Exchangeability Assumption Research Articles

Exchangeable coalescents beyond the Cannings class

We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to Ξ-coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built-in (fitness) inheritance mechanism, can be brought into our setting.

Sensitivity Analysis for Attributable Fraction in the Presence of Unmeasured Confounding.

A main goal of epidemiology is to provide an impact of an exposure on health outcomes. The attributable fraction (AF) is a widely used measure for quantifying its contribution. Various methods have been developed to estimate AF, including standardization, inverse probability of treatment weighting, and doubly robust methods. However, the validity of these methods is established based on the conditional exchangeability assumption, which cannot be tested using only observed data. To assess how vulnerable the research findings are to departures from this assumption, researchers need to conduct a sensitivity analysis. In this study, we propose novel sensitivity analysis methods for AF. Sensitivity analysis problems are formulated as optimization problems, and analytic solutions for the problem are derived. We illustrate our proposed sensitivity analysis methods with a publicly available dataset and examine how the AF of the mother's smoking status during pregnancy for low birth weight changes to the degree of unmeasured confounding.

Target Trial Emulation Using Cohort Studies: Estimating the Effect of Antihypertensive Medication Initiation on Incident Dementia.

Observational studies link high midlife systolic blood pressure to increased dementia risk. However, the synthesis of evidence from randomized controlled trials has not definitively demonstrated that antihypertensive medication use reduces dementia risk. Here, we emulate target trials of antihypertensive medication initiation on incident dementia using three cohort studies, with attention to potential violations of necessary assumptions. We emulated trials of antihypertensive medication initiation on incident dementia using data from the Atherosclerosis Risk in Communities study, Cardiovascular Health Study, and Health and Retirement Study. We used data-driven methods to restrict participants to initiators and noninitiators with overlap in propensity scores and positive control outcomes to look for violations of positivity and exchangeability assumptions. Analyses were limited by the small number of cohort participants who met eligibility criteria. Associations between antihypertensive medication initiation and incident dementia were inconsistent and imprecise (Atherosclerosis Risk in Communities: HR = 0.30 [0.05, 1.93]; Cardiovascular Health Study: HR = 0.66 [0.27, 1.64]; Health and Retirement Study: HR = 1.09 [0.75, 1.59]). More stringent propensity score restrictions had little effect on findings. Sensitivity analyses using a positive control outcome unexpectedly suggested antihypertensive medication initiation increased the risk of coronary heart disease in all three samples. Positive control outcome analyses suggested substantial residual confounding in effect estimates from our target trials, precluding conclusions about the impact of antihypertensive medication initiation on dementia risk through target trial emulation. Formalized processes for identifying violations of necessary assumptions will strengthen confidence in target trial emulation and avoid inappropriate confidence in emulated trial results.

Visualizing the assumptions of network meta-analysis.

Network meta-analysis (NMA) incorporates all available evidence into a general statistical framework for comparing multiple treatments. Standard NMAs make three major assumptions, namely homogeneity, similarity, and consistency, and violating these assumptions threatens an NMA's validity. In this article, we suggest a graphical approach to assessing these assumptions and distinguishing between qualitative and quantitative versions of these assumptions. In our plot, the absolute effect of each treatment arm is plotted against the level of effect modifiers, and the three assumptions of NMA can then be visually evaluated. We use four hypothetical scenarios to show how violating these assumptions can lead to different consequences and difficulties in interpreting an NMA. We present an example of an NMA evaluating steroid use to treat septic shock patients to demonstrate how to use our graphical approach to assess an NMA's assumptions and how this approach can help with interpreting the results. We also show that all three assumptions of NMA can be summarized as an exchangeability assumption. Finally, we discuss how reporting of NMAs can be improved to increase transparency of the analysis and interpretability of the results.

Discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data" by Ethan M. Alt, Xiuya Chang, Xun Jiang, Qing Liu, May Mo, H. Amy Xia, and Joseph G. Ibrahim.

