Statistical inference on nonparametric regression model with approximation of Fourier series function: Estimation and hypothesis testing.

Nonparametric regression is an approximation method in regression analysis that is not constrained by the assumption of knowing the regression curve. One of the functions to approximate the curve is a Fourier series function. The nonparametric regression model with approximation of a Fourier series function has been widely discussed by several researchers. However, discussions on statistical inference, particularly in partial hypothesis testing, has not been carried out previously. Therefore, the purpose of this research is to discuss the statistical inference on nonparametric regression model with approximation of a Fourier series function. The discussion includes parameter and model estimations, simultaneous and partial hypotheses testing. In the application, we use life expectancy data from East Java Province during 2022. Based on data analysis, we obtain a model estimation with an R-square value of 96.24 %. At a 5 % significance level, the parameters simultaneously have a significant influence on the model. Partially, four parameters are not significant. However, overall, the predictor variables significantly influence the life expectancy data.•The Fourier series function used is a Fourier series function introduced by Bilodeau (1992).•The model estimation is obtained by selecting the optimal number of oscillation parameters.•The statistical test is obtained using the LRT method.

Improved inference of population histories by integrating genomic and epigenomic data.

With the availability of high-quality full genome polymorphism (SNPs) data, it becomes feasible to study the past demographic and selective history of populations in exquisite detail. However, such inferences still suffer from a lack of statistical resolution for recent, for example bottlenecks, events, and/or for populations with small nucleotide diversity. Additional heritable (epi)genetic markers, such as indels, transposable elements, microsatellites, or cytosine methylation, may provide further, yet untapped, information on the recent past population history. We extend the Sequential Markovian Coalescent (SMC) framework to jointly use SNPs and other hyper-mutable markers. We are able to (1) improve the accuracy of demographic inference in recent times, (2) uncover past demographic events hidden to SNP-based inference methods, and (3) infer the hyper-mutable marker mutation rates under a finite site model. As a proof of principle, we focus on demographic inference in Arabidopsis thaliana using DNA methylation diversity data from 10 European natural accessions. We demonstrate that segregating single methylated polymorphisms (SMPs) satisfy the modeling assumptions of the SMC framework, while differentially methylated regions (DMRs) are not suitable as their length exceeds that of the genomic distance between two recombination events. Combining SNPs and SMPs while accounting for site- and region-level epimutation processes, we provide new estimates of the glacial age bottleneck and post-glacial population expansion of the European A. thaliana population. Our SMC framework readily accounts for a wide range of heritable genomic markers, thus paving the way for next-generation inference of evolutionary history by combining information from several genetic and epigenetic markers.

Effectiveness of probabilistic contact tracing in epidemic containment: The role of superspreaders and transmission path reconstruction.

The recent COVID-19 pandemic underscores the significance of early stage nonpharmacological intervention strategies. The widespread use of masks and the systematic implementation of contact tracing strategies provide a potentially equally effective and socially less impactful alternative to more conventional approaches, such as large-scale mobility restrictions. However, manual contact tracing faces strong limitations in accessing the network of contacts, and the scalability of currently implemented protocols for smartphone-based digital contact tracing becomes impractical during the rapid expansion phases of the outbreaks, due to the surge in exposure notifications and associated tests. A substantial improvement in digital contact tracing can be obtained through the integration of probabilistic techniques for risk assessment that can more effectively guide the allocation of diagnostic tests. In this study, we first quantitatively analyze the diagnostic and social costs associated with these containment measures based on contact tracing, employing three state-of-the-art models of SARS-CoV-2 spreading. Our results suggest that probabilistic techniques allow for more effective mitigation at a lower cost. Secondly, our findings reveal a remarkable efficacy of probabilistic contact-tracing techniques in performing backward and multistep tracing and capturing superspreading events.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring.

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

Bayesian reweighting of biomolecular structural ensembles using heterogeneous cryo-EM maps with the cryoENsemble method.

Cryogenic electron microscopy (cryo-EM) has emerged as a powerful method for the determination of structures of complex biological molecules. The accurate characterisation of the dynamics of such systems, however, remains a challenge. To address this problem, we introduce cryoENsemble, a method that applies Bayesian reweighting to conformational ensembles derived from molecular dynamics simulations to improve their agreement with cryo-EM data, thus enabling the extraction of dynamics information. We illustrate the use of cryoENsemble to determine the dynamics of the ribosome-bound state of the co-translational chaperone trigger factor (TF). We also show that cryoENsemble can assist with the interpretation of low-resolution, noisy or unaccounted regions of cryo-EM maps. Notably, we are able to link an unaccounted part of the cryo-EM map to the presence of another protein (methionine aminopeptidase, or MetAP), rather than to the dynamics of TF, and model its TF-bound state. Based on these results, we anticipate that cryoENsemble will find use for challenging heterogeneous cryo-EM maps for biomolecular systems encompassing dynamic components.

