Akaike Weights Research Articles

Single-time-point dosimetry using model selection and nonlinear mixed-effects modelling: a proof of concept

PurposeThis project aims to develop and evaluate a method for accurately determining time-integrated activities (TIAs) in single-time-point (STP) dosimetry for molecular radiotherapy. It performs a model selection (MS) within the framework of the nonlinear mixed-effects (NLME) model (MS–NLME).MethodsBiokinetic data of [111In]In-DOTATATE activity in kidneys at T1 = (2.9 ± 0.6) h, T2 = (4.6 ± 0.4) h, T3 = (22.8 ± 1.6) h, T4 = (46.7 ± 1.7) h, and T5 = (70.9 ± 1.0) h post injection were obtained from eight patients using planar imaging. Eleven functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions’ fixed and random effects parameters were fitted simultaneously (in the NLME framework) to the biokinetic data of all patients. The Akaike weights were used to select the fit function most supported by the data. The relative deviations (RD) and the root-mean-square error (RMSE) of the calculated TIAs for the STP dosimetry at T3 = (22.8 ± 1.6) h and T4 = (46.7 ± 1.7) h p.i. were determined for all functions passing the goodness-of-fit test.ResultsThe function f_{4d} left( t right) = A_{1} /left{ {left( {frac{1 - alpha }{{lambda_{1} + lambda_{{{text{phys}}}} }}} right) - left( {frac{alpha }{{lambda_{2} + lambda_{{{text{phys}}}} }}} right) - left( {frac{1 - 2alpha }{{lambda_{bc} + lambda_{{{text{phys}}}} }}} right)} right} cdot e^{{ - lambda_{{{text{phys}}}} t}} cdot left{ {left( {1 - alpha } right) cdot e^{{ - lambda_{1} t}} - alpha cdot e^{{ - lambda_{2} t}} - left( {1 - 2alpha } right) cdot e^{{ - lambda_{bc} t}} } right} with four adjustable parameters and lambda_{bc} = frac{{{text{ln}}left( 2 right)}}{{1;{text{ min}}}} was selected as the function most supported by the data with an Akaike weight of (45 ± 6) %. RD and RMSE values show that the MS–NLME method performs better than functions with three or five adjustable parameters. The RMSEs of TIANLME–PBMS and TIA3-parameters were 7.8% and 10.9% (for STP at T3), and 4.9% and 10.7% (for STP at T4), respectively.ConclusionAn MS–NLME method was developed to determine the best fit function for calculating TIAs in STP dosimetry for a given radiopharmaceutical, organ, and patient population. The proof of concept was demonstrated for biokinetic 111In-DOTATATE data, showing that four-parameter functions perform better than three- and five-parameter functions.

Validity and Accuracy of Impulse-Response Models for Modeling and Predicting Training Effects on Performance of Swimmers.

The aim of this study was to compare the suitability of models for practical applications in training planning. We tested six impulse-response models, including Banister's model (Model Ba), a variable dose-response model (Model Bu), and indirect-response models differing in the way they account or not for the effect of previous training on the ability to respond effectively to a given session. Data from 11 swimmers were collected during 61 wk across two competitive seasons. Daily training load was calculated from the number of pool-kilometers and dry land workout equivalents, weighted according to intensity. Performance was determined from 50-m trials done during training sessions twice a week. Models were ranked on the base of Aikaike's information criterion along with measures of goodness of fit. Models Ba and Bu gave the greatest Akaike weights, 0.339 ± 0.254 and 0.360 ± 0.296, respectively. Their estimates were used to determine the evolution of performance over time after a training session and the optimal characteristics of taper. The data of the first 20 wk were used to train these two models and predict performance for the after 8 wk (validation data set 1) and for the following season (validation data set 2). The mean absolute percentage error between real and predicted performance using Model Ba was 2.02% ± 0.65% and 2.69% ± 1.23% for validation data sets 1 and 2, respectively, and 2.17% ± 0.65% and 2.56% ± 0.79% with Model Bu. The findings showed that although the two top-ranked models gave relevant approximations of the relationship between training and performance, their ability to predict future performance from past data was not satisfactory for individual training planning.

Integrated intravoxel incoherent motion tensor and diffusion tensor brain MRI in a single fast acquisition.

