Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm.

The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.

The performance of restricted AIC for irregular histogram models.

Histograms are frequently used to perform a preliminary study of data, such as finding outliers and determining the distribution's shape. It is common knowledge that choosing an appropriate number of bins is crucial to revealing the right information. It's also well known that using bins of different widths, which called unequal bin width, is preferable to using bins of equal width if the bin width is selected carefully. However this is a much difficult issue. In this research, a novel approach to AIC for histograms with unequal bin widths was proposed. We demonstrate the advantage of the suggested approach in comparison to others using both extensive Monte Carlo simulations and empirical examples.

Testing conditional quantile independence with functional covariate.

We propose a new non-parametric conditional independence test for a scalar response and a functional covariate over a continuum of quantile levels. We build a Cramer-von Mises type test statistic based on an empirical process indexed by random projections of the functional covariate, effectively avoiding the "curse of dimensionality" under the projected hypothesis, which is almost surely equivalent to the null hypothesis. The asymptotic null distribution of the proposed test statistic is obtained under some mild assumptions. The asymptotic global and local power properties of our test statistic are then investigated. We specifically demonstrate that the statistic is able to detect a broad class of local alternatives converging to the null at the parametric rate. Additionally, we recommend a simple multiplier bootstrap approach for estimating the critical values. The finite-sample performance of our statistic is examined through several Monte Carlo simulation experiments. Finally, an analysis of an EEG data set is used to show the utility and versatility of our proposed test statistic.

Spatial-temporal Bayesian accelerated failure time models for survival endpoints with applications to prostate cancer registry data.

Prostate cancer is the most common cancer after non-melanoma skin cancer and the second leading cause of cancer deaths in US men. Its incidence and mortality rates vary substantially across geographical regions and over time, with large disparities by race, geographic regions (i.e., Appalachia), among others. The widely used Cox proportional hazards model is usually not applicable in such scenarios owing to the violation of the proportional hazards assumption. In this paper, we fit Bayesian accelerated failure time models for the analysis of prostate cancer survival and take dependent spatial structures and temporal information into account by incorporating random effects with multivariate conditional autoregressive priors. In particular, we relax the proportional hazards assumption, consider flexible frailty structures in space and time, and also explore strategies for handling the temporal variable. The parameter estimation and inference are based on a Monte Carlo Markov chain technique under a Bayesian framework. The deviance information criterion is used to check goodness of fit and to select the best candidate model. Extensive simulations are performed to examine and compare the performances of models in different contexts. Finally, we illustrate our approach by using the 2004-2014 Pennsylvania Prostate Cancer Registry data to explore spatial-temporal heterogeneity in overall survival and identify significant risk factors.

A Comparison of Markov and Mechanistic Models for Soil-Transmitted Helminth Prevalence Projections in the Context of Survey Design.

Globally, there are over 1 billion people infected with soil-transmitted helminths (STHs), mostly living in marginalized settings with inadequate sanitation in sub-Saharan Africa and Southeast Asia. The World Health Organization recommends an integrated approach to STH morbidity control through improved access to sanitation and hygiene education and the delivery of preventive chemotherapy (PC) to school-age children delivered through schools. Progress of STH control programs is currently estimated using a baseline (pre-PC) school-based prevalence survey and then monitored using periodical school-based prevalence surveys, known as Impact Assessment Surveys (IAS). We investigated whether integrating geostatistical methods with a Markov model or a mechanistic transmission model for projecting prevalence forward in time from baseline can improve IAS design strategies. To do this, we applied these 2 methods to prevalence data collected in Kenya, before evaluating and comparing their performance in accurately informing optimal survey design for a range of IAS sampling designs. We found that, although both approaches performed well, the mechanistic method more accurately projected prevalence over time and provided more accurate information for guiding survey design. Both methods performed less well in areas with persistent STH hotspots where prevalence did not decrease despite multiple rounds of PC. Our findings show that these methods can be useful tools for more efficient and accurate targeting of PC. The general framework built in this paper can also be used for projecting prevalence and informing survey design for other neglected tropical diseases.

Implications of variability on medical device chemical equivalence assessment.