In the following discussion, we describe the various assumptions of exchangeability that have been made in the context of Bayesian borrowing and related models. In this context, we are able to highlight the difficulty of dynamic Bayesian borrowing under the assumption of individuals in the historical data being exchangeable with the current data and thus the strengths and novel features of the latent exchangeability prior. As borrowing methods are popular within clinical trials to augment the control arm, some potential challenges are identified with the application of the approach in this setting.

Depicting deterministic variables within directed acyclic graphs (DAGs): An aid for identifying and interpreting causal effects involving derived variables and compositional data.

Deterministic variables are variables that are functionally determined by one or more parent variables. They commonly arise when a variable has been functionally created from one or more parent variables, as with derived variables, and in compositional data, where the 'whole' variable is determined from its 'parts'. This article introduces how deterministic variables may be depicted within directed acyclic graphs (DAGs) to help with identifying and interpreting causal effects involving derived variables and/or compositional data. We propose a two-step approach in which all variables are initially considered, and a choice is made whether to focus on the deterministic variable or its determining parents. Depicting deterministic variables within DAGs brings several benefits. It is easier to identify and avoid misinterpreting tautological associations, i.e., self-fulfilling associations between deterministic variables and their parents, or between sibling variables with shared parents. In compositional data, it is easier to understand the consequences of conditioning on the 'whole' variable, and correctly identify total and relative causal effects. For derived variables, it encourages greater consideration of the target estimand and greater scrutiny of the consistency and exchangeability assumptions. DAGs with deterministic variables are a useful aid for planning and interpreting analyses involving derived variables and/or compositional data.

Learning about treatment effects in a new target population under transportability assumptions for relative effect measures.

Investigators often believe that relative effect measures conditional on covariates, such as risk ratios and mean ratios, are "transportable" across populations. Here, we examine the identification of causal effects in a target population using an assumption that conditional relative effect measures are transportable from a trial to the target population. We show that transportability for relative effect measures is largely incompatible with transportability for difference effect measures, unless the treatment has no effect on average or one is willing to make even stronger transportability assumptions that imply the transportability of both relative and difference effect measures. We then describe how marginal (population-averaged) causal estimands in a target population can be identified under the assumption of transportability of relative effect measures, when we are interested in the effectiveness of a new experimental treatment in a target population where the only treatment in use is the control treatment evaluated in the trial. We extend these results to consider cases where the control treatment evaluated in the trial is only one of the treatments in use in the target population, under an additional partial exchangeability assumption in the target population (i.e., an assumption of no unmeasured confounding in the target population with respect to potential outcomes under the control treatment in the trial). We also develop identification results that allow for the covariates needed for transportability of relative effect measures to be only a small subset of the covariates needed to control confounding in the target population. Last, we propose estimators that can be easily implemented in standard statistical software and illustrate their use using data from a comprehensive cohort study of stable ischemic heart disease.

Reporting and Description of Research Methodology in Studies Estimating Effects of Firearm Policies.

Evidence about which firearm policies work, to what extent, and for whom is hotly debated, perhaps partly because variation in research methodology has produced mixed and inconclusive effect estimates. We conducted a scoping review of firearm policy research in the health sciences in the United States, focusing on methodological considerations for causal inference. We identified original, empirical articles indexed in PubMed from 1 January 2000 to 1 September 2021 that examined any of 18 prespecified firearm policies. We extracted key study components, including policy type(s) examined, policy operationalization, outcomes, study setting and population, study approach and design, causal language, and whether and how authors acknowledged potential sources of bias. We screened 7733 articles and included 124. A plurality of studies used a legislative score as their primary exposure (n = 39; 32%) and did not examine change in policies over time (n = 47; 38%). Most examined firearm homicide (n = 51; 41%) or firearm suicide (n = 40; 32%) as outcomes. One-third adjusted for other firearm policies (n = 41; 33%). Three studies (2%) explicitly mentioned that their goal was to estimate causal effects, but over half used language implying causality (n = 72; 58%). Most acknowledged causal identification assumptions of temporality (n = 91; 73%) and exchangeability (n = 111; 90%); other assumptions were less often acknowledged. One-third of studies included bias analyses (n = 42; 34%). We identified a range of methodologic approaches in firearm policy research in the health sciences. Acknowledging the imitations of data availability and quality, we identify opportunities to improve causal inferences about and reporting on the effects of firearm policies on population health.

