A Novel Methodology for GB-SAR Estimating Parameters of the Atmospheric Phase Correction Model Based on Maximum Likelihood Estimation and the Gauss-Newton Algorithm.

Atmospheric phase error is the main factor affecting the accuracy of ground-based synthetic aperture radar (GB-SAR). The atmospheric phase screen (APS) may be very complicated, so the atmospheric phase correction (APC) model is very important; in particular, the parameters to be estimated in the model are the key to improving the accuracy of APC. However, the conventional APC method first performs phase unwrapping and then removes the APS based on the least-squares method (LSM), and the general phase unwrapping method is prone to introducing unwrapping error. In particular, the LSM is difficult to apply directly due to the phase wrapping of permanent scatterers (PSs). Therefore, a novel methodology for estimating parameters of the APC model based on the maximum likelihood estimation (MLE) and the Gauss-Newton algorithm is proposed in this paper, which first introduces the MLE method to provide a suitable objective function for the parameter estimation of nonlinear far-end and near-end correction models. Then, based on the Gauss-Newton algorithm, the parameters of the objective function are iteratively estimated with suitable initial values, and the Matthews and Davies algorithm is used to optimize the Gauss-Newton algorithm to improve the accuracy of parameter estimation. Finally, the parameter estimation performance is evaluated based on Monte Carlo simulation experiments. The method proposed in this paper experimentally verifies the feasibility and superiority, which avoids phase unwrapping processing unlike the conventional method.

A novel flexible T-X family for generating new distributions with applications to lifetime data.

In recent decades, many research studies have been conducted for the development of some new modifications of different baseline distributions to cope with real-world problems. This paper proposes a novel generalization of probability distributions, called modified type- II half-logistic distribution. We have derived the new family of probability distributions using T-X family with input as a type II variant of the half-logistic distribution. For the purpose of demonstration, the Weibull distribution is considered as a sub-model. Various algebraic properties of the suggested distribution have been discussed. For efficient parameter estimation, we have used the maximum likelihood principle. Additionally, two real-world data sets from the literature have been considered to illustrate the practical usefulness and significance of the suggested model.

Properties, estimation, and applications of the extended log-logistic distribution.

This paper presents the exponentiated alpha-power log-logistic (EAPLL) distribution, which extends the log-logistic distribution. The EAPLL distribution emphasizes its suitability for survival data modeling by providing analytical simplicity and accommodating both monotone and non-monotone failure rates. We derive some of its mathematical properties and test eight estimation methods using an extensive simulation study. To determine the best estimation approach, we rank mean estimates, mean square errors, and average absolute biases on a partial and overall ranking. Furthermore, we use the EAPLL distribution to examine three real-life survival data sets, demonstrating its superior performance over competing log-logistic distributions. This study adds vital insights to survival analysis methodology and provides a solid framework for modeling various survival data scenarios.

Different estimation techniques and data analysis for constant-partially accelerated life tests for power half-logistic distribution.

Partial accelerated life tests (PALTs) are employed when the results of accelerated life testing cannot be extended to usage circumstances. This work discusses the challenge of different estimating strategies in constant PALT with complete data. The lifetime distribution of the test item is assumed to follow the power half-logistic distribution. Several classical and Bayesian estimation techniques are presented to estimate the distribution parameters and the acceleration factor of the power half-logistic distribution. These techniques include Anderson-Darling, maximum likelihood, Cramér von-Mises, ordinary least squares, weighted least squares, maximum product of spacing and Bayesian. Additionally, the Bayesian credible intervals and approximate confidence intervals are constructed. A simulation study is provided to compare the outcomes of various estimation methods that have been provided based on mean squared error, absolute average bias, length of intervals, and coverage probabilities. This study shows that the maximum product of spacing estimation is the most effective strategy among the options in most circumstances when adopting the minimum values for MSE and average bias. In the majority of situations, Bayesian method outperforms other methods when taking into account both MSE and average bias values. When comparing approximation confidence intervals to Bayesian credible intervals, the latter have a higher coverage probability and smaller average length. Two authentic data sets are examined for illustrative purposes. Examining the two real data sets shows that the value methods are workable and applicable to certain engineering-related problems.