The acquisition of intravoxel incoherent motion (IVIM) data and diffusion tensor imaging (DTI) data from the brain can be integrated into a single measurement, which offers the possibility to determine orientation-dependent (tensorial) perfusion parameters in addition to established IVIM and DTI parameters. The purpose of this study was to evaluate the feasibility of such a protocol with a clinically feasible scan time below 6 min and to use a model-selection approach to find a set of DTI and IVIM tensor parameters that most adequately describes the acquired data. Diffusion-weighted images of the brain were acquired at 3 T in 20 elderly participants with cerebral small vessel disease using a multiband echoplanar imaging sequence with 15 b-values between 0 and 1000 s/mm2 and six non-collinear diffusion gradient directions for each b-value. Seven different IVIM-diffusion models with 4 to 14 parameters were implemented, which modeled diffusion and pseudo-diffusion as scalar or tensor quantities. The models were compared with respect to their fitting performance based on the goodness of fit (sum of squared fit residuals, chi2 ) and their Akaike weights (calculated from the corrected Akaike information criterion). Lowest chi2 values were found using the model with the largest number of model parameters. However, significantly highest Akaike weights indicating the most appropriate models for the acquired data were found with a nine-parameter IVIM-DTI model (with isotropic perfusion modeling) in normal-appearing white matter (NAWM), and with an 11-parameter model (IVIM-DTI with additional pseudo-diffusion anisotropy) in white matter with hyperintensities (WMH) and in gray matter (GM). The latter model allowed for the additional calculation of the fractional anisotropy of the pseudo-diffusion tensor (with a median value of 0.45 in NAWM, 0.23 in WMH, and 0.36 in GM), which is not accessible with the usually performed IVIM acquisitions based on three orthogonal diffusion-gradient directions.

Population-based model selection for an accurate estimation of time-integrated activity using non-linear mixed-effects modelling

PurposePersonalized treatment planning in Molecular Radiotherapy (MRT) with accurately determining the absorbed dose is highly desirable. The absorbed dose is calculated based on the Time-Integrated Activity (TIA) and the dose conversion factor. A crucial unresolved issue in MRT dosimetry is which fit function to use for the TIA calculation. A data-driven population-based fitting function selection could help solve this problem. Therefore, this project aims to develop and evaluate a method for accurately determining TIAs in MRT, which performs a Population-Based Model Selection within the framework of the Non-Linear Mixed-Effects (NLME-PBMS) model. MethodsBiokinetic data of a radioligand for the Prostate-Specific Membrane Antigen (PSMA) for cancer treatment were used. Eleven fit functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions' fixed and random effects parameters were fitted (in the NLME framework) to the biokinetic data of all patients. The goodness of fit was assumed acceptable based on the visual inspection of the fitted curves and the coefficients of variation of the fitted fixed effects. The Akaike weight, the probability that the model is the best among the whole set of considered models, was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit. NLME-PBMS Model Averaging (MA) was performed with all functions having acceptable goodness of fit. The Root-Mean-Square Error (RMSE) of the calculated TIAs from individual-based model selection (IBMS), a shared-parameter population-based model selection (SP-PBMS) reported in the literature, and the functions from NLME-PBMS method to the TIAs from MA were calculated and analysed. The NLME-PBMS (MA) model was used as the reference as this model considers all relevant functions with corresponding Akaike weights. ResultsThe function f3a=A1e-λ1+λphyst+A2e-λphyst was selected as the function most supported by the data with an Akaike weight of (54 ± 11) %. Visual inspection of the fitted graphs and the RMSE values show that the NLME model selection method has a relatively better or equivalent performance than the IBMS or SP-PBMS methods. The RMSEs of the IBMS, SP-PBMS, and NLME-PBMS (f3a) methods are 7.4%, 8.8%, and 2.4%, respectively. ConclusionA procedure including fitting function selection in a population-based method was developed to determine the best fit function for calculating TIAs in MRT for a given radiopharmaceutical, organ and set of biokinetic data. The technique combines standard practice approaches in pharmacokinetics, i.e. an Akaike-weight-based model selection and the NLME model framework.

The role of patch closure in current-day carotid endarterectomy.

