Statistical Challenges Research Articles

Individual participant data meta-analysis with mixed-effects transformation models.

SummaryOne-stage meta-analysis of individual participant data (IPD) poses several statistical and computational challenges. For time-to-event outcomes, the approach requires the estimation of complicated nonlinear mixed-effects models that are flexible enough to realistically capture the most important characteristics of the IPD. We present a model class that incorporates general normally distributed random effects into linear transformation models. We discuss extensions to model between-study heterogeneity in baseline risks and covariate effects and also relax the assumption of proportional hazards. Within the proposed framework, data with arbitrary random censoring patterns can be handled. The accompanying n}{}textsf{R} package tramME utilizes the Laplace approximation and automatic differentiation to perform efficient maximum likelihood estimation and inference in mixed-effects transformation models. We compare several variants of our model to predict the survival of patients with chronic obstructive pulmonary disease using a large data set of prognostic studies. Finally, a simulation study is presented that verifies the correctness of the implementation and highlights its efficiency compared to an alternative approach.

Operationalizing Healthspan as an Outcome for Clinical Trials in Geroscience

Efforts targeting biological aging pathways are advancing interventions which could extend healthy lifespan. Design of clinical trials to test such interventions necessitates an operational definition of healthspan, such as slowed accumulation or progression of multiple chronic diseases, functional decline, and disability. In this talk we explore these composite measures of healthspan proposed as outcomes for clinical trials in aging. This will be examined in example cases including multimorbidity and deficit accumulation frailty indices in an 8‐Year intensive lifestyle intervention trial, and an update on multimordbity, functional, and biomarker endpoints in the trial Targeting Aging with MEtformin (TAME). Through these examples we will explore issues related to effect sizes and statistical challenges related to composite endpoints. Finally, we will discuss the role existing and emerging biomarkers of aging in clinical trials in geroscience and summarize evidence linking biomarkers to clinically meaningful outcomes.

Invited Commentary: Predicting Incidence Rates of Rare Cancers-Adding Epidemiologic and Spatial Contexts.

There are unique challenges to identifying causes of and developing strategies for prevention of rare cancers, driven by the difficulty in estimating incidence, prevalence, and survival due to small case numbers. Using a Poisson modeling approach, Salmerón et al. (Am J Epidemiol. 2022;191(3):487-498) built upon their previous work to estimate incidence rates of rare cancers in Europe using a Bayesian framework, establishing a uniform prior for a measure of variability for country-specific incidence rates. They offer a methodology with potential transferability to other settings with similar cancer surveillance infrastructure. However, the approach does not consider the spatiotemporal correlation of rare cancer case counts and other, potentially more appropriate nonnormal probability distributions. In this commentary, we discuss the implications of future work from cancer epidemiology and spatial epidemiology perspectives. We describe the possibility of developing prediction models tailored to each type of rare cancer; incorporating the spatial heterogeneity in at-risk populations, surveillance coverage, and risk factors in these predictions; and considering a modeling framework with which to address the inherent spatiotemporal components of these data. We note that extension of this methodology to estimate subcountry rates at provincial, state, or smaller geographic levels would be useful but would pose additional statistical challenges.

When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence

When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence Service times of customers often depend on the delay they experience in queue, as was recently demonstrated empirically in restaurants, call centers, and intensive care units. Two forms of dependence mechanisms in service systems with customer abandonment are studied in this paper: First, the service requirement of a customer may evolve while waiting in queue. Second, customers may arrive to the system with an exogenous service and patience time that are stochastically dependent. Because either dependence mechanism can have significant impacts on a system's performance, it should be identified and taken into consideration for performance evaluation and decision-making purposes. However, identifying the source of dependence from observed data is hard because both the service times and patience times are censored due to customer abandonment. Further, even if the dependence is known to be the latter exogenous one, there remains the difficult task of fitting a joint service-patience times distribution to the censored data. In “When Service Times Depend on Customers’ Delays: A Relationship Between Two Models of Dependence”, Wu, Bassamboo, and Perry provide a solution to address these statistical challenges.

Adaptive designs for clinical trials have potential advantages, but statistical challenges lurk!

Linked Article: Cro et al. Br J Dermatol 2022; 186:245–256.