A birth-death model to understand bacterial antimicrobial heteroresistance from time-kill curves.

Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test.

Structured methods for parameter inference and uncertainty quantification for mechanistic models in the life sciences.

Parameter inference and uncertainty quantification are important steps when relating mathematical models to real-world observations and when estimating uncertainty in model predictions. However, methods for doing this can be computationally expensive, particularly when the number of unknown model parameters is large. The aim of this study is to develop and test an efficient profile likelihood-based method, which takes advantage of the structure of the mathematical model being used. We do this by identifying specific parameters that affect model output in a known way, such as a linear scaling. We illustrate the method by applying it to three toy models from different areas of the life sciences: (i) a predator-prey model from ecology; (ii) a compartment-based epidemic model from health sciences; and (iii) an advection-diffusion reaction model describing the transport of dissolved solutes from environmental science. We show that the new method produces results of comparable accuracy to existing profile likelihood methods but with substantially fewer evaluations of the forward model. We conclude that our method could provide a much more efficient approach to parameter inference for models where a structured approach is feasible. Computer code to apply the new method to user-supplied models and data is provided via a publicly accessible repository.

Factor-augmented transformation models for interval-censored failure time data.

Interval-censored failure time data frequently arise in various scientific studies where each subject experiences periodical examinations for the occurrence of the failure event of interest, and the failure time is only known to lie in a specific time interval. In addition, collected data may include multiple observed variables with a certain degree of correlation, leading to severe multicollinearity issues. This work proposes a factor-augmented transformation model to analyze interval-censored failure time data while reducing model dimensionality and avoiding multicollinearity elicited by multiple correlated covariates. We provide a joint modeling framework by comprising a factor analysis model to group multiple observed variables into a few latent factors and a class of semiparametric transformation models with the augmented factors to examine their and other covariate effects on the failure event. Furthermore, we propose a nonparametric maximum likelihood estimation approach and develop a computationally stable and reliable expectation-maximization algorithm for its implementation. We establish the asymptotic properties of the proposed estimators and conduct simulation studies to assess the empirical performance of the proposed method. An application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) study is provided. An R package ICTransCFA is also available for practitioners. Data used in preparation of this article were obtained from the ADNI database.

Developing equity-aware safety performance functions for identifying hotspots of pedestrian-involved crashes.

Crashes are frequently disproportionally observed in disadvantaged areas. Despite the evident disparities in transportation safety, there has been limited exploration of quantitative approaches to incorporating equity considerations into road safety management. This study proposes a novel concept of equity-aware safety performance functions (SPFs), enabling a distinct treatment of equity-related variables such as race and income. Equity-aware SPFs introduce a fairness distance and integrate it into the log-likelihood function of the negative binomial regression as a form of partial lasso regularization. A parameter λ is used to control the importance of the regularization term. Equity-aware SPFs are developed for pedestrian-involved crashes at the census tract level in Virginia, USA, and then employed to compute the potential for safety improvement (PSI), a prevalent metric used in hotspot identification. Results show that equity-aware SPFs can diminish the effects of equity-related variables, including poverty ratio, black ratio, Asian ratio, and the ratio of households without vehicles, on the expected crash frequencies, generating higher PSIs for disadvantaged areas. Based on the results of Wilcoxon signed-rank tests, it is evident that there are significant differences in the rankings of PSIs when equity awareness is considered, especially for disadvantaged areas. This study adds to the literature a new quantitative approach to harmonize equity and effectiveness considerations, empowering more equitable decision-making in safety management, such as allocating resources for safety enhancement.

Current status data with two competing risks and time-dependent missing failure types.