Global transcription regulation revealed from dynamical correlations in time-resolved single-cell RNA sequencing.

Single-cell transcriptomics reveals significant variations in transcriptional activity across cells. Yet, it remains challenging to identify mechanisms of transcription dynamics from static snapshots. It is thus still unknown what drives global transcription dynamics in single cells. We present a stochastic model of gene expression with cell size- and cell cycle-dependent rates in growing and dividing cells that harnesses temporal dimensions of single-cell RNA sequencing through metabolic labeling protocols and cel lcycle reporters. We develop a parallel and highly scalable approximate Bayesian computation method that corrects for technical variation and accurately quantifies absolute burst frequency, burst size, and degradation rate along the cell cycle at a transcriptome-wide scale. Using Bayesian model selection, we reveal scaling between transcription rates and cell size and unveil waves of gene regulation across the cell cycle-dependent transcriptome. Our study shows that stochastic modeling of dynamical correlations identifies global mechanisms of transcription regulation. A record of this paper's transparent peer review process is included in the supplemental information.

Inference on an interacting diffusion system with application to in vitro glioblastoma migration (publication template).

Glioblastoma multiforme is a highly aggressive form of brain cancer, with a median survival time for diagnosed patients of 15 months. Treatment of this cancer is typically a combination of radiation, chemotherapy and surgical removal of the tumour. However, the highly invasive and diffuse nature of glioblastoma makes surgical intrusions difficult, and the diffusive properties of glioblastoma are poorly understood. In this paper, we introduce a stochastic interacting particle system as a model of in vitro glioblastoma migration, along with a maximum likelihood-algorithm designed for inference using microscopy imaging data. The inference method is evaluated on in silico simulation of cancer cell migration, and then applied to a real data set. We find that the inference method performs with a high degree of accuracy on the in silico data, and achieve promising results given the in vitro data set.

Estimating linear mixed effect models with non-normal random effects through saddlepoint approximation and its application in retail pricing analytics.

Linear Mixed Effects (LME) models are powerful statistical tools that have been employed in many different real-world applications such as retail data analytics, marketing measurement, and medical research. Statistical inference is often conducted via maximum likelihood estimation with Normality assumptions on the random effects. Nevertheless, for many applications in the retail industry, it is often necessary to consider non-Normal distributions on the random effects when considering the unknown parameters' business interpretations. Motivated by this need, a linear mixed effects model with possibly non-Normal distribution is studied in this research. We propose a general estimating framework based on a saddlepoint approximation (SA) of the probability density function of the dependent variable, which leads to constrained nonlinear optimization problems. The classical LME model with Normality assumption can then be viewed as a special case under the proposed general SA framework. Compared with the existing approach, the proposed method enhances the real-world interpretability of the estimates with satisfactory model fits.

Mathematical modeling in semelparous biological species through two-sex branching processes.

This research focused its interest on the mathematical modeling of the demographic dynamics of semelparous biological species through branching processes. We continued the research line started in previous papers, providing new methodological contributions of biological and ecological interest. We determined the probability distribution associated with the number of generations elapsed before the possible extinction of the population in its natural habitat. We mathematically modeled the phenomenon of populating or repopulating habitats with semelparous species. We also proposed estimates for the offspring parameters governing the reproductive strategies of the species. To this purpose, we used the maximum likelihood and Bayesian estimation methodologies. The statistical results are illustrated through a simulated example contextualized with Labord chameleon (Furcifer labordi) species.

Sliding window functional connectivity inference with nonstationary autocorrelations and cross-correlations.

Functional connectivity (FC) is the degree of synchrony of time series between distinct, spatially separated brain regions. While traditional FC analysis assumes the temporal stationarity throughout a brain scan, there is growing recognition that connectivity can change over time and is not stationary, leading to the concept of dynamic FC (dFC). Resting-state functional magnetic resonance imaging (fMRI) can assess dFC using the sliding window method with the correlation analysis of fMRI signals. Accurate statistical inference of sliding window correlation must consider the autocorrelated nature of the time series. Currently, the dynamic consideration is mainly confined to the point estimation of sliding window correlations. Using in vivo resting-state fMRI data, we first demonstrate the non-stationarity in both the cross-correlation function (XCF) and the autocorrelation function (ACF). Then, we propose the variance estimation of the sliding window correlation considering the nonstationary of XCF and ACF. This approach provides a means to dynamically estimate confidence intervals in assessing dynamic connectivity. Using simulations, we compare the performance of the proposed method with other methods, showing the impact of dynamic ACF and XCF on connectivity inference. Accurate variance estimation can help in addressing the critical issue of false positivity and negativity.

