual") treatment and an "upwind" (or "neighborhood") treatment. Estimation is carried out using a semi-parametric adjustment approach based on joint propensity scores. A reduced-complexity atmospheric model is deployed to characterize the structure of the interference network by modeling the movement of air parcels through time and space. The new methods are deployed to evaluate the effectiveness of installing flue-gas desulfurization scrubbers on 472 coal-burning power plants (the interventional units) in reducing Medicare hospitalizations among 21,577,552 Medicare beneficiaries residing across 25,553 ZIP codes in the United States (the outcome units).

Understanding causal relationships lies at the heart of scientific inquiry across diverse disciplines including economics, political science, public health, medicine, and education. The potential outcomes framework, originally introduced by Neyman and further developed by Rubin, offers a rigorous conceptual foundation for defining, identifying, and estimating causal effects. In this framework, causal inference is framed as a problem of missing data-at most one potential outcome is observed for each unit, corresponding to the treatment actually received, yet causal effects are contrasts of potential outcomes on a common set of units. Translating this conceptual framework into practice entails numerous methodological and practical challenges. These challenges differ in randomized experiments versus observational studies, but both settings demand careful attention to study design, assumptions, and methods for uncertainty quantification. I explore key issues in causal inference with an emphasis on Bayesian approaches, which offer distinct advantages in both the design and analysis stages of causal studies.

A key element in the education of youths is their sensitization to historical and artistic heritage. We analyze a field experiment conducted in Florence (Italy) to assess how appropriate incentives assigned to high-school classes may induce teens to visit museums in their free time. Non-compliance and spillover effects make the impact evaluation of this clustered encouragement design challenging. We propose to blend principal stratification and causal mediation, by defining sub-populations of units according to their compliance behavior and using the information on their friendship networks as mediator. We formally define principal natural direct and indirect effects and principal controlled direct and spillover effects, and use them to disentangle spillovers from other causal channels. We adopt a Bayesian approach for inference.

Principal stratification provides a causal inference framework for investigating treatment effects in the presence of a post-treatment variable. Principal strata play a key role in characterizing the treatment effect by identifying groups of units with the same or similar values for the potential post-treatment variable at all treatment levels. The literature has focused mainly on binary post-treatment variables. Few papers considered continuous post-treatment variables. In the presence of a continuous post-treatment, a challenge is how to identify and characterize meaningful coarsening of the latent principal strata that lead to interpretable principal causal effects. This paper introduces the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with binary treatment and continuous post-treatment variables. CASBAH leverages Bayesian nonparametric priors with an innovative hierarchical structure for the potential post-treatment outcomes that overcomes some of the limitations of previous works. Specifically, the novel features of our method allow for (i) identifying coarsened principal strata through a data-adaptive approach and (ii) providing a comprehensive quantification of the uncertainty surrounding stratum membership. Through Monte Carlo simulations, we show that the proposed methodology performs better than existing methods in characterizing the principal strata and estimating principal effects of the treatment. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

Principal stratification provides a causal inference framework that allows adjustment for confounded post-treatment variables when comparing treatments. Although the literature has focused mainly on binary post-treatment variables, there is a growing interest in principal stratification involving continuous post-treatment variables. However, characterizing the latent principal strata with a continuous post-treatment presents a significant challenge, which is further complicated in observational studies where the treatment is not randomized. In this paper, we introduce the Confounders-Aware SHared atoms BAyesian mixture (CASBAH), a novel approach for principal stratification with continuous post-treatment variables that can be directly applied to observational studies. CASBAH leverages a dependent Dirichlet process, utilizing shared atoms across treatment levels, to effectively control for measured confounders and facilitate information sharing between treatment groups in the identification of principal strata membership. CASBAH also offers a comprehensive quantification of uncertainty surrounding the membership of the principal strata. Through Monte Carlo simulations, we show that the proposed methodology has excellent performance in characterizing the latent principal strata and estimating the effects of treatment on post-treatment variables and outcomes. Finally, CASBAH is applied to a case study in which we estimate the causal effects of US national air quality regulations on pollution levels and health outcomes.