In competing risks data, in practice, there may be lack of information or uncertainty about the true failure type, termed as 'missing failure type', for some subjects. We consider a general pattern of missing failure type in which we observe, if not the true failure type, a set of possible failure types containing the true one. In this work, we focus on both parametric and non-parametric estimation based on current status data with two competing risks and the above-mentioned missing failure type. Here, the missing probabilities are assumed to be time-dependent, that is, dependent on both failure and monitoring time points, in addition to being dependent on the true failure type. This makes the missing mechanism non-ignorable. We carry out maximum likelihood estimation and obtain the asymptotic properties of the estimators. Simulation studies are conducted to investigate the finite sample properties of the estimators. Finally, the methods are illustrated through a data set on hearing loss.

Assessment of wind energy resource in the western region of Somaliland.

As the population of Somaliland continues to grow rapidly, the demand for electricity is anticipated to rise exponentially over the next few decades. The provision of reliable and cost-effective electricity service is at the core of the economic and social development of Somaliland. Wind energy might offer a sustainable solution to the exceptionally high electricity prices. In this study, a techno-economic assessment of the wind energy potential in some parts of the western region of Somaliland is performed. Measured data of wind speed and wind direction for three sites around the capital city of Hargeisa are utilized to characterize the resource using Weibull distribution functions. Technical and economic performances of several commercial wind turbines are examined. Out of the three sites, Xumba Weyne stands out as the most favorable site for wind energy harnessing with average annual power and energy densities at 80 m hub height of 317 kW/m2 and 2782 kWh/m2, respectively. Wind turbines installed in Xumba Weyne yielded the lowest levelized cost of electricity (LCOE) of not more than 0.07 $/kWh, shortest payback times (i.e., less than 7.2 years) with minimum return on investment (ROI) of approximately 150%.

Analysis of incorporating modified Weibull model fault detection rate function into software reliability modeling.

When software systems are introduced, they are typically deployed in field environments similar to those used during development and testing. However, these systems may also be used in various other locations with different environmental conditions, making it challenging to improve software reliability. Factors such as the specific operating environment and the location of bugs in the code contribute to this difficulty. In this paper, we propose a new software reliability model that accounts for the uncertainty of operating environments. We present the explicit closed-form mean value function solution for the proposed model. The model's goodness of fit is demonstrated by comparing it to the nonhomogeneous Poisson process (NHPP) model based on Weibull model, using four sets of failure data sets from software applications. The proposed model performs well under various estimation techniques, making it a versatile tool for practitioners and researchers alike. The proposed model outperforms other existing NHPP Weibull based in terms of fitting accuracy under two different methods of estimation and provides a more detailed and precise evaluation of software reliability. Additionally, sensitivity analysis shows that the parameters of the suggested distribution significantly impact the mean value function.

A targeted likelihood estimation comparing cefepime and piperacillin/tazobactam in critically ill patients with community-acquired pneumonia (CAP).

Cefepime and piperacillin/tazobactam are antimicrobials recommended by IDSA/ATS guidelines for the empirical management of patients admitted to the intensive care unit (ICU) with community-acquired pneumonia (CAP). Concerns have been raised about which should be used in clinical practice. This study aims to compare the effect of cefepime and piperacillin/tazobactam in critically ill CAP patients through a targeted maximum likelihood estimation (TMLE). A total of 2026 ICU-admitted patients with CAP were included. Among them, (47%) presented respiratory failure, and (27%) developed septic shock. A total of (68%) received cefepime and (32%) piperacillin/tazobactam-based treatment. After running the TMLE, we found that cefepime and piperacillin/tazobactam-based treatments have comparable 28-day, hospital, and ICU mortality. Additionally, age, PTT, serum potassium and temperature were associated with preferring cefepime over piperacillin/tazobactam (OR 1.14 95% CI [1.01-1.27], p = 0.03), (OR 1.14 95% CI [1.03-1.26], p = 0.009), (OR 1.1 95% CI [1.01-1.22], p = 0.039) and (OR 1.13 95% CI [1.03-1.24], p = 0.014)]. Our study found a similar mortality rate among ICU-admitted CAP patients treated with cefepime and piperacillin/tazobactam. Clinicians may consider factors such as availability and safety profiles when making treatment decisions.

Compartmental modeling for pandemic data analysis: The gap between statistics and models.

