Benchmarking predictive methods for small-angle X-ray scattering from atomic coordinates of proteins using maximum likelihood consensus data.

Stimulated by informal conversations at the XVII International Small Angle Scattering (SAS) conference (Traverse City, 2017), an international team of experts undertook a round-robin exercise to produce a large dataset from proteins under standard solution conditions. These data were used to generate consensus SAS profiles for xylose isomerase, urate oxidase, xylanase, lysozyme and ribonuclease A. Here, we apply a new protocol using maximum likelihood with a larger number of the contributed datasets to generate improved consensus profiles. We investigate the fits of these profiles to predicted profiles from atomic coordinates that incorporate different models to account for the contribution to the scattering of water molecules of hydration surrounding proteins in solution. Programs using an implicit, shell-type hydration layer generally optimize fits to experimental data with the aid of two parameters that adjust the volume of the bulk solvent excluded by the protein and the contrast of the hydration layer. For these models, we found the error-weighted residual differences between the model and the experiment generally reflected the subsidiary maxima and minima in the consensus profiles that are determined by the size of the protein plus the hydration layer. By comparison, all-atom solute and solvent molecular dynamics (MD) simulations are without the benefit of adjustable parameters and, nonetheless, they yielded at least equally good fits with residual differences that are less reflective of the structure in the consensus profile. Further, where MD simulations accounted for the precise solvent composition of the experiment, specifically the inclusion of ions, the modelled radius of gyration values were significantly closer to the experiment. The power of adjustable parameters to mask real differences between a model and the structure present in solution is demonstrated by the results for the conformationally dynamic ribonuclease A and calculations with pseudo-experimental data. This study shows that, while methods invoking an implicit hydration layer have the unequivocal advantage of speed, care is needed to understand the influence of the adjustable parameters. All-atom solute and solvent MD simulations are slower but are less susceptible to false positives, and can account for thermal fluctuations in atomic positions, and more accurately represent the water molecules of hydration that contribute to the scattering profile.

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%.

Multivariate disturbance filtering in auditory fNIRS signals using maximum likelihood gradient estimation method: Feasibility study using sound quality indices.

Functional near-infrared spectroscopy (fNIRS) technology has been widely used to analyze biomechanics and diagnose brain activity. Despite being a promising tool for assessing the brain cortex status, this system is susceptible to disturbances and noise from electrical instrumentation and basal metabolism. In this study, an alternative filtering method, maximum likelihood generalized extended stochastic gradient (ML-GESG) estimation, is proposed to overcome the limitations of these disturbance factors. The proposed algorithm was designed to reduce multiple disturbances originating from heartbeats, breathing, shivering, and instrumental noises as multivariate parameters. To evaluate the effectiveness of the algorithm in filtering involuntary signals, a comparative analysis was conducted with a conventional filtering method, using hemodynamic responses to auditory stimuli and psycho-acoustic factors as quality indices. Using auditory sound stimuli consisting of 12 voice sources (six males and six females), the fNIRS test was configured with 18 channels and conducted on 10 volunteers. The psycho-acoustic factors of loudness and sharpness were used to evaluate physiological responses to the stimuli. Applying the proposed filtering method, the oxygenated hemoglobin concentration correlated better with the psychoacoustic analysis of each auditory stimulus than that of the conventional filtering method.

Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.

Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5):798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.

In some cases more complicated approaches to refinement of macromolecular structures are not necessary.

The manuscript `Modeling a unit cell: crystallographic refinement procedure using the biomolecular MD simulation platform Amber' presents a novel protein structure refinement method claimed to offer improvements over traditional techniques like Refmac5 and Phenix. Our re-evaluation suggests that while the new method provides improvements, traditional methods achieve comparable results with less computational effort.

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.

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.

Exploring the Influence of Initial Estimates on Iterative Maximum Likelihood Expectation-maximization in Tomographic Reconstruction.