It has long been debated whether it is preferable to perform conventional carotid endarterectomy (CEA) with or without patch closure. Although most contemporary surgeons patch, many still do not. Recent small studies have surfaced implying patching is unnecessary. The objective of our analysis was to determine the difference in short- and long-term outcomes according to patch use in a large modern, cross-specialty database. Analyzing more than 118,000 records from the Vascular Quality Initiative, multimodel inference was used to evaluate the effect of patch use on important outcomes of conventional CEA. The composite short-term outcome included any ipsilateral neurological event, return to the operating room for a neurological event, and an increase in the Rankin score postoperatively. Late composite outcome incorporated restenosis as well as early and late ipsilateral neurological events. Patch use for conventional CEA closure was found to be a strong predictor of both early and late outcomes, as evidenced by its Akaike importance weight of 0.99. Examining predischarge events, patch closure is associated with a decrease in major negative events (odds ratio, 0.5; 95% confidence interval, 0.4-0.6). For long-term events, such closure offers a decrease in untoward outcome (odds ratio, 0.8; 95% confidence interval, 0.7-0.9). Analysis in a large current-day database suggests that patch closure of conventional CEA effects superior short- and long-term outcomes.

Recovering crossed random effects in mixed-effects models using model averaging

Random effects contain crucial information to understand the variability of the processes under study in mixed-effects models with crossed random effects (MEMs-CR). Given that model selection makes all-or-nothing decisions regarding to the inclusion of model parameters, we evaluated if model averaging could deal with model uncertainty to recover random effects of MEMs-CR. Specifically, we analyzed the bias and the root mean squared error (RMSE) of the estimations of the variances of random effects using model averaging with Akaike weights and Bayesian model averaging with BIC posterior probabilities, comparing them with two alternative analytical strategies as benchmarks: AIC and BIC model selection, and fitting a full random structure. A simulation study was conducted manipulating sample sizes for subjects and items, and the variance of random effects. Results showed that model averaging, especially Akaike weights, can adequately recover random variances, given a minimum sample size in the modeled clusters. Thus, we endorse using model averaging to deal with model uncertainty in MEMs-CR. An empirical illustration is provided to ease the usability of model averaging.

Corrigendum

Global Ecology and BiogeographyVolume 32, Issue 1 p. 191-192 CORRIGENDUMFree Access Corrigendum This article corrects the following: Plant mycorrhizal status, but not type, shifts with latitude and elevation in Europe C. Guillermo Bueno, Mari Moora, Maret Gerz, John Davison, Maarja Öpik, Meelis Pärtel, Aveliina Helm, Argo Ronk, Ingolf Kühn, Martin Zobel, Brody Sandel, Volume 26Issue 6Global Ecology and Biogeography pages: 690-699 First Published online: March 31, 2017 First published: 16 December 2022 https://doi.org/10.1111/geb.13606AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat In the article by Bueno et al. (2017) entitled, “Plant mycorrhizal status, but not type, shifts with latitude and elevation in Europe”, which was published in Global Ecology and Biogeography 26(6) (pages 690–699), contained errors in Figures 1e, 3a, and 3c. The corrected versions are provided below: Figure 1e. The maximum value of the legend was corrected. Figure 3a, The symbols in the plot were fixed to match the ones in the legend. Figure 3c. The order of the legend elements and the colour code were corrected to match the presentation of the same categories in other figures in the paper. Figure 1e. The share of obligately mycorrhizal (OM) plants in 50 km × 50 km grid cells in Europe. Values in legend represent the respective maximum, median and minimum proportions. ‘M' stands for mycorrhizal plant species. Figure 3a. Model averaged (ΔAIC <7) predictor coefficients with one confidence interval describing the proportion of plant species with plant mycorrhizal types in Europe. AM, arbuscular mycorrhizal; ECM, ectomycorrhizal; ERM, ericoid mycorrhizal; NM, non-mycorrhizal; NPP, net primary productivity; MAT(r), residuals of mean annual temperature excluding the effect of pH and NPP; MDR, mean diurnal temperature range; APP, annual precipitation; PPS, precipitation seasonality. Figure 3c. Model averaged (ΔAIC <7) variable importance plots describing the proportion of plant species with plant mycorrhizal statuses in Europe. The importance for each variable was calculated as the sum of the Akaike weights for all the models where each particular variable appears. Variable importance is used to rank the relevance of the predictors, as it indicates the relative probability of each variable belonging to the best model set. AM, arbuscular mycorrhizal; ECM, ectomycorrhizal; ERM, ericoid mycorrhizal; NM, non-mycorrhizal; OM, obligate mycorrhizal; NPP, net primary productivity; MAT(r), residuals of mean annual temperature excluding the effect of pH and NPP; MDR, mean diurnal temperature range; APP, annual precipitation; PPS, precipitation seasonality. REFERENCE Bueno, C. G., Moora, M., Gerz, M., Davison, J., Öpik, M., Pärtel, M., Helm, A., Ronk, A., Kühn, I., & Zobel, M. (2017). Plant mycorrhizal status, but not type, shifts with latitude and elevation in Europe. Global Ecology and Biogeography, 26, 690– 699. https://doi.org/10.1111/geb.12582 Volume32, Issue1January 2023Pages 191-192 ReferencesRelatedInformation