Uncertainty Quantification of a Machine Learning Model for Identification of Isolated Nonlinearities with Conformal Prediction

Abstract Structural nonlinearities are often spatially localized, such joints and interfaces, localized damage, or isolated connections, in an otherwise linearly behaving system. Quinn and Brink [12] modeled this localized nonlinearity as a deviatoric force component. In other previous work [13], the authors proposed a physics-informed machine learning framework to determine the deviatoric force from measurements obtained only at the boundary of the nonlinear region, assuming a noise-free environment. However, in real experimental applications, the data are expected to contain noise from a variety of sources. In the present work, we explore the sensitivity of the trained network by comparing the network responses when trained on deterministic (“noise-free”) model data and model data with additive noise (“noisy”). As the neural network does not yield a closed-form transformation from the input distribution to the response distribution, we leverage the use of conformal sets to build an illustration of sensitivity. Through the conformal set assumption of exchangeability, we may build a distribution-free prediction interval for both network responses of the clean and noisy training sets. This work will explore the application of conformal sets for uncertainty quantification of a deterministic structure-preserving neural network and its deployment in a structural health monitoring framework to detect deviations from a baseline state based on noisy measurements.

A basket trial design based on constrained hierarchical Bayesian model for latent subgroups

ABSTRACT It is well known a basket trial consisting of multiple cancer types has the potential of borrowing strength across the baskets defined by the cancer types, leading to an efficient design in terms of sample size and trial duration. The treatment effects in those baskets are often heterogeneous and categorized by the cancer types being sensitive or insensitive to the treatment. Hence, the assumption of exchangeability in many existing basket trials may be violated, and there is a need to design trials without this assumption. In this paper, we simplify the constrained hierarchical Bayesian model for latent subgroups (CHBM-LS) for two classifiers to deal with the potential heterogeneity of treatment effects due to the single classifier of the cancer type. Different baskets are aggregated into subgroups using a latent subgroup modeling approach. The treatment effects are similar and exchangeable to facilitate information borrowing within each latent subgroup. Applying the simplified CHBM-LS approach to the real basket trials where baskets defined by only cancer types shows better performance than other available approaches. Further simulation study also demonstrates this CHBM-LS approach outperforms other approaches with higher statistical power and better-controlled type I error rates under various scenarios.

Conformal Loss-Controlling Prediction.

Conformal prediction (CP) is a learning framework controlling prediction coverage of prediction sets, which can be built on any learning algorithm for point prediction. This work proposes a learning framework named conformal loss-controlling prediction, which extends CP to the situation where the value of a loss function needs to be controlled. Different from existing works about risk-controlling prediction sets and conformal risk control with the purpose of controlling the expected values of loss functions, the proposed approach in this article focuses on the loss for any test object, which is an extension of CP from miscoverage loss to some general loss. The controlling guarantee is proved under the assumption of exchangeability of data in finite-sample cases and the framework is tested empirically for classification with a class-varying loss and statistical postprocessing of numerical weather forecasting applications, which are introduced as point-wise classification and point-wise regression problems. All theoretical analysis and experimental results confirm the effectiveness of our loss-controlling approach.

Bayesian Methods for Information Borrowing in Basket Trials: An Overview.

Basket trials allow simultaneous evaluation of a single therapy across multiple cancer types or subtypes of the same cancer. Since the same treatment is tested across all baskets, it may be desirable to borrow information across them to improve the statistical precision and power in estimating and detecting the treatment effects in different baskets. We review recent developments in Bayesian methods for the design and analysis of basket trials, focusing on the mechanism of information borrowing. We explain the common components of these methods, such as a prior model for the treatment effects that embodies an assumption of exchangeability. We also discuss the distinct features of these methods that lead to different degrees of borrowing. Through simulation studies, we demonstrate the impact of information borrowing on the operating characteristics of these methods and discuss its broader implications for drug development. Examples of basket trials are presented in both phase I and phase II settings.

Navigating Mendelian Randomization in Sleep Medicine: Challenges, Opportunities, and Best Practices.