Purpose: To explore the influence of initial guess or estimate (uniform as "ones" and "zeros" vs. filtered back projection [FBP] image) as an input image for maximum likelihood expectation-maximization (MLEM) tomographic reconstruction algorithm and provide the curves of error or convergence for each of these three initial estimates. Methods: Two phantoms, created as digital images, were utilized: one was a simple noiseless object and the other was a more complicated, noise-degraded object of the section of lower thorax in a matrix of 256 × 256 pixels. Both underwent radon transform or forward projection process and the corresponding sinograms were generated. For filtering during tomographic image reconstruction, ramp and Butterworth filters, as high-pass and low-pass ones, were applied to images. The second phantom (lower thorax) was radon-transformed and the resulting sinogram was degraded by noise. As initial guess or estimate images, in addition to FBP tomographic image, two uniform images, one with all pixels having a value of 1 ("ones") and the other with all having zero ("zeros"), were created. The three initial estimates (FBP, ones, and zeros) were reconstructed with iterative MLEM tomographic reconstruction (with 1, 2, 4, 8, 16, 32, and 64 iterations). The difference between the object and the updated slice was calculated at the end of each iteration (as error matrix), and the mean squared error (MSE) was computed and plotted separately or in conjunction with the MSE curves of other initial estimates. All computations were implemented in MATLAB software. Results: The results of ones and zeros seemed strikingly similar. The curves of uniform ones and uniform zeros were so close to each other that overlap near-perfectly. However, in the FBP slice as an initial estimate, the resulting tomographic slice was similar with a much higher extent to the object even after 1 or 2 iterations. The pattern of convergence for all three curves was roughly similar. The normalized MSE decreased sharply up to 5 iterations and then, after 10 iterations, the curves reached a plateau until 32 iterations. For the phantom of the lower thorax section with its noise-degraded sinogram, similar to the pattern observed for simple disk-shaped phantom, the curves (normalized MSE) fell sharply up to 10 iterations and then rapidly converged thereafter until 64 iterations. Conclusion: Similar results are observed when choosing different initial guesses or estimates (uniform vs. FBP) as the starting point, based on the error calculation using MSE. The algorithm converges almost similarly for all initial estimates. Therefore, selecting a uniform initial guess image can be an appropriate choice and may be preferred over an FBP image. Reducing the processing time can be a valid reason for this choice.

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.

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.

Improved Positron Emission Tomography Quantification: Evaluation of a Maximum-Likelihood Scatter Scaling Algorithm.

Incorrect scatter scaling of positron emission tomography (PET) images can lead to halo artifacts, quantitative bias, or reconstruction failure. Tail-fitted scatter scaling (TFSS) possesses performance limitations in multiple cases. This study aims to investigate a novel method for scatter scaling: maximum-likelihood scatter scaling (MLSS) in scenarios where TFSS tends to induce artifacts or are observed to cause reconstruction abortion. [68Ga]Ga-RGD PET scans of nine patients were included in cohort 1 in the scope of investigating the reduction of halo artifacts relative to the scatter estimation method. PET scans of 30 patients administrated with [68Ga]Ga-uPAR were included in cohort 2, used for an evaluation of the robustness of MLSS in cases where TFSS-integrated reconstructions are observed to fail. A visual inspection of MLSS-corrected images scored higher than TFSS-corrected reconstructions of cohort 1. The quantitative investigation near the bladder showed a relative difference in tracer uptake of up to 94.7%. A reconstruction of scans included in cohort 2 resulted in failure in 23 cases when TFSS was used. The lesion uptake values of cohort 2 showed no significant difference. MLSS is suggested as an alternative scatter-scaling method relative to TFSS with the aim of reducing halo artifacts and a robust reconstruction process.

A generalized Gompertz promotion time cure model and its fitness to cancer data.

The cure models based on standard distributions like exponential, Weibull, lognormal, Gompertz, gamma, are often used to analyze survival data from cancer clinical trials with long-term survivors. Sometimes, the data is simple, and the standard cure models fit them very well, however, most often the data are complex and the standard cure models don't fit them reasonably well. In this article, we offer a novel generalized Gompertz promotion time cure model and illustrate its fitness to gastric cancer data by three different methods. The generalized Gompertz distribution is as simple as the generalized Weibull distribution and is not computationally as intensive as the generalized F distribution. One detailed real data application is provided for illustration and comparison purposes.

The influence of the number of tree searches on maximum likelihood inference in phylogenomics.

Maximum likelihood (ML) phylogenetic inference is widely used in phylogenomics. As heuristic searches most likely find suboptimal trees, it is recommended to conduct multiple (e.g., ten) tree searches in phylogenetic analyses. However, beyond its positive role, how and to what extent multiple tree searches aid ML phylogenetic inference remains poorly explored. Here, we found that a random starting tree was not as effective as the BioNJ and parsimony starting trees in inferring ML gene tree and that RAxML-NG and PhyML were less sensitive to different starting trees than IQ-TREE. We then examined the effect of the number of tree searches on ML tree inference with IQ-TREE and RAxML-NG, by running 100 tree searches on 19,414 gene alignments from 15 animal, plant, and fungal phylogenomic datasets. We found that the number of tree searches substantially impacted the recovery of the best-of-100 ML gene tree topology among 100 searches for a given ML program. In addition, all of the concatenation-based trees were topologically identical if the number of tree searches was ≥ 10. Quartet-based ASTRAL trees inferred from 1 to 80 tree searches differed topologically from those inferred from 100 tree searches for 6 /15 phylogenomic datasets. Lastly, our simulations showed that gene alignments with lower difficulty scores had a higher chance of finding the best-of-100 gene tree topology and were more likely to yield the correct trees.