A scrutiny analysis of the COVID-19 data is required to get insights into effective strategies for pandemic control. However, there is a gap between official data and methods used to assess the effectiveness of the potential measures, which was partly addressed in an editorial-letter-type discussion on the impact of the COVID-19 passport in Lithuania. The therein-applied descriptive statistics method provides only limited evidence, while detailed analysis requires more sensitive and reliable methods. In this regard, this paper advocates a maximum likelihood compartmental modeling approach, which provides the flexibility to raise various hypotheses about infection, recovery, and mortality dynamics and to find the most likely answers given the data. Our paper is based on COVID-19 deaths, which are more reliable and essential than infection cases. It should also be noted that officially collected data are unsuitable for in-depth analyses, including compartmental modeling, as they do not capture important information. Overall, this paper does not aim to solve the underlying problems completely but rather stimulate a discussion.

Family of bivariate distributions on the unit square: theoretical properties and applications.

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets.

A robust regression model for bounded count health data.

Bounded count response data arise naturally in health applications. In general, the well-known beta-binomial regression model form the basis for analyzing this data, specially when we have overdispersed data. Little attention, however, has been given to the literature on the possibility of having extreme observations and overdispersed data. We propose in this work an extension of the beta-binomial regression model, named the beta-2-binomial regression model, which provides a rather flexible approach for fitting a regression model with a wide spectrum of bounded count response data sets under the presence of overdispersion, outliers, or excess of extreme observations. This distribution possesses more skewness and kurtosis than the beta-binomial model but preserves the same mean and variance form of the beta-binomial model. Additional properties of the beta-2-binomial distribution are derived including its behavior on the limits of its parametric space. A penalized maximum likelihood approach is considered to estimate parameters of this model and a residual analysis is included to assess departures from model assumptions as well as to detect outlier observations. Simulation studies, considering the robustness to outliers, are presented confirming that the beta-2-binomial regression model is a better robust alternative, in comparison with the binomial and beta-binomial regression models. We also found that the beta-2-binomial regression model outperformed the binomial and beta-binomial regression models in our applications of predicting liver cancer development in mice and the number of inappropriate days a patient spent in a hospital.

QMix: An Efficient Program to Automatically Estimate Multi-Matrix Mixture Models for Amino Acid Substitution Process.

The single-matrix amino acid (AA) substitution models are widely used in phylogenetic analyses; however, they are unable to properly model the heterogeneity of AA substitution rates among sites. The multi-matrix mixture models can handle the site rate heterogeneity and outperform the single-matrix models. Estimating multi-matrix mixture models is a complex process and no computer program is available for this task. In this study, we implemented a computer program of the so-called QMix based on the algorithm of LG4X and LG4M with several enhancements to automatically estimate multi-matrix mixture models from large datasets. QMix employs QMaker algorithm instead of XRATE algorithm to accurately and rapidly estimate the parameters of models. It is able to estimate mixture models with different number of matrices and supports multi-threading computing to efficiently estimate models from thousands of genes. We re-estimate mixture models LG4X and LG4M from 1471 HSSP alignments. The re-estimated models (HP4X and HP4M) are slightly better than LG4X and LG4M in building maximum likelihood trees from HSSP and TreeBASE datasets. QMix program required about 10 hours on a computer with 18 cores to estimate a mixture model with four matrices from 200 HSSP alignments. It is easy to use and freely available for researchers.

An Evaluation of Fit Indices Used in Model Selection of Dichotomous Mixture IRT Models.

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's information criterion (DIC), sample size adjusted BIC (SABIC), relative entropy, the integrated classification likelihood criterion (ICL-BIC), the adjusted Lo-Mendell-Rubin (LMR), and Vuong-Lo-Mendell-Rubin (VLMR). The accuracy of the fit indices was assessed for correct detection of the number of latent classes for different simulation conditions including sample size (2,500 and 5,000), test length (15, 30, and 45), mixture proportions (equal and unequal), number of latent classes (2, 3, and 4), and latent class separation (no-separation and small separation). Simulation study results indicated that as the number of examinees or number of items increased, correct identification rates also increased for most of the indices. Correct identification rates by the different fit indices, however, decreased as the number of estimated latent classes or parameters (i.e., model complexity) increased. Results were good for BIC, CAIC, DIC, SABIC, ICL-BIC, LMR, and VLMR, and the relative entropy index tended to select correct models most of the time. Consistent with previous studies, AIC and AICc showed poor performance. Most of these indices had limited utility for three-class and four-class mixture 3PL model conditions.