Mendelian randomization (MR) has become an influential method for elucidating causal links between sleep traits and disorders, and health outcomes. This article provides sleep medicine specialists with an overview of MR, emphasizing its applications and limitations in health research, particularly in the context of sleep research. The article addresses key challenges in conducting and interpreting MR studies on sleep, focusing on the core assumptions of relevance, exchangeability, and exclusion restriction. The importance of proper genetic instrument selection, bias mitigation, and cautious result interpretation is emphasized. Strategies are recommended to enhance the quality of MR studies in sleep medicine, including collaborations between MR experts and sleep specialists. The paper also explores sleep medicine-specific issues like analyzing binary traits and addressing heterogeneity in pooled analyses. Guidance is provided on transparent reporting of MR findings, stressing the need for comprehensive effect estimates, confidence intervals, and p-values. We conclude by advocating for rigorous MR implementation in sleep research to deepen our understanding of sleep-health relationships. By following best practices in study design, analysis, and reporting, researchers can reinforce the credibility and impact of MR findings in sleep medicine, ultimately improving patient care and public health strategies.

Directed Acyclic Graph Assisted Method For Estimating Average Treatment Effect

ABSTRACT Observational data, such as electronic clinical records and claims data, can prove invaluable for evaluating the Average Treatment Effect (ATE) and supporting decision-making, provided they are employed correctly. The Inverse Probability of Treatment Weighting (IPTW) method, based on propensity scores, has demonstrated remarkable efficacy in estimating ATE, assuming that the assumptions of exchangeability, consistency, and positivity are met. Directed Acyclic Graphs (DAGs) offer a practical approach to assess the exchangeability assumption, which asserts that treatment assignment and potential outcomes are independent given a set of confounding variables that block all backdoor paths from treatment assignment to potential outcomes. To ensure a consistent ATE estimator, one can adjust for a minimally sufficient adjustment set of confounding variables that block all backdoor paths from treatment assignment to the outcome. To enhance the efficiency of ATE estimators, our proposal involves incorporating both the minimally sufficient adjustment set of confounding variables and predictors into the propensity score model. Extensive simulations were conducted to evaluate the performance of propensity score-based IPTW methods in estimating ATE when different sets of covariates were included in the propensity score models. The simulation results underscored the significance of including the minimally sufficient adjustment set of confounding variables along with predictors in the propensity score models to obtain a consistent and efficient ATE estimator. We applied this proposed method to investigate whether tracheostomy was causally associated with in-hospital infant mortality, utilizing the 2016 Healthcare Cost and Utilization Project Kids’ Inpatient Database. The estimated ATE was found to be approximately 2.30%–2.46% with p-value >0.05.

Improving conformalized quantile regression through cluster-based feature relevance

Conformalized quantile regression, a cutting-edge and model-agnostic algorithm, has emerged as a recent innovation to generate valid prediction intervals on finite samples while addressing heteroscedasticity. It starts by employing quantile regression to estimate conditional quantiles. Subsequently, these estimated conditional quantiles undergo a rectification process using conformal prediction. Under the assumption of exchangeability, a slightly weaker form of independent and identically distributed (i.i.d.) data, the resulting prediction intervals are valid in finite samples. However, a drawback of the proposed conformalization step is identified: it lacks the capacity to adapt to heteroscedasticity due to its independence from the input. To overcome this limitation, we propose an improvement that involves partitioning the covariates space into clusters, assigning higher weights to features with greater predictive power. Following that, within each cluster, a conformal step is applied, leveraging a rectification that is reliant on the input cluster-wise.To demonstrate the superiority of our improved version over the classic version of conformalized quantile regression, we conducted a comprehensive comparison of their respective prediction intervals using synthetic data.

Investigation of the structure and magnitude of time-varying uncontrolled confounding in simulated cohort data analyzed using g-computation.

