Estimation Of Prediction Accuracy Research Articles

Alternative methods improve the accuracy of genomic prediction using information from a causal point mutation in a dairy sheep model

BackgroundGenomic evaluation is usually based on a set of markers assumed to be linked with causal mutations. Selection and precise management of major genes and the remaining polygenic component might be improved by including causal polymorphisms in the evaluation models. In this study, various methods involving a known mutation were used to estimate prediction accuracy. The SOCS2 gene, which influences body growth, milk production and somatic cell scores, a proxy for mastitis, was studied as an example in dairy sheep.MethodsThe data comprised 1,503,148 phenotypes and 9844 54K SNPs genotypes. The SOCS2 SNP was genotyped for 4297 animals and imputed in the above 9844 animals. Breeding values and their accuracies were estimated for each of nine traits by using single-step approaches. Pedigree-based BLUP, single-step genomic BLUP (ssGBLUP) involving the 54K ovine SNPs chip, and four weighted ssGBLUP (WssGBLUP) methods were compared. In WssGBLUP methods, weights are assigned to SNPs depending on their effect on the trait. The ssGBLUP and WssGBLUP methods were again tested after including the SOCS2 causal mutation as a SNP. Finally, the Gene Content approach was tested, which uses a multiple-trait model that considers the SOCS2 genotype as a trait.ResultsEBV accuracies were increased by 14.03% between the pedigree-based BLUP and ssGBLUP methods and by 3.99% between ssGBLUP and WssGBLUP. Adding the SOCS2 SNP to ssGBLUP methods led to an average gain of 0.26%. Construction of the kinship matrix and estimation of breeding values was generally improved by placing emphasis on SNPs in regions with a strong effect on traits. In the absence of chip data, the Gene Content method, compared to pedigree-based BLUP, efficiently accounted for partial genotyping information on SOCS2 as accuracy was increased by 6.25%. This method also allowed dissociation of the genetic component due to the major gene from the remaining polygenic component.ConclusionsCausal mutations with a moderate to strong effect can be captured with conventional SNP chips by applying appropriate genomic evaluation methods. The Gene Content method provides an efficient way to account for causal mutations in populations lacking genome-wide genotyping.

141 Using Random Forest Plots to Examine Predictive and Discriminative Ability of Mobility Measures for Future Falls

Abstract Background Slow gait speed and Timed Up-and Go (TUG) are often independent predictors of falls in regression analysis, although their ability to discriminate between fallers and non-fallers is questionable. Random forest plots can model complex interactions between predictor variables and have high classification accuracy. We compare the predictive and discriminative ability of UGS and TUG in predicting recurrent falls over 4 years using poisson regression and random forest plots. Methods Data from the first three waves of The Irish Longitudinal Study on Ageing (TILDA), a population-based study of community-dwelling adults aged ≥50 years were used. Baseline physical, neuro-cognitive, sensory and behavioural health were assessed. The outcome was recurrent (≥2) falls at Wave 2 or Wave 3. Poisson regression analysis was used to examine associations between UGS, TUG and falls adjusting for covariates. Random forest models were used. Predictive accuracy was calculated using 5 fold cross-validation and as there was class imbalance, the algorithm was trained using under-sampling of the larger class. Classification rate, area under the receiver operating characteristic curve (AUC) and area under the precision recall curve (PRROC) were obtained to assess predictive accuracy. Results In poisson regression analysis (n=4918), TUG predicted recurrent falls independent of covariates including UGS (IRR=1.06, 95% CI: 1.01, 1.12, p<0.05). The random forest model predicted 60.82% of participants correctly (61.85% of non-fallers; 55.37% of fallers). AUC was 0.63 and PRROC was 0.28. Conclusion Impaired mobility i.e. slower TUG performance, is an independent predictor of future recurrent falls, however it does not discriminate well between fallers and non-fallers. This is highlighted by the PRROC which provides a more conservative estimate of predictive accuracy than AUC as it accounts for the ability to identify both fallers and non-fallers. The analysis highlights the multifactorial nature and complexity of falls, and supports the need for comprehensive falls assessment.