Aging Intensity for Step-Stress Accelerated Life Testing Experiments.

The aging intensity (AI), defined as the ratio of the instantaneous hazard rate and a baseline hazard rate, is a useful tool for the describing reliability properties of a random variable corresponding to a lifetime. In this work, the concept of AI is introduced in step-stress accelerated life testing (SSALT) experiments, providing new insights to the model and enabling the further clarification of the differences between the two commonly employed cumulative exposure (CE) and tampered failure rate (TFR) models. New AI-based estimators for the parameters of a SSALT model are proposed and compared to the MLEs in terms of examples and a simulation study.

Impact of LS Mutation on Pharmacokinetics of Preventive HIV Broadly Neutralizing Monoclonal Antibodies: A Cross-Protocol Analysis of 16 Clinical Trials in People without HIV.

Monoclonal antibodies are commonly engineered with an introduction of Met428Leu and Asn434Ser, known as the LS mutation, in the fragment crystallizable region to improve pharmacokinetic profiles. The LS mutation delays antibody clearance by enhancing binding affinity to the neonatal fragment crystallizable receptor found on endothelial cells. To characterize the LS mutation for monoclonal antibodies targeting HIV, we compared pharmacokinetic parameters between parental versus LS variants for five pairs of anti-HIV immunoglobin G1 monoclonal antibodies (VRC01/LS/VRC07-523LS, 3BNC117/LS, PGDM1400/LS PGT121/LS, 10-1074/LS), analyzing data from 16 clinical trials of 583 participants without HIV. We described serum concentrations of these monoclonal antibodies following intravenous or subcutaneous administration by an open two-compartment disposition, with first-order elimination from the central compartment using non-linear mixed effects pharmacokinetic models. We compared estimated pharmacokinetic parameters using the targeted maximum likelihood estimation method, accounting for participant differences. We observed lower clearance rate, central volume, and peripheral volume of distribution for all LS variants compared to parental monoclonal antibodies. LS monoclonal antibodies showed several improvements in pharmacokinetic parameters, including increases in the elimination half-life by 2.7- to 4.1-fold, the dose-normalized area-under-the-curve by 4.1- to 9.5-fold, and the predicted concentration at 4 weeks post-administration by 3.4- to 7.6-fold. Results suggest a favorable pharmacokinetic profile of LS variants regardless of HIV epitope specificity. Insights support lower dosages and/or less frequent dosing of LS variants to achieve similar levels of antibody exposure in future clinical applications.

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes.

The added value of candidate predictors for risk modeling is routinely evaluated by comparing the performance of models with or without including candidate predictors. Such comparison is most meaningful when the estimated risk by the two models are both unbiased in the target population. Very often data for candidate predictors are sourced from nonrepresentative convenience samples. Updating the base model using the study data without acknowledging the discrepancy between the underlying distribution of the study data and that in the target population can lead to biased risk estimates and therefore an unfair evaluation of candidate predictors. To address this issue assuming access to a well-calibrated base model, we propose a semiparametric method for model fitting that enforces good calibration. The central idea is to calibrate the fitted model against the base model by enforcing suitable constraints in maximizing the likelihood function. This approach enables unbiased assessment of model improvement offered by candidate predictors without requiring a representative sample from the target population, thus overcoming a significant practical challenge. We study theoretical properties for model parameter estimates, and demonstrate improvement in model calibration via extensive simulation studies. Finally, we apply the proposed method to data extracted from Penn Medicine Biobank to inform the added value of breast density for breast cancer risk assessment in the Caucasian woman population.