When estimating the effect of time-varying exposures on longer-term outcomes, the assumption of conditional exchangeability or no uncontrolled confounding extends beyond baseline confounding to include time-varying confounding. We illustrate the structures and magnitude of uncontrolled time-varying confounding in exposure effect estimates obtained from g-computation when sequential conditional exchangeability is violated. We used directed acyclic graphs (DAGs) to depict time-varying uncontrolled confounding. We performed simulations and used g-computation to quantify the effects of each time-varying exposure for each DAG type. Models adjusting all time-varying confounders were considered the true (bias-adjusted) estimate. The exclusion of time-varying uncontrolled confounders represented the biased effect estimate and an unmet 'no uncontrolled confounding' assumption. True and biased estimates were compared across DAGs, with different magnitudes of uncontrolled confounding. Time-varying uncontrolled confounding can present in several scenarios, including relationships into subsequently measured exposure(s), outcome, unmeasured confounder(s) and other measured confounder(s). In simulations, effect estimates obtained from g-computation were more biased in DAGs when the uncontrolled confounders were directly related to the outcome. Complex DAGs that included relationships between uncontrolled confounders and other variables and relationships where exposures caused uncontrolled confounders at the next time point resulted in the most biased effect estimates. In these complex DAGs, excluding uncontrolled confounders affected the multiple effect estimates. Time-varying uncontrolled confounding has the potential to substantially impact observed effect estimates. Given the importance of longitudinal studies in advising public health, the impact of time-varying uncontrolled confounding warrants more recognition and evaluation using quantitative bias analysis.

Exact first moments of the RV coefficient by invariant orthogonal integration

The RV coefficient measures the similarity between two multivariate configurations, and its significance testing has attracted various proposals in the last decades. We present a new approach, the invariant orthogonal integration, permitting to obtain the exact first four moments of the RV coefficient under the null hypothesis.Our proposal can be applied to any multivariate setting endowed with Euclidean distances between the observations. It also covers the weighted setting of observations of unequal importance, where the exchangeability assumption, justifying the usual permutation tests, breaks down.The proposed RV moments express as simple functions of the kernel eigenvalues occurring in the weighted multidimensional scaling of the two configurations (spectral effective dimensionality, spectral skewness and spectral excess kurtosis). The expressions for the third and fourth moments seem original, and explain the marked asymmetry and kurtosis of the RV coefficient. They permit to test the significance of the RV coefficient by Cornish–Fisher cumulant expansion, beyond the normal approximation, as illustrated on a small dataset.The first three moments can be obtained by elementary means, but computing the fourth moment requires a more sophisticated apparatus, the Weingarten calculus for orthogonal groups.

Regression of binary network data with exchangeable latent errors

AbstractUndirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

Approximating Full Conformal Prediction at Scale via Influence Functions

Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, a CP guarantees that the error rate is at most a chosen significance level, irrespective of whether the underlying model is misspecified. However, the prohibitive computational costs of full CP led researchers to design scalable alternatives, which alas do not attain the same guarantees or statistical power of full CP. In this paper, we use influence functions to efficiently approximate full CP. We prove that our method is a consistent approximation of full CP, and empirically show that the approximation error becomes smaller as the training set increases; e.g., for 1,000 training points the two methods output p-values that are

Reliability analysis for system with dependent components based on survival signature and copula theory

Recently, survival signature theory has been widely used in system reliability analysis. However, there are few studies that address the extension of survival signature theory to component-dependent systems. This study proposes a copula-based survival signature method to obtain an analytical solution for system reliability considering component dependence. It consists of two steps: constructing the dependence structure and utilizing the copula function to compute the analytical probability structure. The effectiveness of the Archimedean copula function in describing component dependence and its compliance with the exchangeability assumption in survival signature theory are first derived. Then, using Sklar's theorem, the analytical solution for the probability structure is determined based on the inclusion-exclusion principle. Finally, the hierarchical Archimedean copula function is employed to build a more sophisticated dependent structure. It is demonstrated that the satisfaction of the exchangeability assumption under the hierarchical Archimedean copula structures depends only on whether the joint distribution probability function of the components in the same type is constructed by a unique Archimedean copula function. Three separate systems with imprecise dependent information are employed in the reliability analysis in order to show the validity of the proposed method. The findings show that given a straightforward series-parallel system with a single type of component, the system reliability initially drops and then rises as the dependence parameters in the copula function grow at each time point. Additionally, the approach is more precise and effective than the simulation method when it comes to the study of complex systems.