Chemical equivalence testing can be used to assess the biocompatibility implications of a materials or manufacturing change for a medical device. This testing can provide a relatively facile means to evaluate whether the change may result in additional or different toxicological concerns. However, one of the major challenges in the interpretation of chemical equivalence data is the lack established criteria for determining if two sets of extractables data are effectively equivalent. To address this gap, we propose a two-part approach based upon a relatively simple statistical model. First, the probability of a false positive conclusion, wherein there is an incorrectly perceived increase for a given analyte in the comparator relative to the baseline device, can be reduced to a prescribed level by establishing an appropriate acceptance criterion for the ratio of the observed means. Second, the probability of a false negative conclusion, where an actual increase in a given analyte cannot be discerned from the test results, can be minimized by specifying a limiting value of applicability based on the margin of safety (MoS) of the analyte. This approach provides a quantitative, statistically motivated method to interpret chemical equivalence data, despite the relatively high intrinsic variability and small number of replicates typically associated with a chemical characterization evaluation.

Bootstrap-quantile ridge estimator for linear regression with applications.

Bootstrap is a simple, yet powerful method of estimation based on the concept of random sampling with replacement. The ridge regression using a biasing parameter has become a viable alternative to the ordinary least square regression model for the analysis of data where predictors are collinear. This paper develops a nonparametric bootstrap-quantile approach for the estimation of ridge parameter in the linear regression model. The proposed method is illustrated using some popular and widely used ridge estimators, but this idea can be extended to any ridge estimator. Monte Carlo simulations are carried out to compare the performance of the proposed estimators with their baseline counterparts. It is demonstrated empirically that MSE obtained from our suggested bootstrap-quantile approach are substantially smaller than their baseline estimators especially when collinearity is high. Application to real data sets reveals the suitability of the idea.

Sociocognitive and Argumentation Perspectives on Psychometric Modeling in Educational Assessment.

Rapid advances in psychology and technology open opportunities and present challenges beyond familiar forms of educational assessment and measurement. Viewing assessment through the perspectives of complex adaptive sociocognitive systems and argumentation helps us extend the concepts and methods of educational measurement to new forms of assessment, such as those involving interaction in simulation environments and automated evaluation of performances. I summarize key ideas for doing so and point to the roles of measurement models and their relation to sociocognitive systems and assessment arguments. A game-based learning assessment SimCityEDU: Pollution Challenge! is used to illustrate ideas.

Supporting equitable and responsible highway safety improvement funding allocation strategies - Why AI prediction biases matter.

The existing methodologies for allocating highway safety improvement funding closely rely on the utilization of crash prediction models. Specifically, these models produce predictions that estimate future crash hazard levels in different geographical areas, which subsequently support the future funding allocation strategies. In recent years, there is a burgeoning interest in applying artificial intelligence (AI)-based models to perform crash prediction tasks. Despite the remarkable accuracy of these AI-based crash prediction models, they have been observed to yield biased prediction outcomes across areas of different socioeconomic statuses. These biases are primarily attributed to the inherent measurement and representation biases of AI-based prediction models. More precisely, measurement bias arises from the selection of target variables to reflect crash hazard levels, while representation bias results from the issue of imbalanced number of samples representing areas with different socioeconomic statuses within the dataset. Consequently, these biased prediction outcomes have the potential to perpetuate an unfair allocation of funding resources, contributing to worsen social inequality over time. Drawing upon a real-world case study in North Carolina, this study designs an AI-based crash prediction model that utilizes previous sociodemographic and crash-related variables to predict future severe crash rate of each area to reflect the crash hazardous level. By incorporating a fair regression framework, this study endeavors to transform the crash prediction model to become both fair and accurate, aiming to support equitable and responsible safety improvement funding allocation strategies.

Assessing the Negative Binomial-Lindley model for crash hotspot identification: Insights from Monte Carlo simulation analysis.