Protocol and Software for Automated Detection of Lysosome Active "Runs" and "Flights" with Wavelet Transform Approach.

Lysosomes are highly dynamic degradation/recycling organelles that harbor sophisticated molecular sensors and signal transduction machinery through which theycontrol cell adaptation to environmental cues and nutrients. The movements of these signaling hubs comprise persistent, directional runs-active, ATP-dependent transport along the microtubule tracks-interspersed by short, passive movements and pauses imposed by cytoplasmic constraints. The trajectories of individual lysosomes are usually obtained by time-lapse imaging of the acidic organelles labeled with LysoTracker dyes or fluorescently-tagged lysosomal-associated membrane proteins LAMP1 and LAMP2. Subsequent particle tracking generates large data sets comprising thousands of lysosome trajectories and hundreds of thousands of data points. Analyzing such data sets requires unbiased, automated methods to handle large data sets while capturing the temporal heterogeneity of lysosome trajectory data. This chapter describes integrated and largely automated workflow from live cell imaging to lysosome trajectories to computing the parameters of lysosome dynamics. We describe an open-source code for implementing the continuous wavelet transform (CWT) to distinguish trajectory segments corresponding to active transport (i.e., "runs" and "flights") versus passive lysosome movements. Complementary cumulative distribution functions (CDFs) of the "runs/flights" are generated, and Akaike weight comparisons with several competing models (lognormal, power law, truncated power law, stretched exponential, exponential) are performed automatically. Such high-throughput analyses yield useful aggregate/ensemble metrics for lysosome active transport.

Research on the relationship between the formation of local construction culture and geographical environment based on adaptability analysis

ObjectivesSince the natural ecology and geographical environment are the basis for the formation of local architecture, based on the adaptability analysis, the article analyzes the natural ecology and geographical environment that affect the creation of regional local architecture, and analyzes the adaptability of traditional architecture to natural ecology and the impact of traditional culture. Methods: The summary of the response methods is to try to find the substantive connotation of vernacular architecture in order to provide basic theoretical support for contemporary vernacular architecture creation. At the same time, combined with the characteristics of the times of the contemporary area, it proposes a typical site design adaptability analysis, a suitability climate adaptability analysis and a construction adaptability analysis returning to the local culture. And for the coastal cultural and historical background of the region, the development of regional ancient towns is discussed, and the location of regional coastal ancient towns is analyzed for the coastal environment. ResultsThe final selected model was a weighted average based on Akaike weights of 71 logistic candidate models that included all the variables in these 71 candidate models. The importance weights of variables are the criteria for assessing the impact and contribution rate of environmental factors on survival and dispersal, and are the sum of the Akaike weights of all candidate models containing a given predictor variable. The connection between households basically uses the scattered water of the building, does not occupy the foundation, and basically does not damage the landform. The entrance to the building is determined by the terrain on the one hand, and the road on the other, and is generally set on one side of the road. Finally, the coastal environmental background and historical and cultural background of regional ancient towns are summarized, and the research roughly explores the region. Conclusions: At the end of the article, through the interpretation of actual cases, it provides certain evidence and explanations for adaptability analysis, and expresses the design ideas of comprehensive trade-offs in the process of adaptability analysis, in order to provide contemporary local architectural design for the extensive urban and rural construction in the region with theories and adaptability analysis.

