Type 2 diabetes mellitus (T2DM) is one of the most common metabolic diseases in the world and poses a significant public health challenge. Early detection and management of this metabolic disorder is crucial to prevent complications and improve outcomes. This paper aims to find core differences in male and female markers to detect T2DM by their clinic and anthropometric features, seeking out ranges in potential biomarkers identified to provide useful information as a pre-diagnostic tool whie excluding glucose-related biomarkers using machine learning (ML) models. We used a dataset containing clinical and anthropometric variables from patients diagnosed with T2DM and patients without TD2M as control. We applied feature selection with three different techniques to identify relevant biomarker models: an improved recursive feature elimination (RFE) evaluating each set from all the features to one feature with the Akaike information criterion (AIC) to find optimal outputs; Least Absolute Shrinkage and Selection Operator (LASSO) with glmnet; and Genetic Algorithms (GA) with GALGO and forward selection (FS) applied to GALGO output. We then used these for comparison with the AIC to measure the performance of each technique and collect the optimal set of global features. Then, an implementation and comparison of five different ML models was carried out to identify the most accurate and interpretable one, considering the following models: logistic regression (LR), artificial neural network (ANN), support vector machine (SVM), k-nearest neighbors (KNN), and nearest centroid (Nearcent). The models were then combined in an ensemble to provide a more robust approximation. The results showed that potential biomarkers such as systolic blood pressure (SBP) and triglycerides are together significantly associated with T2DM. This approach also identified triglycerides, cholesterol, and diastolic blood pressure as biomarkers with differences between male and female actors that have not been previously reported in the literature. The most accurate ML model was selection with RFE and random forest (RF) as the estimator improved with the AIC, which achieved an accuracy of 0.8820. In conclusion, this study demonstrates the potential of ML models in identifying potential biomarkers for early detection of T2DM, excluding glucose-related biomarkers as well as differences between male and female anthropometric and clinic profiles. These findings may help to improve early detection and management of the T2DM by accounting for differences between male and female subjects in terms of anthropometric and clinic profiles, potentially reducing healthcare costs and improving personalized patient attention. Further research is needed to validate these potential biomarkers ranges in other populations and clinical settings.

Most statistical modeling applications involve the consideration of a candidate collection of models based on various sets of explanatory variables. The candidate models may also differ in terms of the structural formulations for the systematic component and the posited probability distributions for the random component. A common practice is to use an information criterion to select a model from the collection that provides an optimal balance between fidelity to the data and parsimony. The analyst then typically proceeds as if the chosen model was the only model ever considered. However, such a practice fails to account for the variability inherent in the model selection process, which can lead to inappropriate inferential results and conclusions. In recent years, inferential methods have been proposed for multimodel frameworks that attempt to provide an appropriate accounting of modeling uncertainty. In the frequentist paradigm, such methods should ideally involve model selection probabilities, i.e., the relative frequencies of selection for each candidate model based on repeated sampling. Model selection probabilities can be conveniently approximated through bootstrapping. When the Akaike information criterion is employed, Akaike weights are also commonly used as a surrogate for selection probabilities. In this work, we show that the conventional bootstrap approach for approximating model selection probabilities is impacted by bias. We propose a simple correction to adjust for this bias. We also argue that Akaike weights do not provide adequate approximations for selection probabilities, although they do provide a crude gauge of model plausibility.

Previous studies have validated a performance equation (PE) and its generalized version (GPE) in describing the rotated and right-shifted Lorenz curves of organ size (e.g., leaf area and fruit volume) distributions of herbaceous plants. Nevertheless, there are still two questions that have not been adequately addressed by prior work: (i) whether the PE and GPE apply to woody plant species and (ii) how do the PE and GPE perform in comparison with other Lorenz equations when fitting data. To address these deficiencies, we measured the lamina length and width of each leaf on 60 Alangium chinense saplings to compare the performance of the PE and GPE with three other Lorenz equations in quantifying the inequality of leaf area distributions across individual trees. Leaf area is shown to be the product of a proportionality coefficient (k) and leaf length and width. To determine the numerical value of k, we scanned 540 leaves to obtain the leaf area empirically. Using the estimated k, the leaf areas of 60 A. chinense saplings were calculated. Using these data, the two performance equations and three other Lorenz equations were then compared and assessed using the root-mean-square error (RMSE) and Akaike information criterion (AIC). The PE and GPE were found to be valid in describing the rotated and right-shifted Lorenz curves of the A. chinense leaf area distributions, and GPE has the lowest RMSE and AIC values. This work validates the GPE as the best model in gauging variations in leaf area of the woody species.

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.

Hierarchical models can express ecological dynamics using a combination of fixed and random effects, and measurement of their complexity (effective degrees of freedom, EDF) requires estimating how much random effects are shrunk toward a shared mean. Estimating EDF is helpful to (1) penalize complexity during model selection and (2) to improve understanding of model behavior. I applied the conditional Akaike Information Criterion (cAIC) to estimate EDF from the finite-difference approximation to the gradient of model predictions with respect to each datum. I confirmed that this has similar behavior to widely used Bayesian criteria, and I illustrated ecological applications using three case studies. The first compared model parsimony with or without time-varying parameters when predicting density-dependent survival, where cAIC favors time-varying demographic parameters more than conventional Akaike Information Criterion. The second estimates EDF in a phylogenetic structural equation model, and identifies a larger EDF when predicting longevity than mortality rates in fishes. The third compares EDF for a species distribution model fitted for 20 bird species and identifies those species requiring more model complexity. These highlight the ecological and statistical insight from comparing EDF among experimental units, models, and data partitions, using an approach that can be broadly adopted for nonlinear ecological models.