Background: The non-inferiority of the efficacy of subcutaneous (SC) vs intravenous (IV) administration of natalizumab (NTZ) once every 4 weeks in relapsing-remitting multiple sclerosis (RRMS) was recently demonstrated on the primary outcome of the REFINE study, i.e. MRI "combined unique active lesions number" (CUAL). To provide further evidence on the comparative efficacy of the two NTZ formulations, the effect of NTZ-SC vs NTZ-IV on annualized relapse rate (ARR) was investigated re-analysing the REFINE dataset. Methods: Post-hoc analysis of the REFINE study dataset aimed at exploring the non-inferiority of the efficacy of NTZ-SC vs NTZ-IV on ARR, i.e. the main secondary outcome of the REFINE study. Robustness of the non- inferiority analysis on CUAL with respect to the presence of cases from the SC arm who received a rescue treatment, including NTZ-IV, was also assessed by sensitivity analyses. Three non-inferiority margins were selected, corresponding to 25 %, 33 %, and 50 % fractions of the effect size of NTZ-IV vs placebo observed in the AFFIRM study on ARR (i.e. 0.125, 0.170, and 0.250). Results: Ninety-nine RRMS patients were included. The mean difference in the effect of NTZ-SC vs NTZ-IV on ARR was close to 0. The lower bound of the 95 % confidence interval (worst case scenario) was -0.119, corresponding to 25 % (p p = 0.025) of the effect of NTZ-IV vs placebo on ARR. Sensitivity analyses confirmed the results of the primary non-inferiority analysis on the outcome CUAL. Conclusions: NTZ-SC resulted not inferior to NTZ-IV on ARR for all the non-inferiority margins. The non- inferiority analysis of the efficacy of NTZ-SC vs NTZ-IV on CUAL was demonstrated to be robust with respect to rescued patients.

To quantify the probability that monthly intravenous (IV) and subcutaneous (SC) natalizumab (NTZ) had similar efficacy in relapsing-remitting multiple sclerosis (RRMS), non-inferiority of efficacy of NTZ-SC versus NTZ-IV on combined MRI unique active lesions number (CUAL) was explored re-analysing the REFINE data set. Non-inferiority margins were selected equal to 25%/33%/50% fractions of the effect size of NTZ-IV versus placebo observed in the AFFIRM study. Ninety-nine RRMS were included. NTZ-SC resulted not inferior to NTZ-IV on CUAL for all margins at 2.5% significance level, and, in worst-case scenario, its effect over NTZ-IV did not exceed 3.5% (or 2.8%) of the effect of NTZ-IV versus placebo.

Guido Wilhelmus Imbens is the Applied Econometrics Professor and Professor of Economics with a joint appointment at the Graduate School of Business and the Department of Economics at Stanford University. He has made fundamental contributions to econometric and statistical methods for drawing causal inferences in experimental and observational studies, and applications to a wide range of disciplines beyond economics, including psychology, education, policy, law, epidemiology, public health and other social and biomedical sciences. Together with his longtime collaborator, Joshua Angrist, Guido was awarded half the 2021 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for their methodological contributions to the analysis of causal relationships, with the other half going to David Card.

In causal inference studies, interest often lies in understanding the mechanisms through which a treatment affects an outcome. One approach is principal stratification (PS), which introduces well-defined causal effects in the presence of confounded post-treatment variables, or mediators, and clearly defines the assumptions for identification and estimation of those effects. The goal of this paper is to extend the PS framework to studies with continuous treatments and continuous post-treatment variables, which introduces a number of unique challenges both in terms of defining causal effects and performing inference. This manuscript provides three key methodological contributions: 1) we introduce novel principal estimands for continuous treatments that provide valuable insights into different causal mechanisms, 2) we utilize Bayesian nonparametric approaches to model the joint distribution of the potential mediating variables based on both Gaussian processes and Dirichlet process mixtures to ensure our approach is robust to model misspecification, and 3) we provide theoretical and numerical justification for utilizing a model for the potential outcomes to identify the joint distribution of the potential mediating variables. Lastly, we apply our methodology to a novel study of the relationship between the economy and arrest rates, and how this is potentially mediated by police capacity.