Extracorporeal cardiopulmonary resuscitation versus standard treatment for refractory out-of-hospital cardiac arrest: a Bayesian meta-analysis.

BACKGROUND: The outcomes of several randomized trials on extracorporeal cardiopulmonary resuscitation (ECPR) in patients with refractory out-of-hospital cardiac arrest were examined using frequentist methods, resulting in a dichotomous interpretation of results based on p-values rather than in the probability of clinically relevant treatment effects. To determine such a probability of a clinically relevant ECPR-based treatment effect on neurological outcomes, the authors of these trials performed a Bayesian meta-analysis of the totality of randomized ECPR evidence. METHODS: A systematic search was applied to three electronic databases. Randomized trials that compared ECPR-based treatment with conventional CPR for refractory out-of-hospital cardiac arrest were included. The study was preregistered in INPLASY (INPLASY2023120060). The primary Bayesian hierarchical meta-analysis estimated the difference in 6-month neurologically favorable survival in patients with all rhythms, and a secondary analysis assessed this difference in patients with shockable rhythms (Bayesian hierarchical random-effects model). Primary Bayesian analyses were performed under vague priors. Outcomes were formulated as estimated median relative risks, mean absolute risk differences, and numbers needed to treat with corresponding 95% credible intervals (CrIs). The posterior probabilities of various clinically relevant absolute risk difference thresholds were estimated. RESULTS: Three randomized trials were included in the analysis (ECPR, n = 209 patients; conventional CPR, n = 211 patients). The estimated median relative risk of ECPR for 6-month neurologically favorable survival was 1.47 (95%CrI 0.73-3.32) with a mean absolute risk difference of 8.7% (- 5.0; 42.7%) in patients with all rhythms, and the median relative risk was 1.54 (95%CrI 0.79-3.71) with a mean absolute risk difference of 10.8% (95%CrI - 4.2; 73.9%) in patients with shockable rhythms. The posterior probabilities of an absolute risk difference > 0% and > 5% were 91.0% and 71.1% in patients with all rhythms and 92.4% and 75.8% in patients with shockable rhythms, respectively. CONCLUSION: The current Bayesian meta-analysis found a 71.1% and 75.8% posterior probability of a clinically relevant ECPR-based treatment effect on 6-month neurologically favorable survival in patients with all rhythms and shockable rhythms. These results must be interpreted within the context of the reported credible intervals and varying designs of the randomized trials. REGISTRATION: INPLASY (INPLASY2023120060, December 14th, 2023, https://doi.org/10.37766/inplasy2023.12.0060 ).

Average treatment effects on binary outcomes with stochastic covariates.

When evaluating the effect of psychological treatments on a dichotomous outcome variable in a randomized controlled trial (RCT), covariate adjustment using logistic regression models is often applied. In the presence of covariates, average marginal effects (AMEs) are often preferred over odds ratios, as AMEs yield a clearer substantive and causal interpretation. However, standard error computation of AMEs neglects sampling-based uncertainty (i.e., covariate values are assumed to be fixed over repeated sampling), which leads to underestimation of AME standard errors in other generalized linear models (e.g., Poisson regression). In this paper, we present and compare approaches allowing for stochastic (i.e., randomly sampled) covariates in models for binary outcomes. In a simulation study, we investigated the quality of the AME and stochastic-covariate approaches focusing on statistical inference in finite samples. Our results indicate that the fixed-covariate approach provides reliable results only if there is no heterogeneity in interindividual treatment effects (i.e., presence of treatment-covariate interactions), while the stochastic-covariate approaches are preferable in all other simulated conditions. We provide an illustrative example from clinical psychology investigating the effect of a cognitive bias modification training on post-traumatic stress disorder while accounting for patients' anxiety using an RCT.

Research on Active Safety Situation of Road Passenger Transportation Enterprises: Evaluation, Prediction, and Analysis.

The road passenger transportation enterprise is a complex system, requiring a clear understanding of their active safety situation (ASS), trends, and influencing factors. This facilitates transportation authorities to promptly receive signals and take effective measures. Through exploratory factor analysis and confirmatory factor analysis, we delved into potential factors for evaluating ASS and extracted an ASS index. To predict obtaining a higher ASS information rate, we compared multiple time series models, including GRU (gated recurrent unit), LSTM (long short-term memory), ARIMA, Prophet, Conv_LSTM, and TCN (temporal convolutional network). This paper proposed the WDA-DBN (water drop algorithm-Deep Belief Network) model and employed DEEPSHAP to identify factors with higher ASS information content. TCN and GRU performed well in the prediction. Compared to the other models, WDA-DBN exhibited the best performance in terms of MSE and MAE. Overall, deep learning models outperform econometric models in terms of information processing. The total time spent processing alarms positively influences ASS, while variables such as fatigue driving occurrences, abnormal driving occurrences, and nighttime driving alarm occurrences have a negative impact on ASS.

