A unified exponential-H family for modeling real-life data: Properties and inference

The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.

A novel extension of half-logistic distribution with statistical inference, estimation and applications

In the present study, we develop and investigate the odd Frechet Half-Logistic (OFHL) distribution that was developed by incorporating the half-logistic and odd Frechet-G family. The OFHL model has very adaptable probability functions: decreasing, increasing, bathtub and inverted U shapes are shown for the hazard rate functions, illustrating the model's capacity for flexibility. A comprehensive account of the mathematical and statistical properties of the proposed model is presented. In estimation viewpoint, six distinct estimation methodologies are used to estimate the unknown parameters of the OFHL model. Furthermore, an extensive Monte Carlo simulation analysis is used to evaluate the effectiveness of these estimators. Finally, two applications to real data are used to demonstrate the versatility of the suggested method, and the comparison is made with the half-logistic and some of its well-known extensions. The actual implementation shows that the suggested model performs better than competing models.

Comparison of Two Methods for Determining Item Characteristic Functions and Latent Variable Time-Course for Pharmacometric Item Response Models

There are examples in the literature demonstrating different approaches to defining the item characteristic functions (ICF) and characterizing the latent variable time-course within a pharmacometrics item response theory (IRT) framework. One such method estimates both the ICF and latent variable time-course simultaneously, and another method establishes the ICF first then models the latent variable directly. To date, a direct comparison of the "simultaneous" and "sequential" methodologies described in this work has not yet been systematically investigated. Item parameters from a graded response IRT model developed from Parkinson's Progression Marker Initiative (PPMI) study data were used as simulation parameters. Each method was evaluated under the following conditions: (i) with and without drug effect and (ii) slow progression rate with smaller sample size and rapid progression rate with larger sample size. Overall, the methods performed similarly, with low bias and good precision for key parameters and hypothesis testing for drug effect. The ICF parameters were well determined when the model was correctly specified, with an increase in precision in the scenario with rapid progression. In terms of drug effect, both methods had large estimation bias for the slow progression rate; however, this bias can be considered small relative to overall progression rate. Both methods demonstrated type 1 error control and similar discrimination between model with and without drug effect. The simultaneous method was slightly more precise than the sequential method while the sequential method was more robust towards longitudinal model misspecification and offers practical advantages in model building.

Estimation of the global number of e-cigarette users in 2020

Background

The combustion of tobacco is the main cause of tobacco-related morbidity and mortality. E-cigarettes are potentially disruptive innovations with considerable potential for population health. A key question is whether e-cigarettes are replacing tobacco cigarettes, which requires mapping their prevalence. Collecting information on nicotine use is difficult for many countries due to cost. The objective of this study was to derive a global estimate of e-cigarette use (vaping).

Methods

Since 2018 we have collected information on the prevalence of e-cigarette use. To estimate the prevalence of vaping in countries lacking information, we used the method of assumed similarity between countries in the same region and economic condition. Based on surveys, we calculated the average prevalence of vaping for each WHO region, World Bank income classification group, and the legal status of e-cigarettes in each country. For each of these groups the average prevalence of vaping was calculated. These values were used as substitutes for the prevalence figures in the countries with absent data. The number of vapers was calculated by taking as the denominator the adult population.

Results

Survey data on e-cigarette users were available for 49 countries covering 2.8 b of the adult population in 2018 and unavailable for 2.9 b. Information on vaping was lacking for half of the world's population. We estimated a total of 58.1 m vapers worldwide in 2018. By reference to market growth the data were adjusted to arrive at estimates for 2020. Results were fitted to revenue data at the 2018. For the year 2020, the projection is for 68 m vapers globally.

Conclusions

Many global epidemiological studies use the method of assumed similarity between countries with shared characteristics in order to estimate missing data. The methodological limitations are likely to overestimate the global number of vapers. Our estimate of 68 m vapers indicates considerable uptake given that: e-cigarettes have been available on most markets for only a decade; there is either no support, or there is opposition to vaping in many countries; and countries which regulate e-cigarettes have controls over advertising and promotion. However, given the global scale of tobacco smoking (at 1.1 billion people), progress in adoption of alternative products is slow. Those using e-cigarettes are still a small fraction of those who smoke.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12954-021-00556-7.

Determination of total and lung-deposited particle surface area concentrations, in central Athens, Greece