Prediction of sports injuries in football: a recurrent time-to-event approach using regularized Cox models

Data-based methods and statistical models are given special attention to the study of sports injuries to gain in-depth understanding of its risk factors and mechanisms. The objective of this work is to evaluate the use of shared frailty Cox models for the prediction of occurring sports injuries, and to compare their performance with different sets of variables selected by several regularized variable selection approaches. The study is motivated by specific characteristics commonly found for sports injury data, that usually include reduced sample size and even fewer number of injuries, coupled with a large number of potentially influential variables. Hence, we conduct a simulation study to address these statistical challenges and to explore regularized Cox model strategies together with shared frailty models in different controlled situations. We show that predictive performance greatly improves as more player observations are available. Methods that result in sparse models and favour interpretability, e.g. Best Subset Selection and Boosting, are preferred when the sample size is small. We include a real case study of injuries of female football players of a Spanish football club.

Predicting clinical events using Bayesian multivariate linear mixed models with application to scleroderma

BackgroundScleroderma is a serious chronic autoimmune disease in which a patient’s disease state manifests in several irregularly spaced longitudinal measures of lung, heart, skin, and other organ systems. Threshold crossings of pulmonary and cardiac measures indicate potentially life-threatening key clinical events including interstitial lung disease (ILD), cardiomyopathy, and pulmonary hypertension (PH). The statistical challenge is to accurately and precisely predict these events by using all of the clinical history for the patient at hand and for a reference population of patients.MethodsWe use a Bayesian mixed model approach to simultaneously characterize each individual’s future trajectories for several biomarkers. We estimate this model using a large population of patients from the Johns Hopkins Scleroderma Center Research Registry. The joint probabilities of critical lung and heart events are then calculated as a byproduct of the mixed model.ResultsThe performance of this approach is substantially better than standard, more common alternatives. In order to predict an individual’s risks in a clinical setting, we also develop a cross-validated, sequential prediction (CVSP) algorithm. As additional data are observed during a patient’s visit, the algorithm sequentially produces updated predictions for the future longitudinal trajectories and for ILD, cardiomyopathy, and PH. The updated prediction distributions with little additional computing, for example within an electronic health record (EHR).ConclusionsThis method that generates real-time personalized risk estimates has been implemented within the electronic health record system for clinical testing. To our knowledge, this work represents the first approach to compute personalized risk estimates for multiple scleroderma complications.

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACTObtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

Geometric Complexity and the Information-Theoretic Comparison of Functional-Response Models

The assessment of relative model performance using information criteria like AIC and BIC has become routine among functional-response studies, reflecting trends in the broader ecological literature. Such information criteria allow comparison across diverse models because they penalize each model's fit by its parametric complexity—in terms of their number of free parameters—which allows simpler models to outperform similarly fitting models of higher parametric complexity. However, criteria like AIC and BIC do not consider an additional form of model complexity, referred to as geometric complexity, which relates specifically to the mathematical form of the model. Models of equivalent parametric complexity can differ in their geometric complexity and thereby in their ability to flexibly fit data. Here we use the Fisher Information Approximation to compare, explain, and contextualize how geometric complexity varies across a large compilation of single-prey functional-response models—including prey-, ratio-, and predator-dependent formulations—reflecting varying apparent degrees and forms of non-linearity. Because a model's geometric complexity varies with the data's underlying experimental design, we also sought to determine which designs are best at leveling the playing field among functional-response models. Our analyses illustrate (1) the large differences in geometric complexity that exist among functional-response models, (2) there is no experimental design that can minimize these differences across all models, and (3) even the qualitative nature by which some models are more or less flexible than others is reversed by changes in experimental design. Failure to appreciate model flexibility in the empirical evaluation of functional-response models may therefore lead to biased inferences for predator–prey ecology, particularly at low experimental sample sizes where its impact is strongest. We conclude by discussing the statistical and epistemological challenges that model flexibility poses for the study of functional responses as it relates to the attainment of biological truth and predictive ability.

INSTITUTIONAL PRINCIPLES OF FORMATION OF CROSS-BORDER TRANSPORT AND LOGISTICS CLUSTER IN THE CONDITIONS OF DIGITAL AND SUSTAINABLE DEVELOPMENT