The inequality in leaf and fruit size distribution per plant can be quantified using the Gini index, which is linked to the Lorenz curve depicting the cumulative proportion of leaf (or fruit) size against the cumulative proportion of the number of leaves (or fruits). Prior researches have predominantly employed empirical models-specifically the original performance equation (PE-1) and its generalized counterpart (GPE-1)-to fit rotated and right-shifted Lorenz curves. Notably, another potential performance equation (PE-2), capable of generating similar curves to PE-1, has been overlooked and not systematically compared with PE-1 and GPE-1. Furthermore, PE-2 has been extended into a generalized version (GPE-2). In the present study, we conducted a comparative analysis of these four performance equations, evaluating their applicability in describing Lorenz curves related to plant organ (leaf and fruit) size. Leaf area was measured on 240 culms of dwarf bamboo (Shibataea chinensis Nakai), and fruit volume was measured on 31 field muskmelon plants (Cucumis melo L. var. agrestis Naud.). Across both datasets, the root-mean-square errors of all four performance models were consistently smaller than 0.05. Paired t-tests indicated that GPE-1 exhibited the lowest root-mean-square error and Akaike information criterion value among the four performance equations. However, PE-2 gave the best close-to-linear behavior based on relative curvature measures. This study presents a valuable tool for assessing the inequality of plant organ size distribution.

BACKGROUND: In literature are reported different analytical methods (AM) to choose the proper fit model and to fit data of the time-activity curve (TAC). On the other hand, Machine Learning algorithms (ML) are increasingly used for both classification and regression tasks. The aim of this work was to investigate the possibility of employing ML both to classify the most appropriate fit model and to predict the area under the curve (τ).
METHODS: Two different ML systems have been developed for classifying the fit model and to predict the biokinetic parameters. The two systems were trained and tested with synthetic TACs simulating a whole-body Fraction Injected Activity for patients affected by metastatic Differentiated Thyroid Carcinoma, administered with [131I]I-NaI. Test performances, defined as classification accuracy (CA) and percentage difference between the actual and the estimated area under the curve (Δτ), were compared with those obtained using AM varying the number of points (N) of the TACs. A comparison between AM and ML were performed using data of 20 real patients.
RESULTS: As N varies, CA remains constant for ML (about 98%), while it improves for F-test (from 62 to 92%) and AICc (from 50 to 92%), as N increases. With AM, [Formula: see text] can reach down to - 67%, while using ML [Formula: see text] ranges within ± 25%. Using real TACs, there is a good agreement between τ obtained with ML system and AM.
CONCLUSIONS: The employing of ML systems may be feasible, having both a better classification and a better estimation of biokinetic parameters.

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study\'s goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Change points indicate significant shifts in the statistical properties in data streams at some time points. Detecting change points efficiently and effectively are essential for us to understand the underlying data-generating mechanism in modern data streams with versatile parameter-varying patterns. However, it becomes a highly challenging problem to locate multiple change points in the noisy data. Although the Bayesian information criterion has been proven to be an effective way of selecting multiple change points in an asymptotical sense, its finite sample performance could be deficient. In this article, we have reviewed a list of information criterion-based methods for multiple change point detection, including Akaike information criterion, Bayesian information criterion, minimum description length, and their variants, with the emphasis on their practical applications. Simulation studies are conducted to investigate the actual performance of different information criteria in detecting multiple change points with possible model mis-specification for the practitioners. A case study on the SCADA signals of wind turbines is conducted to demonstrate the actual change point detection power of different information criteria. Finally, some key challenges in the development and application of multiple change point detection are presented for future research work.

Microbial colony counts of food samples in microbiological examinations are one of the most important items. The probability distributions for the colony counts per agar plate at the dilution of counting had not been intensively studied so far. Recently we analyzed the colony counts of food samples with several probability distributions using the Pearson\'s chi-square value by the \"traditional\" statistics as the index of fit [Fujikawa and Tsubaki, Food Hyg.Saf.Sc., 60, 88-95 (2019)]. As a result, the selected probability distributions depended on the samples. In this study we newly selected a probability distribution, namely a statistical model, suitable for the above data with the method of maximum likelihood from the probabilistic point of view. The Akaike\'s Information Criterion (AIC) was used as the index of fit. Consequently, the Poisson model were better than the negative binomial model for all of four food samples. The Poisson model was also better than the binomial for three of four microbial culture samples. With Baysian Information Criterion (BIC), the Poisson model was also better than these two models for all the samples. These results suggested that the Poisson distribution would be the best model to estimate the colony counts of food samples. The present study would be the first report on the statistical model selection for the colony counts of food samples with AIC and BIC.