Numerous health studies have linked the exposure to particulate matter with adverse health effects, while there is an increasing scientific interest in the particle metrics of surface area (SA) and lung-deposited SA (LDSA) concentration. In the present study, two integrated SA estimation methods, both based on widely used instrumentation, were applied at an urban traffic environment in Athens for a 6-month period. The first estimation method used the size distribution by number to estimate SA (average SA₁ 669.3 ± 229.0 μm² cm^-3), while the second method used a simple inversion scheme that incorporates number and mass concentrations (average SA₂ 1627.9 ± 562.8 μm² cm^-3). In pairwise comparisons, SA₂ levels were found two times greater than the corresponding SA₁, but exhibited a strong correlation (r = 0.73). SA₁ and SA₂ concentrations correlated well with the traffic-related pollutants NO_x (r = 0.64 and 0.78) and equivalent black carbon (r = 0.53 and 0.51). The diurnal variation of SA₁ concentrations by size range indicated traffic as a major controlling factor. Estimated LDSA (53.9 μm² cm^-3 on average) concentrations were also clearly affected by anthropogenic emissions with more pronounced associations in the 0.01-0.4 μm range (r = 0.66 with NO_x and r = 0.65 with equivalent black carbon). Validating estimated LDSA through simultaneous measurements with a reference instrument revealed that the estimation method underestimates LDSA by a factor between 2 and 3, exhibiting, however, a high correlation (r = 0.79). Overall, the performance of estimation methods appear satisfactory and indicate that a trustworthy assessment of the temporal variability of SA and LDSA concentration metrics can be provided in real time, on the basis of relatively lower-cost instrumentation, especially in view of recent advances in particle sensing technologies.

Estimating sea lice infestation pressure on salmon farms: Comparing different methods using multivariate state-space models

Sea lice are ectoparasites of salmonids, and are considered to be one of the main threats to Atlantic salmon farming. Sea lice infestation on a farm is usually initiated by attachment of the free-living copepodid stage derived from the surrounding water, frequently originating from adult lice on the same farm or from neighboring salmonid farms, referred to as internal and external sources, respectively. Various approaches have been proposed to quantify sea lice infestation pressure on farms to improve the management of this pest. Here, we review and compare five of these methods based on sea lice data from 20 farms located near Grand Manan island in the Bay of Fundy, New Brunswick, Canada. Internal and external infestation pressures (IIP and EIP, respectively) were estimated using different approaches, and their effects were modeled either by a unique parameter for all production cycles or by different parameters for each production cycle, using a multivariate state-space model. Predictive variables, such as water temperature and sea lice treatments, were included in the model, and their effects across production cycles were estimated along with those of other model parameters. Results showed that models with only EIP explained the variation in the data better than models with only IIP, and that models with unique IIP and unique EIP for all cycles were generally associated with the best model fit. The simplest, fixed lag method for calculating infestation pressure had the best predictive performance in our models among the methods studied.

Performance comparison of first-order conditional estimation with interaction and Bayesian estimation methods for estimating the population parameters and its distribution from data sets with a low number of subjects

Background

Exploratory preclinical, as well as clinical trials, may involve a small number of patients, making it difficult to calculate and analyze the pharmacokinetic (PK) parameters, especially if the PK parameters show very high inter-individual variability (IIV). In this study, the performance of a classical first-order conditional estimation with interaction (FOCE-I) and expectation maximization (EM)-based Markov chain Monte Carlo Bayesian (BAYES) estimation methods were compared for estimating the population parameters and its distribution from data sets having a low number of subjects.

Methods

In this study, 100 data sets were simulated with eight sampling points for each subject and with six different levels of IIV (5%, 10%, 20%, 30%, 50%, and 80%) in their PK parameter distribution. A stochastic simulation and estimation (SSE) study was performed to simultaneously simulate data sets and estimate the parameters using four different methods: FOCE-I only, BAYES(C) (FOCE-I and BAYES composite method), BAYES(F) (BAYES with all true initial parameters and fixed ω²), and BAYES only. Relative root mean squared error (rRMSE) and relative estimation error (REE) were used to analyze the differences between true and estimated values. A case study was performed with a clinical data of theophylline available in NONMEM distribution media. NONMEM software assisted by Pirana, PsN, and Xpose was used to estimate population PK parameters, and R program was used to analyze and plot the results.

Results

The rRMSE and REE values of all parameter (fixed effect and random effect) estimates showed that all four methods performed equally at the lower IIV levels, while the FOCE-I method performed better than other EM-based methods at higher IIV levels (greater than 30%). In general, estimates of random-effect parameters showed significant bias and imprecision, irrespective of the estimation method used and the level of IIV. Similar performance of the estimation methods was observed with theophylline dataset.

Conclusions

The classical FOCE-I method appeared to estimate the PK parameters more reliably than the BAYES method when using a simple model and data containing only a few subjects. EM-based estimation methods can be considered for adapting to the specific needs of a modeling project at later steps of modeling.

Electronic supplementary material

The online version of this article (10.1186/s12874-017-0427-0) contains supplementary material, which is available to authorized users.