At the present stage, the strategic vector of transformation of transport and logistics systems in the border regions of Ukraine and the Visegrad Four countries is the integration of transport and logistics infrastructure into a transport and logistics cluster. The purpose of the paper is to substantiate the institutional basis for the formation of a cross-border transport and logistics cluster as an effective form of cooperation between the border regions of Ukraine (Volyn, Zakarpattya and Lviv regions) and the Visegrad Four (Poland, Slovakia, Hungary). Methodology. The theoretical and methodological basis of the study is the provisions of institutional theory, in particular the paradigms of evolutionary development, the theory of clustering, the concepts of strategic and logistical management, enterprise development management. The following general scientific methods were used in the research process: analysis and synthesis, statistical analysis, classification and systems approach, comparison and structural-logical generalization. The article presents the results of analytical assessment of the current state of development of transport and logistics systems of the Visegrad Four. Based on statistical analysis, features, trends, barriers and challenges to the functioning of transport and logistics systems in the border regions of Ukraine have been identified. Results. In order to modernize the regional ecosystems of Ukraine and the Visegrad Four countries, the conceptual provisions for the creation of a cross-border transport and logistics cluster are substantiated. It is proved that this cluster structure should include enterprises in the field of transport and logistics, innovation infrastructure (technology parks, business incubators, industrial parks, etc.), state, regional and local authorities, NGOs, research institutions and centers, higher education institutions that are geographically concentrated in cross-border regions. It is established that for the implementation of the conceptual foundations of the formation of cross-border transport and logistics cluster it is necessary to use a set of mechanisms, which include: regulatory, institutional, organizational and economic, financial, social, informational, environmental. Practical implications. The results of the study can be used to refine the current legal and regulatory framework, namely in amending the Association Agreement between Ukraine and the EU, the Laws of Ukraine “On Cross-Border Cooperation” and “On Principles of State Regional Policy”, the State Development Program cross-border cooperation for 2021-2027, Regional Development Strategies of Volyn, Zakarpattya and Lviv regions until 2027 in terms of creating appropriate institutional conditions for the formation of cross-border transport and logistics cluster and determining the mechanism of financial support for its operation. Value/originality. The author's approach to the improvement of legal and institutional support for the development of cross-border cluster structures in Ukraine is formulated, taking into account European practice.

The cost of privacy: Optimal rates of convergence for parameter estimation with differential privacy

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the (ε,δ)-differential privacy constraint. By refining the “tracing adversary” technique for lower bounds in the theoretical computer science literature, we improve existing minimax lower bound for low-dimensional mean estimation and establish new lower bounds for high-dimensional mean estimation and linear regression problems. We also design differentially private algorithms that attain the minimax lower bounds up to logarithmic factors. In particular, for high-dimensional linear regression, a novel private iterative hard thresholding algorithm is proposed. The numerical performance of differentially private algorithms is demonstrated by simulation studies and applications to real data sets.

Conceptualizing and quantifying body condition using structural equation modelling: A user guide.

Body condition is an important concept in behaviour, evolution and conservation, commonly used as a proxy of an individual's performance, for example in the assessment of environmental impacts. Although body condition potentially encompasses a wide range of health state dimensions (nutritional, immune or hormonal status), in practice most studies operationalize body condition using a single (univariate) measure, such as fat storage. One reason for excluding additional axes of variation may be that multivariate descriptors of body condition impose statistical and analytical challenges.Structural equation modelling (SEM) is used in many fields to study questions relating multidimensional concepts, and we here explain how SEM is a useful analytical tool to describe the multivariate nature of body condition. In this ‘Research Methods Guide’ paper, we show how SEM can be used to resolve different challenges in analysing the multivariate nature of body condition, such as (a) variable reduction and conceptualization, (b) specifying the relationship of condition to performance metrics, (c) comparing competing causal hypothesis and (d) including many pathways in a single model to avoid stepwise modelling approaches. We illustrated the use of SEM on a real‐world case study and provided R‐code of worked examples as a learning tool.We compared the predictive power of SEM with conventional statistical approaches that integrate multiple variables into one condition variable: multiple regression and principal component analyses. We show that model performance on our dataset is higher when using SEM and led to more accurate and precise estimates compared to conventional approaches.We encourage researchers to consider SEM as a flexible framework to describe the multivariate nature of body condition and thus understand how it affects biological processes, thereby improving the value of body condition proxies for predicting organismal performance. Finally, we highlight that it can be useful for other multidimensional ecological concepts as well, such as immunocompetence, oxidative stress and environmental conditions.

Modeling past event feedback through biomarker dynamics in the multistate event analysis for cardiovascular disease data

In cardiovascular studies we often observe ordered multiple events along disease progression which are, essentially, a series of recurrent events and terminal events with competing risk structure. One of the main interests is to explore the event specific association with the dynamics of longitudinal biomarkers. A new statistical challenge arises when the biomarkers carry information from the past event history, providing feedbacks for the occurrences of future events and, particularly, when these biomarkers are only intermittently observed with measurement errors. In this paper we propose a novel modeling framework where the recurrent events and terminal events are modeled as multistate processes and the longitudinal covariates that account for event feedbacks are described by random effects models. Considering the nature of long-term observation in cardiac studies, flexible models with semiparametric coefficients are adopted. To improve computation efficiency, we develop an one-step estimator of the regression coefficients and derive their asymptotic variances for the computation of the confidence intervals, based on the proposed asymptotically unbiased estimating equation. Simulation studies show that the naive estimators, which either ignore the past event feedbacks or the measurement errors, are biased. Our method achieves better coverage probability, compared to the naive methods. The model is motivated and applied to a dataset from the Atherosclerosis Risk in Communities Study.