Multimodel Approaches Are Not the Best Way to Understand Multifactorial Systems.

Information-theoretic (IT) and multi-model averaging (MMA) statistical approaches are widely used but suboptimal tools for pursuing a multifactorial approach (also known as the method of multiple working hypotheses) in ecology. (1) Conceptually, IT encourages ecologists to perform tests on sets of artificially simplified models. (2) MMA improves on IT model selection by implementing a simple form of shrinkage estimation (a way to make accurate predictions from a model with many parameters relative to the amount of data, by "shrinking" parameter estimates toward zero). However, other shrinkage estimators such as penalized regression or Bayesian hierarchical models with regularizing priors are more computationally efficient and better supported theoretically. (3) In general, the procedures for extracting confidence intervals from MMA are overconfident, providing overly narrow intervals. If researchers want to use limited data sets to accurately estimate the strength of multiple competing ecological processes along with reliable confidence intervals, the current best approach is to use full (maximal) statistical models (possibly with Bayesian priors) after making principled, a priori decisions about model complexity.

Practical Bayesian Inference in Neuroscience: Or How I Learned to Stop Worrying and Embrace the Distribution.

Typical statistical practices in the biological sciences have been increasingly called into question due to difficulties in the replication of an increasing number of studies, many of which are confounded by the relative difficulty of null significance hypothesis testing designs and interpretation of p-values. Bayesian inference, representing a fundamentally different approach to hypothesis testing, is receiving renewed interest as a potential alternative or complement to traditional null significance hypothesis testing due to its ease of interpretation and explicit declarations of prior assumptions. Bayesian models are more mathematically complex than equivalent frequentist approaches, which have historically limited applications to simplified analysis cases. However, the advent of probability distribution sampling tools with exponential increases in computational power now allows for quick and robust inference under any distribution of data. Here we present a practical tutorial on the use of Bayesian inference in the context of neuroscientific studies in both rat electrophysiological and computational modeling data. We first start with an intuitive discussion of Bayes' rule and inference followed by the formulation of Bayesian-based regression and ANOVA models using data from a variety of neuroscientific studies. We show how Bayesian inference leads to easily interpretable analysis of data while providing an open-source toolbox to facilitate the use of Bayesian tools.

Robust inference methods for meta-analysis involving influential outlying studies.

Meta-analysis is an essential tool to comprehensively synthesize and quantitatively evaluate results of multiple clinical studies in evidence-based medicine. In many meta-analyses, the characteristics of some studies might markedly differ from those of the others, and these outlying studies can generate biases and potentially yield misleading results. In this article, we provide effective robust statistical inference methods using generalized likelihoods based on the density power divergence. The robust inference methods are designed to adjust the influences of outliers through the use of modified estimating equations based on a robust criterion, even when multiple and serious influential outliers are present. We provide the robust estimators, statistical tests, and confidence intervals via the generalized likelihoods for the fixed-effect and random-effects models of meta-analysis. We also assess the contribution rates of individual studies to the robust overall estimators that indicate how the influences of outlying studies are adjusted. Through simulations and applications to two recently published systematic reviews, we demonstrate that the overall conclusions and interpretations of meta-analyses can be markedly changed if the robust inference methods are applied and that only the conventional inference methods might produce misleading evidence. These methods would be recommended to be used at least as a sensitivity analysis method in the practice of meta-analysis. We have also developed an R package, robustmeta, that implements the robust inference methods.

Data Science Methods for Real-World Evidence Generation in Real-World Data.

In the healthcare landscape, data science (DS) methods have emerged as indispensable tools to harness real-world data (RWD) from various data sources such as electronic health records, claim and registry data, and data gathered from digital health technologies. Real-world evidence (RWE) generated from RWD empowers researchers, clinicians, and policymakers with a more comprehensive understanding of real-world patient outcomes. Nevertheless, persistent challenges in RWD (e.g., messiness, voluminousness, heterogeneity, multimodality) and a growing awareness of the need for trustworthy and reliable RWE demand innovative, robust, and valid DS methods for analyzing RWD. In this article, I review some common current DS methods for extracting RWE and valuable insights from complex and diverse RWD. This article encompasses the entire RWE-generation pipeline, from study design with RWD to data preprocessing, exploratory analysis, methods for analyzing RWD, and trustworthiness and reliability guarantees, along with data ethics considerations and open-source tools. This review, tailored for an audience that may not be experts in DS, aspires to offer a systematic review of DS methods and assists readers in selecting suitable DS methods and enhancing the process of RWE generation for addressing their specific challenges.