Identifying hazardous crash sites (or hotspots) is a crucial step in highway safety management. The Negative Binomial (NB) model is the most common model used in safety analyses and evaluations - including hotspot identification. The NB model, however, is not without limitations. In fact, this model does not perform well when data are highly dispersed, include excess zero observations, or have a long tail. Recently, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB. The NB-L model overcomes several limitations related to the NB, such as addressing the issue of excess zero observations in highly dispersed data. However, it is not clear how the NB-L model performs regarding the hotspot identification. In this paper, an innovative Monte Carlo simulation protocol was designed to generate a wide range of simulated data characterized by different means, dispersions, and percentage of zeros. Next, the NB-L model was written as a Full-Bayes hierarchical model and compared with the Full-Bayes NB model for hotspot identification using extensive simulation scenarios. Most previous studies focused on statistical fit, and showed that the NB-L model fits the data better than the NB. In this research, however, we investigated the performance of the NB-L model in identifying the hazardous sites. We showed that there is a trade-off between the NB-L and NB when it comes to hotspot identification. Multiple performance metrics were used for the assessment. Among those, the results show that the NB-L model provides a better specificity in identifying hotspots, while the NB model provides a better sensitivity, especially for highly dispersed data. In other words, while the NB model performs better in identifying hazardous sites, the NB-L model performs better, when budget is limited, by not selecting non-hazardous sites as hazardous.

Inequities in Conversion Practice Exposure at the Intersection of Ethnoracial and Gender Identities.

Objectives. To examine inequities in conversion practice exposure across intersections of ethnoracial groups and gender identity in the United States. Methods. Data were obtained from The Population Research in Identity and Disparities for Equality Study of sexual and gender minority people from 2019 to 2021 (n = 9274). We considered 3 outcomes: lifetime exposure, age of first exposure, and period between first and last exposure among those exposed to conversion practices. We used log-binomial, Cox proportional hazards, and negative binomial models to examine inequities by ethnoracial groups and gender identity adjusting for confounders. We considered additive interaction. Results. Conversion practice prevalence was highest among minoritized ethnoracial transgender and nonbinary participants (TNB; 8.6%). Compared with White cisgender participants, minoritized ethnoracial TNB participants had twice the prevalence (prevalence ratio = 2.16; 95% confidence interval [CI] = 1.62, 2.86) and risk (hazard ratio = 2.04; 95% CI = 1.51, 2.69) of conversion practice exposure. Furthermore, there was evidence of a positive additive interaction for age of first exposure. Conclusions. Minoritized ethnoracial TNB participants were most likely to recall experiencing conversion practices. Public Health Implications. Policies banning conversion practices may reduce the disproportionate burden experienced by minoritized ethnoracial TNB participants. (Am J Public Health. 2024;114(4):424-434. https://doi.org/10.2105/AJPH.2024.307580).

Statistical modelling of determinants of child stunting using secondary data and Bayesian networks: a UKRI Global Challenges Research Fund (GCRF) Action Against Stunting Hub protocol paper.

INTRODUCTION: Several factors have been implicated in child stunting, but the precise determinants, mechanisms of action and causal pathways remain poorly understood. The objective of this study is to explore causal relationships between the various determinants of child stunting. METHODS AND ANALYSIS: The study will use data compiled from national health surveys in India, Indonesia and Senegal, and reviews of published evidence on determinants of child stunting. The data will be analysed using a causal Bayesian network (BN)-an approach suitable for modelling interdependent networks of causal relationships. The model's structure will be defined in a directed acyclic graph and illustrate causal relationship between the variables (determinants) and outcome (child stunting). Conditional probability distributions will be generated to show the strength of direct causality between variables and outcome. BN will provide evidence of the causal role of the various determinants of child stunning, identify evidence gaps and support in-depth interrogation of the evidence base. Furthermore, the method will support integration of expert opinion/assumptions, allowing for inclusion of the many factors implicated in child stunting. The development of the BN model and its outputs will represent an ideal opportunity for transdisciplinary research on the determinants of stunting. ETHICS AND DISSEMINATION: Not applicable/no human participants included.

Modelling the GDP of KSA using linear and non-linear NNAR and hybrid stochastic time series models.

BACKGROUND: Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. METHODOLOGY: Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. RESULTS: The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. CONCLUSION: The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

Estimation of racial and language disparities in pediatric emergency department triage using statistical modeling and natural language processing.