Suspended sediment in a high-Arctic river: An appraisal of flux estimation methods

Quantifying fluxes of water, sediment and dissolved compounds through Arctic rivers is important for linking the glacial, terrestrial and marine ecosystems and to quantify the impact of a warming climate. The quantification of fluxes is not trivial. This study uses a 8-years data set (2005-2012) of daily measurements from the high-Artic Zackenberg River in Northeast Greenland to estimate annual suspended sediment fluxes based on four commonly used methods: M1) is the discharge weighted mean and uses direct measurements, while M2-M4) are one uncorrected and two bias corrected rating curves extrapolating a continuous concentration trace from measured values. All methods are tested on complete and reduced datasets. The average annual runoff in the period 2005-2012 was 190±25mio·m³y^-1. The different estimation methods gave a range of average annual suspended sediment fluxes between 43,000±10,000ty^-1 and 61,000±16,000ty^-1. Extreme events with high discharges had a mean duration of 1day. The average suspended sediment flux during extreme events was 17,000±5000ty^-1, which constitutes a year-to-year variation of 20-37% of the total annual flux. The most accurate sampling strategy was bi-daily sampling together with a sampling frequency of 2h during extreme events. The most consistent estimation method was an uncorrected rating curve of bi-daily measurements (M2), combined with a linear interpolation of extreme event fluxes. Sampling can be reduced to every fourth day, with both method-agreements and accuracies <±10%, using 7year averages. The specific annual method-agreements were <±10% for all years and the specific annual accuracies <±20% for 6years out of 7. The rating curves were less sensitive to day-to-day variations in the measured suspended sediment concentrations. The discharge weighted mean was not recommended in the high-Arctic Zackenberg River, unless sampling was done bi-daily, every day and events sampled high-frequently.

Approaches for estimating PUF-air partitions coefficient for semi-volatile organic compounds: A critical comparison

Partition coefficients between polyurethane foam (PUF) and air (K_PUF-Air) are important when using PUF as a passive air sampler for semi-volatile organic compounds (SVOCs) and when considering the fate of SVOCs indoors where PUF is a common material. Here, K_PUF-Air for selected SVOCs was estimated using published methods, since measured data are unavailable for most of these compounds. Estimates of K_PUF-Air were within one order of magnitude for SVOCs having values of log octanol-air partition coefficient (K_OA) of 5, but differed by nearly three orders of magnitude for SVOCs with log K_OA of 12. Of all the methods, the correlation developed using experimental measurements gave the lowest estimates for the high K_OA compounds, likely because the compounds did not reach equilibrium throughout the PUF sample. The surface area/volume ratio of the PUF sample was shown to influence the observed correlation, a reflection of the equilibration status of the PUF. For quantitative comparison, the poly parameter linear free energy relationship (pp-LFER) model of Kamprad and Goss (2007) was used here as a "surrogate" standard. The correlations developed with vapor pressure and K_OA produced estimates that were closest to those obtained using the pp-LFER model. COSMO-RS theory, in which intimate and unimpeded contact is assumed between the compound in air and PUF molecules, gave lower estimates for low K_OA compounds, but good average agreement for high K_OA compounds. When used in modeling applications, the selection of the method for estimating K_PUF-Air should reflect the configuration of the products containing PUF and the model assumptions regarding compound homogeneity within the PUF.

Assessment of the cell biovolume of phytoplankton widespread in coastal and inland water bodies

The biovolume of phytoplankton must be assessed accurately in order to identify the ecological status of water bodies in line with the WFD requirements. Hence, the current study has been carried out to verify and improve the precision of as well as to facilitate and accelerate estimations of phytoplankton biovolume by reviewing and rearranging the basic geometrical shapes of these organisms applied in such evaluations. The latest standards comprise 17 geometric shapes and equations suitable for estimations of cell/filament/colony biovolume and additionally include taxa-specific 'geometric correction factors' to fit real shapes and 'hidden dimension factors' to achieve data on hardly measureable dimensions. This paper also discusses possible obstacles to making correct biovolume assessments, especially when analyzing taxa of special concern, e.g. Ceratium hirundinella, C. furcoides or Pediastrum duplex and Pseudopediastrum boryanum. Our comparison of two approaches, the previous and the new one, revealed that they yield statistically significantly different biovolume results of these species. Some recommendations how to deal with the new and old methods of biovolume estimations and how to reduce the possibility of errors with overestimation and underestimation were also given. The more recent method can be said to give more precise estimates of phytoplankton biovolume. Besides, it facilitates more rapid phytoplankton analyses in most cases, which is very useful when assessing the ecological status of lakes during routine monitoring programs.

Prediction of enthalpy and standard Gibbs energy of vaporization of haloaromatics from atomic properties

Halogenated benzenes form a class of pollutants with a huge number of members - 1504 distinct benzene compounds, where one or more hydrogen atoms are replaced by halogens, may exist theoretically. This study presents a user friendly method for accurate prediction of vapor pressures and enthalpies of vaporization, at 298.15 K, of any mono or poly halobenzene compound. The derived equations for the prediction of those vaporization properties depend just on the number of each constituent halogen atom. This is a consequence of the absence of intramolecular interactions between the halogen atoms, revealed after examining vaporization results of ca. 40 halogenated benzenes. In order to rationalize the estimation equations, the contribution of the halogen atoms for the referred to above properties of vaporization was decomposed into two atomic properties - the volume and electron affinity. Extension of the applicability of the estimation method to substituted benzenes containing other substituent groups beyond halogen atoms as well as to some polycyclic aromatic species was tested with success.