Mid-term outcomes of off-pump versus on-pump coronary artery bypass graft surgery; statistical challenges in comparison

BackgroundDespite several studies comparing off- and on-pump coronary artery bypass grafting (CABG), the effectiveness and outcomes of off-pump CABG still remain uncertain.MethodsIn this registry-based study, we assessed 8163 patients who underwent isolated CABG between 2014 and 2016. Propensity score matching (PSM), inverse probability of weighting (IPW) and covariate adjustment were performed to correct for and minimize selection bias.ResultsThe overall mean age of the patients was 62 years, and 25.7% were women. Patients who underwent off-pump CABG had shorter length of hospitalization (p < 0.001), intubation time (p = 0.003) and length of ICU admission (p < 0.001). Off-pump CABG was associated with higher risk of 30-days mortality (OR: 1.7; 95% CI 1.09–2.65; p = 0.019) in unadjusted analysis. After covariate adjustment and matching (PSM and IPW), this difference was not statistically significant. After an average of 36.1 months follow-up, risk of MACCE and all-cause mortality didn’t have significant differences in both surgical methods by adjusting with IPW (HR: 1.03; 95% CI 0.87–1.24; p = 0.714; HR: 0.91; 95% CI 0.73–1.14; p = 578, respectively).ConclusionOff-pump and on-pump techniques have similar 30-day mortality (adjusted, PSM and IPW). Off-pump surgery is probably more cost-effective in short term; however, mid-term survival and MACCE trends in both surgical methods are comparable.

A review and evaluation of secondary school accountability in England: Statistical strengths, weaknesses and challenges for 'Progress 8' raised by COVID-19.

School performance measures are published annually in England to hold schools to account and to support parental school choice. This article reviews and evaluates the ‘Progress 8’ secondary school accountability system for state‐funded schools. We assess the statistical strengths and weaknesses of Progress 8 relating to: choice of pupil outcome attainment measure; potential adjustments for pupil input attainment and background characteristics; decisions around which schools and pupils are excluded from the measure; presentation of Progress 8 to users, choice of statistical model, and calculation of statistical uncertainty; and issues related to the volatility of school performance over time, including scope for reporting multi‐year averages. We then discuss challenges for Progress 8 raised by the COVID‐19 pandemic. Six simple recommendations follow to improve Progress 8 and school accountability in England. Context and implicationRationale for this studyThis study fulfils a need for a comprehensive statistical evaluation of the Progress 8 school accountability system in England, which has been in place since 2016.Why the new findings matterA review of Progress 8 is an important contribution as decisions on its calculation and presentation have important consequences for schools and pupils.Implications for educational researchers and policy makersOur findings on the statistical strengths and weaknesses of Progress 8 and the resulting recommendations made for improvements to the measure and school accountability have clear implications for informing policy makers in the educational system. This includes wider lessons extending beyond Progress 8 to other performance metrics and to other school systems internationally where similar issues apply. Additionally, the review highlights key concerns that the public and school practitioners may like to consider when drawing upon Progress 8 to make decisions around school choice and in assessing how well a school is performing.

The Role of the Ostensives in Understanding Quantitative Statistical Variables

Background: One of the main challenges of teaching statistics in basic education is the treatment of quantitative statistical variables because, besides the calculations involved in the abstract measures, understanding the behaviour of these variables and the meaning of their statistics is complex by their very nature. In this sense, using manipulable concrete materials and the student’s action as ostensive mathematical objects in the management and representation of this type of variable can help understand them. Objectives: this research investigates how the concrete manipulable materials and the student’s action contribute to understanding and representing quantitative statistical variables in different registers. Design: we make theoretical reflections on the active use of the ostensive objects in the representation and transformation of data into statistics – tables, graphs, and summary measures – in basic education based on the anthropological theory of the didactic and the theory of registers of semiotic representation. Data collection and analysis: this is a theoretical study that uses results already published in related research. Results: the analyses point out that the use of the ostensive objects helps students’ understand the statistical concepts and that from this point on, they represent and transform the representations of statistical information in different registers more fluidly. Conclusions: the study reveals that using the ostensives and the students’ actions in managing statistical concepts is a fundamental aspect of learning.