Solubility and Solvent Effect Analysis of N-Benzyloxycarbonyl-l-tryptophan in 12 Monosolvent Systems at Multiple Temperatures

The solid–liquid equilibrium solubility and solvent effects of N-benzyloxycarbonyl-l-tryptophan in monosolvent systems (water, isopropanol, ethanol, n-propanol, isobutanol, n-butanol, acetonitrile, n-pentanol, 2-butanone, acetone, methyl acetate, and ethyl acetate) were reported in this work. All the solubility data were measured at 283.15–323.15 K (5 K interval) by the static gravimetric method. It was confirmed by powder X-ray diffraction that the crystal form of N-benzyloxycarbonyl-l-tryptophan did not change in the process of solubility determination. Among the 12 pure solvents, the solubility increased with the increase of absolute temperature. The solubility is the largest in acetone and the smallest in water. The solubility behavior and solvent effects in different monosolvents were first analyzed by taking the empirical solvent polarity parameter (ET(30)) as the main factor. Then the natural logarithm of solubility (lnx1) was linearly fitted to ET(30) for dipolar protic and aprotic solvents, respectively. Lastly, the special solubility behavior in isopropanol and water/acetonitrile was explained by the hydrogen bond acceptor tendencies and the cohesive energy density, respectively. The solvent effect analysis results illustrated that the solubility sequence of N-benzyloxycarbonyl-l-tryptophan in the test solvents resulted from the comprehensive effect of multiple factors. The Yaws model and the modified Apelblat model were employed to correlate the experimental solubility, and the fitting results of the two models were well. In addition, Akaike Information Criterion values and Akaike weights of the two models were calculated to evaluate the fitting level.

Predation risk can modify the foraging behaviour of frugivorous carnivores: Implications of rewilding apex predators for plant-animal mutualisms.

Apex predators play key roles in food webs and their recovery can trigger trophic cascades in some ecosystems. Intra‐guild competition can reduce the abundances of smaller predators and perceived predation risk can alter their foraging behaviour thereby limiting seed dispersal by frugivorous carnivores. However, little is known about how plant–frugivore mutualisms could be disturbed in the presence of larger predators.We evaluated the top‐down effect of the regional superpredator, the Iberian lynx Lynx pardinus, on the number of visits and fruits consumed by medium‐sized frugivorous carnivores, as well as the foraging behaviour of identified individuals, by examining the consumption likelihood and the foraging time.We carried out a field experiment in which we placed Iberian pear Pyrus bourgaeana fruits beneath fruiting trees and monitored pear removal by frugivorous carnivores, both inside and outside lynx ranges. Using camera traps, we recorded the presence of the red fox Vulpes vulpes, the Eurasian badger Meles meles and the stone marten Martes foina, as well as the number of fruits they consumed and their time spent foraging.Red fox was the most frequent fruit consumer carnivore. We found there were fewer visits and less fruit consumed by foxes inside lynx ranges, but lynx presence did not seem to affect badgers. We did not observe any stone marten visits inside lynx territories. The foraging behaviour of red foxes was also altered inside lynx ranges whereby foxes were less efficient, consuming less fruit per unit of time and having shorter visits. Local availability of fruit resources, forest coverage and individual personality also were important variables to understand visitation and foraging in a landscape of fear.Our results show a potential trophic cascade from apex predators to primary producers. The presence of lynx can reduce frugivorous carnivore numbers and induce shifts in their feeding behaviour that may modify the seed dispersal patterns with likely consequences for the demography of many fleshy‐fruited plant species. We conclude that knowledge of the ecological interactions making up trophic webs is an asset to design effective conservation strategies, particularly in rewilding programs.

Nonmedical prescription drug use among female adolescents: the relative influence of maternal factors, social norms, and perceptions of risk and availability

Increasing understanding of the risk and protective factors for adolescent nonmedical use of prescription drugs (NMUPD) could inform prevention efforts. Several correlates have been identified, including parental factors, perceptions about use and accessibility, social norms, and age. However, these constructs have rarely been simultaneously examined using paired data from parents and adolescents. We aimed to examine the relative influence of these correlates among dyads (N = 349) of mothers and adolescent daughters. Using multiple logistic regression, daughters’ past NMUPD and inclination for future NMUPD were regressed onto descriptive norms for friend use, perceived drug accessibility and risk of harm from use, daughter age, mothers’ disapproval about use, mothers’ past NMUPD and inclination for future NMUPD, and the mother-daughter relationship quality. Akaike weights and lasso regressions were also estimated to evaluate the relative importance of each correlate. Higher descriptive norms for friend use, older age, and mothers’ inclination for NMUPD were risk factors for daughters’ NMUPD, while a closer mother-daughter relationship and mothers’ disapproving attitudes towards NMUPD were protective factors. The three analysis approaches were corroborative. Results suggest friend descriptive norms, mother-daughter relationship quality, and mothers’ attitudes about NMUPD are important prevention targets.

Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos.

Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.

Selection of Formal Baseline Correction Methods in Thermal Analysis

AbstractBaseline correction is a key step in processing of thermal analysis data. Whilst this is a common step, techniques range from linear baselines to use of high‐order polynomials. When considering a formal baseline correction (those without physical or experimental justification), only linear correction methods should be used: linear with time, linear with temperature, and linear with extent of reaction. The absence of baseline correction should also be considered. An in silico study shows that the wrong baseline correction can significantly impact the parameters obtained from kinetic modeling. The four baseline correction methods are demonstrated with a mass spectrometry dataset. It is recommended that the selection of correction method should be based on comparison of Akaike weights.

A population-based method to determine the time-integrated activity in molecular radiotherapy

BackgroundThe calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [177Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient.MethodsRenal biokinetics of [177Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit.ResultsThe function A_{1} { }beta { }e^{{ - left( {lambda_{1} + lambda_{{{text{phys}}}} } right)t}} + A_{1} { }left( {1 - beta } right){ }e^{{ - left( {lambda_{{{text{phys}}}} } right)t}} with shared parameter beta was selected as the function most supported by the data with an Akaike weight of 97%. Parameters A_{1} and lambda_{1} were fitted individually for every patient while parameter beta { } was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037.ConclusionsThe presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

Mapping Female Patients’ Judgments of Satisfaction to Hypothetical Changes in Depression Symptom Severity

Within mental health, approaches to determine whether a patient experienced “meaningful” change from treatment have predominantly involved imposing thresholds on three types of metrics derived from assessments of symptom severity: end score (posttreatment score), absolute change (pre- minus posttreatment score), and proportion of change. However, none of these approaches have considered input from the consumer. This study examined correspondences between various reductions from pre- to posttreatment symptom severity levels and patients’ judgments of satisfaction with change. Former or currently depressed patients were asked to provide judgments of their satisfaction reflected in vignettes that used descriptions from the Hamilton Rating Scale for Depression. Judgments from 108 female participants were fit using four metrics: end score, absolute change, proportion of change, and the combination of end score and absolute change. Akaike information criteria (AICs) and Akaike weights were used to determine the best-fitting model. Cutoffs were calculated for the five levels of satisfaction with change. Proportion of change best accounted for variation in the patients’ ratings. For “slightly … ,” “somewhat … ,” “moderately … ,” and “very … ,” the proportions of reduction that corresponded with each of these ratings of satisfaction were, respectively: 17%, 39%, 62%, and 84%. Our a priori level of satisfaction (between “somewhat” and “moderately”) corresponded to a 50% reduction in pretreatment severity. This study may provide services some insight into their female patients’ satisfaction with change from treatment for depression using only the proportion of reduction from pretreatment severity. A similar procedure could be applied to other diagnostic groups, as well as other constructs that attend to the patient’s perspective.

Solubility and Hansen Solubility Parameters of l-Glutamic Acid 5-Methyl Ester in 12 Organic Solvents from 283.15 to 323.15 K

In this study, the quantitative mole fraction solubility of l-glutamic acid 5-methyl ester in 12 individual organic solvents (water, methanol, ethanol, 1-propanol, 2-propanol, acetone, 2-butanone, acetonitrile, 1,4-dioxane, ethyl acetate, n-hexane, and dichloromethane) were reported. The solubility determinations were performed via the gravimetric method in the temperature range of T = 283.15–323.15 K, except for dichloromethane at T = 283.15–308.15 K. The powder X-ray diffraction test was used to research the polymorphism of l-glutamic acid 5-methyl ester, and the consequence shows that there is no crystal transformation in the process of solubility measurement; besides, it is found that the mole fraction solubility of l-glutamic acid 5-methyl ester is positively correlated with the experimental temperature in the tested solvents. The measured data are observed the highest in water (0.042569), followed by methanol (0.001379), 1,4-dioxane (0.000331), acetone (0.000221), ethanol (0.000212), ethyl acetate (0.000145), 2-propanol (0.000144), n-hexane (0.000132), 1-propanol (0.000116), 2-butanone (0.000107), acetonitrile (0.000034), and dichloromethane (0.000024) at “T = 298.15 K”. Different properties of the chemicals, including solvent polarity, hydrogen bond, molecular structure, and Hansen solubility parameters, were summarized to analyze the solubility behavior of l-glutamic acid 5-methyl ester in the investigated neat solvents. The results show that the mole fraction solubility of l-glutamic acid 5-methyl ester in the selected solvents is a complicated phenomenon affected by multiple factors. Two thermodynamic models, which are the modified Apelblat model and the Yaws model, were employed to correlate the experimental solubility, and the fitting results of the two models were both well. Moreover, the AIC values and the Akaike weights of the two models were computed to assess the fitting level.