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.

Treatments for undefined log ratios in matching analyses.

A challenge in carrying out matching analyses is to deal with undefined log ratios. If any reinforcer or response rate equals zero, the logarithm of the ratio is undefined: data are unsuitable for analyses. There have been some tentative solutions, but they had not been thoroughly investigated. The purpose of this article is to assess the adequacy of five treatments: omit undefined ratios, use full information maximum likelihood, replace undefined ratios by the mean divided by 100, replace them by a constant 1/10, and add the constant .50 to ratios. Based on simulations, the treatments are compared on their estimations of variance accounted for, sensitivity, and bias. The results show that full information maximum likelihood and omiting undefined ratios had the best overall performance, with negligibly biased and more accurate estimates than mean divided by 100, constant 1/10, and constant .50. The study suggests that mean divided by 100, constant 1/10, and constant .50 should be avoided and recommends full information maximum likelihood to deal with undefined log ratios in matching analyses.

OrthoPhyl - Streamlining large scale, orthology-based phylogenomic studies of bacteria at broad evolutionary scales.

There are a staggering number of publicly available bacterial genome sequences (at writing, 2.0 million assemblies in NCBI's GenBank alone), and the deposition rate continues to increase. This wealth of data begs for phylogenetic analyses to place these sequences within an evolutionary context. A phylogenetic placement not only aids in taxonomic classification, but informs the evolution of novel phenotypes, targets of selection, and horizontal gene transfer. Building trees from multi-gene codon alignments is a laborious task that requires bioinformatic expertise, rigorous curation of orthologs, and heavy computation. Compounding the problem is the lack of tools that can streamline these processes for building trees from large scale genomic data. Here we present OrthoPhyl, which takes bacterial genome assemblies and reconstructs trees from whole genome codon alignments. The analysis pipeline can analyze an arbitrarily large number of input genomes (>1200 tested here) by identifying a diversity spanning subset of assemblies and using these genomes to build gene models to infer orthologs in the full dataset. To illustrate the versatility of OrthoPhyl, we show three use-cases: E. coli/Shigella, Brucella/Ochrobactrum, and the order Rickettsiales. We compare trees generated with OrthoPhyl to trees generated with kSNP3 and GToTree along with published trees using alternative methods. We show that OrthoPhyl trees are consistent with other methods while incorporating more data, allowing for greater numbers of input genomes, and more flexibility of analysis.

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.

Estimation of accelerated hazards models based on case K informatively interval-censored failure time data.

The accelerated hazards model is one of the most commonly used models for regression analysis of failure time data and this is especially the case when, for example, the hazard functions may have monotonicity property. Correspondingly a large literature has been established for its estimation or inference when right-censored data are observed. Although several methods have also been developed for its inference based on interval-censored data, they apply only to limited situations or rely on some assumptions such as independent censoring. In this paper, we consider the situation where one observes case K interval-censored data, the type of failure time data that occur most in, for example, medical research such as clinical trials or periodical follow-up studies. For inference, we propose a sieve borrow-strength method and in particular, it allows for informative censoring. The asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The method is applied to a set of real data set arising from an AIDS clinical trial.

Estimating Enzyme Expression and Metabolic Pathway Activity in Borreliella-Infected and Uninfected Mice.

Evaluating changes in metabolic pathway activity is essential for studying disease mechanisms and developing new treatments, with significant benefits extending to human health. Here, we propose EMPathways2, a maximum likelihood pipeline that is based on the expectation-maximization algorithm, which is capable of evaluating enzyme expression and metabolic pathway activity level. We first estimate enzyme expression from RNA-seq data that is used for simultaneous estimation of pathway activity levels using enzyme participation levels in each pathway. We implement the novel pipeline to RNA-seq data from several groups of mice, which provides a deeper look at the biochemical changes occurring as a result of bacterial infection, disease, and immune response. Our results show that estimated enzyme expression, pathway activity levels, and enzyme participation levels in each pathway are robust and stable across all samples. Estimated activity levels of a significant number of metabolic pathways strongly correlate with the infected and uninfected status of the respective rodent types.

Nonparametric empirical Bayes biomarker imputation and estimation.

Biomarkers are often measured in bulk to diagnose patients, monitor patient conditions, and research novel drug pathways. The measurement of these biomarkers often suffers from detection limits that result in missing and untrustworthy measurements. Frequently, missing biomarkers are imputed so that down-stream analysis can be conducted with modern statistical methods that cannot normally handle data subject to informative censoring. This work develops an empirical Bayes g $$ g $$ -modeling method for imputing and denoising biomarker measurements. We establish superior estimation properties compared to popular methods in simulations and with real data, providing the useful biomarker measurement estimations for down-stream analysis.