OBJECTIVES: The study aims to assess racial and language disparities in pediatric emergency department (ED) triage using analytical techniques and provide insights into the extent and nature of the disparities in the ED setting. MATERIALS AND METHODS: The study analyzed a cross-sectional dataset encompassing ED visits from January 2019 to April 2021. The study utilized analytical techniques, including K-mean clustering (KNN), multivariate adaptive regression splines (MARS), and natural language processing (NLP) embedding. NLP embedding and KNN were employed to handle the chief complaints and categorize them into clusters, while the MARS was used to identify significant interactions among the clinical features. The study also explored important variables, including age-adjusted vital signs. Multiple logistic regression models with varying specifications were developed to assess the robustness of analysis results. RESULTS: The study consistently found that non-White children, especially African American (AA) and Hispanic, were often under-triaged, with AA children having >2 times higher odds of receiving lower acuity scores compared to White children. While the results are generally consistent, incorporating relevant variables modified the results for specific patient groups (eg, Asians). DISCUSSION: By employing a comprehensive analysis methodology, the study checked the robustness of the analysis results on racial and language disparities in pediatric ED triage. The study also recognized the significance of analytical techniques in assessing pediatric health conditions and analyzing disparities. CONCLUSION: The study's findings highlight the significant need for equal and fair assessment and treatment in the pediatric ED, regardless of their patients' race and language.

Longitudinal varying coefficient single-index model with censored covariates.

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database.

An information-theoretic approach for the assessment of a continuous outcome as a surrogate for a binary true endpoint based on causal inference: Application to vaccine evaluation.

Within the causal association paradigm, a method is proposed to assess the validity of a continuous outcome as a surrogate for a binary true endpoint. The methodology is based on a previously introduced information-theoretic definition of surrogacy and has two main steps. In the first step, a new model is proposed to describe the joint distribution of the potential outcomes associated with the putative surrogate and the true endpoint of interest. The identifiability issues inherent to this type of models are handled via sensitivity analysis. In the second step, a metric of surrogacy new to this setting, the so-called individual causal association is presented. The methodology is studied in detail using theoretical considerations, some simulations, and data from a randomized clinical trial evaluating an inactivated quadrivalent influenza vaccine. A user-friendly R package Surrogate is provided to carry out the evaluation exercise.

Assessment of nonlinear dose-response relationships via nonparametric regression.

We propose a simple approach to assess whether a nonlinear parametric model is appropriate to depict the dose-response relationships and whether two parametric models can be applied to fit a dataset via nonparametric regression. The proposed approach can compensate for the ANOVA, which is sometimes conservative, and is very easy to implement. We illustrate the performance by analyzing experimental examples and a small simulation study.

Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data.

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

A Mixed-Effects Model in Which the Parameters of the Autocorrelated Error Structure Can Differ between Individuals.

Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.

A Systematic Review of Methodologies Used in Models of the Treatment of Diabetes Mellitus.

BACKGROUND: Diabetes mellitus is a chronic and complex disease, increasing in prevalence and consequent health expenditure. Cost-effectiveness models with long time horizons are commonly used to perform economic evaluations of diabetes' treatments. As such, prediction accuracy and structural uncertainty are important features in cost-effectiveness models of chronic conditions. OBJECTIVES: The aim of this systematic review is to identify and review published cost-effectiveness models of diabetes treatments developed between 2011 and 2022 regarding their methodological characteristics. Further, it also appraises the quality of the methods used, and discusses opportunities for further methodological research. METHODS: A systematic literature review was conducted in MEDLINE and Embase to identify peer-reviewed papers reporting cost-effectiveness models of diabetes treatments, with time horizons of more than 5 years, published in English between 1 January 2011 and 31 of December 2022. Screening, full-text inclusion, data extraction, quality assessment and data synthesis using narrative synthesis were performed. The Philips checklist was used for quality assessment of the included studies. The study was registered in PROSPERO (CRD42021248999). RESULTS: The literature search identified 30 studies presenting 29 unique cost-effectiveness models of type 1 and/or type 2 diabetes treatments. The review identified 26 type 2 diabetes mellitus (T2DM) models, 3 type 1 DM (T1DM) models and one model for both types of diabetes. Fifteen models were patient-level models, whereas 14 were at cohort level. Parameter uncertainty was assessed thoroughly in most of the models, whereas structural uncertainty was seldom addressed. All the models where validation was conducted performed well. The methodological quality of the models with respect to structure was high, whereas with respect to data modelling it was moderate. CONCLUSIONS: Models developed in the past 12 years for health economic evaluations of diabetes treatments are of high-quality and make use of advanced methods. However, further developments are needed to improve the statistical modelling component of cost-effectiveness models and to provide better assessment of structural uncertainty.