Seasonal seismic activity on Mars

The rate of occurrence of High Frequency (HF) marsquakes, as recorded by InSight at Homestead Hollow, Elysium Planitia, increased after about LS=33∘, and ceased almost completely by LS=187∘, following an apparently seasonal variation with a peak rate near aphelion. We define seismic rate models based on the declination of the Sun, annual solar tides, and the annual CO2 cycle as measured by atmospheric pressure. Evaluation of Akaike weights and evidence ratios shows that the declination of the Sun is the most likely, and the CO2 cycle the least likely driver of this seismic activity, although the discrimination is weak, and the occurrence of a few events in August 2020 is in favor for a triggering by CO2 ice load. We also show that no periodicity related to Phobos' orbit is present in the HF event sequence. Event rate forecasts are presented to allow further discrimination of candidate mechanisms from future observations.

Towards a pragmatic use of statistics in ecology.

Although null hypothesis testing (NHT) is the primary method for analyzing data in many natural sciences, it has been increasingly criticized. Recently, approaches based on information theory (IT) have become popular and were held by many to be superior because it enables researchers to properly assess the strength of the evidence that data provide for competing hypotheses. Many studies have compared IT and NHT in the context of model selection and stepwise regression, but a systematic comparison of the most basic uses of statistics by ecologists is still lacking. We used computer simulations to compare how both approaches perform in four basic test designs (t-test, ANOVA, correlation tests, and multiple linear regression). Performance was measured by the proportion of simulated samples for which each method provided the correct conclusion (power), the proportion of detected effects with a wrong sign (S-error), and the mean ratio of the estimated effect to the true effect (M-error). We also checked if the p-value from significance tests correlated to a measure of strength of evidence, the Akaike weight. In general both methods performed equally well. The concordance is explained by the monotonic relationship between p-values and evidence weights in simple designs, which agree with analytic results. Our results show that researchers can agree on the conclusions drawn from a data set even when they are using different statistical approaches. By focusing on the practical consequences of inferences, such a pragmatic view of statistics can promote insightful dialogue among researchers on how to find a common ground from different pieces of evidence. A less dogmatic view of statistical inference can also help to broaden the debate about the role of statistics in science to the entire path that leads from a research hypothesis to a statistical hypothesis.

Delivered dose–effect analysis of radiation induced rib fractures after thoracic SBRT

Background and purposeAnatomical changes during the stereotactic body radiation therapy (SBRT) of early stage non-small cell lung cancer (NSCLC) may cause the delivered dose to deviate from the planned dose. We investigate if normal tissue complication probability (NTCP) models based on the delivered dose predict radiation-induced rib fractures better than models based on the planned dose. Material and methods437 NSCLC patients treated to a median dose of 3x18 Gy were included. Delivered dose was estimated by accumulating EQD2-corrected fraction doses after being deformed with daily CBCT-to-planning CT deformable image registration.Dosimetric parameters Dx (dose to a relative volume x) were extracted for each rib included in the CBCTs field-of-view. An NTCP model was constructed for both planned and delivered dose, optimizing the parameters TD50 (dose with 50% toxicity risk), m (steepness of the curve) and x, using maximum likelihood estimation. Best NTCP model was determined using Akaike weights (Aw). Differences between the models were tested for significance using the Vuong’s test. ResultsMedian time to fracture of 110 fractured ribs was 22.5 months. The maximum rib dose, D0, best predicted fractures for both planned and delivered dose. The average delivered D0 was significantly lower than planned (p < 0.001). NTCP model based on the delivered D0 was the best, with Aw = 0.95. The models were not significantly different. ConclusionDelivered maximum dose to the ribs was significantly lower than planned. The NTCP model based on delivered dose improved predictions of radiation-induced rib fractures but did not reach statistical significance.