Applying a potential outcomes framework to estimate policy-relevant effects of exposure mixtures

BACKGROUND AND AIM: Interest in understanding the joint effects of multiple exposures (i.e., mixtures) is rapidly increasing, with a related proliferation of statistical methods for estimating these effects. However, commonly applied approaches to estimate effects of exposure mixtures often yield results that are difficult to interpret and are not easily mapped to public health actions. METHODS: By applying a potential outcomes framework for causal inference, investigators can ask questions about exposure mixtures that simulate effects of real-world interventions on sources of mixtures components. I discuss how to frame policy-relevant questions on sources of mixture components, and compare the interventions implied by common supervised and unsupervised analytic approaches. I also describe Bayesian g-computation, a promising statistical framework for estimating health effects of interventions on sources of exposure mixture components. RESULTS:Many common statistical approaches to address exposure mixtures yield results in the form of complex exposure-response surfaces or independent effects that do not acknowledge real-world correlation. In contrast, g-computation explicitly specifies a causal question and compares the expected outcome under exposure distributions that would occur with and without a hypothetical intervention on an exposure source. Applying a Bayesian approach to g-computation is useful to address common statistical challenges the occur in mixtures analyses such as high correlation and sparse data. CONCLUSIONS:Framing mixtures questions as potential interventions can improve causal inference and has the advantage of more directly informing potential environmental health practices, programs, and policies. KEYWORDS: Causal inference, Environmental epidemiology, Mixtures analysis

Real-time model calibration with deep reinforcement learning

The real-time, and accurate inference of model parameters is of great importance in many scientific and engineering disciplines that use computational models (such as a digital twin) for the analysis and prediction of complex physical processes. However, fast and accurate inference for processes of complex systems cannot easily be achieved in real-time with state-of-the-art methods under noisy real-world conditions with the requirement of a real-time response. The primary reason is that the inference of model parameters with traditional techniques based on optimization or sampling often suffers from computational and statistical challenges, resulting in a trade-off between accuracy and deployment time. In this paper, we propose a novel framework for inference of model parameters based on reinforcement learning. The proposed methodology is demonstrated and evaluated on two different physics-based models of turbofan engines. The experimental results demonstrate that the proposed methodology outperforms all other tested methods in terms of speed and robustness, with high inference accuracy.

A Metabolomic Aging Clock Using Human Cerebrospinal Fluid.

Quantifying the physiology of aging is essential for improving our understanding of age-related disease and the heterogeneity of healthy aging. Recent studies have shown that, in regression models using "-omic" platforms to predict chronological age, residual variation in predicted age is correlated with health outcomes, and suggest that these "omic clocks" provide measures of biological age. This paper presents predictive models for age using metabolomic profiles of cerebrospinal fluid (CSF) from healthy human subjects and finds that metabolite and lipid data are generally able to predict chronological age within 10 years. We use these models to predict the age of a cohort of subjects with Alzheimer's and Parkinson's disease and find an increase in prediction error, potentially indicating that the relationship between the metabolome and chronological age differs with these diseases. However, evidence is not found to support the hypothesis that our models will consistently overpredict the age of these subjects. In our analysis of control subjects, we find the carnitine shuttle, sucrose, biopterin, vitamin E metabolism, tryptophan, and tyrosine to be the most associated with age. We showcase the potential usefulness of age prediction models in a small data set (n = 85) and discuss techniques for drift correction, missing data imputation, and regularized regression, which can be used to help mitigate the statistical challenges that commonly arise in this setting. To our knowledge, this work presents the first multivariate predictive metabolomic and lipidomic models for age using mass spectrometry analysis of CSF.

Quantitative evaluation of footwear evidence: Initial workflow for an end-to-end system.

In the United States, footwear examiners make decisions about the sources of crime scene shoe impressions using subjective criteria. This has raised questions about the accuracy, repeatability, reproducibility, and scientific validity of footwear examinations. Currently, most footwear examiners follow a workflow that compares a questioned and test impression with regard to outsole design, size, wear, and randomly acquired characteristics (RACs). We augment this workflow with computer algorithms and statistical analysis so as to improve in the following areas: (1) quantifying the degree of correspondence between the questioned and test impressions with respect to design, size, wear, and RACs, (2) reducing the potential for cognitive bias, and (3) providing an empirical basis for examiner conclusions by developing a reference database of case-relevant pairs of impressions containing known mated and known nonmated impressions. Our end-to-end workflow facilitates all three of these points and is directly relatable to current practice. We demonstrate the workflow, which includes obtaining and interpreting outsole pattern scores, RAC comparison scores, and final scores, on two scenarios-a pristine example (involving very high quality Everspry EverOS scanner impressions) and a mock crime scene example that more closely resembles real casework. These examples not only demonstrate the workflow but also help identify the algorithmic, computational, and statistical challenges involved in improving the system for eventual deployment in casework.