Machine learning models accurately predict ozone exposure during wildfire events

Epidemiologists use prediction models to downscale (i.e., interpolate) air pollution exposure where monitoring data is insufficient. This study compares machine learning prediction models for ground-level ozone during wildfires, evaluating the predictive accuracy of ten algorithms on the daily 8-hour maximum average ozone during a 2008 wildfire event in northern California. Models were evaluated using a leave-one-location-out cross-validation (LOLO CV) procedure to account for the spatial and temporal dependence of the data and produce more realistic estimates of prediction error. LOLO CV avoids both the well-known overly optimistic bias of k-fold cross-validation on dependent data and the conservative bias of evaluating prediction error over a coarser spatial resolution via leave-k-locations-out CV. Gradient boosting was the most accurate of the ten machine learning algorithms with the lowest LOLO CV estimated root mean square error (0.228) and the highest LOLO CV Rˆ2 (0.677). Random forest was the second best performing algorithm with an LOLO CV Rˆ2 of 0.661. The LOLO CV estimates of predictive accuracy were less optimistic than 10-fold CV estimates for all ten models. The difference in estimated accuracy between the 10-fold CV and LOLO CV was greater for more flexible models like gradient boosting and random forest. The order of estimated model accuracy depended on the choice of evaluation metric, indicating that 10-fold CV and LOLO CV may select different models or sets of covariates as optimal, which calls into question the reliability of 10-fold CV for model (or variable) selection. These prediction models are designed for interpolating ozone exposure, and are not suited to inferring the effect of wildfires on ozone or extrapolating to predict ozone in other spatial or temporal domains. This is demonstrated by the inability of the best performing models to accurately predict ozone during 2007 southern California wildfires.

Accuracy of Genomic-Polygenic and Polygenic Breeding Values for Age at First Calving and Milk Yield in Thai Multibreed Dairy Cattle

Abstract Single-nucleotide polymorphisms (SNPs) have been used in genomic prediction and shown to increase prediction accuracy and selection responses for economic traits in dairy cattle. The successful report in genomic prediction for improving age at first calving (AFC) and 305-d milk yield (MY) in multibreed dairy population is limited. Therefore, the objective of this research was to compare estimates of variance components, genetic parameters, and prediction accuracies for AFC and MY using a genomic-polygenic model (GPM) and a polygenic model (PM). The AFC and MY records of 9,106 first-lactating multibreed dairy cows, calved between 1991 and 2014, were collected from 1,012 Thai dairy farms. The SNP genotyped individuals were selected from cows that had completed pedigree and phenotypes information. The total genomic DNA samples of 2,661 dairy cattle were genotyped using various GeneSeek Genomic Profiler low-density bead chips (9K, 20K, and 80K). The 2-trait GPM and PM contained herd-year-season and heterosis as fixed effects, and animal additive genetic and residual as random effects. Variance components and genetic parameters were estimated using the procedure of average information-restricted maximum likelihood (AI-REML). Estimates of additive genetic variance components and heritabilities from GPM were higher than PM for AFC and MY. Correlations between AFC and MY were near zero for both models. Mean EBV accuracies were higher for GPM (32.95% for AFC and 38.24% for MY) than for PM (32.65% for AFC, and 32.99% for MY). Mean sire EBV accuracies were higher for GPM (31.35% for AFC and 36.25% for MY) than for PM (28.37% for AFC and 28.80% for MY). Thus, the GPM should be considered the model of choice to increase accuracy of genetic predictions for AFC and MY in the Thai multibreed dairy population.

Threshold values affect predictive accuracy of caries risk assessment

Objective: To evaluate effects of thresholds on estimates of predictive accuracy of methods for caries risk assessment.Material and methods: Adolescents, aged 12 visiting two dental clinics, were examined by visual/tactile examination and bitewing radiography at baseline and after one year. Three methods for caries risk assessment were applied: previous caries experience, dentists’ risk assessment according to set criteria (presence or absence of caries lesion) and acid tolerance of dental biofilm. The measure for validity (the reference standard) comprised caries lesion progression at 1 year. Predictive accuracy estimates were calculated for several thresholds.Results: Accuracy estimates changed with threshold values of the methods and the reference standard. Patient spectrum differed between the clinics, which resulted in different accuracy estimates for the two samples. Generally, negative predictive values were high while positive ones were low indicating that these methods were more efficient in finding individuals who are at low risk of developing caries lesions than those with increased risk.Conclusions: As thresholds and patient spectrum affected predictive accuracy, it may be difficult to design a universal model with set thresholds for caries risk assessment. Foremost, a model should consider the level of aspiration for prediction and clinical decisions that will be made based on the risk assessment in the actual clinical setting.

Analysis of spatial variance clustering in the hedonic modeling of housing prices

ABSTRACTThis paper examines the spatial dependency exhibited by the error term variance of hedonic modeling based on German housing price data. To this end, it applies the spatial autoregressive conditional heteroscedasticity (SARCH) model previously discussed in housing literature, which allows for the consideration of spatial dependency when modeling the error variance of hedonic pricing. This model represents a spatialized version of the well-known ARCH-model used in time series analysis. Consistent with previous findings, this paper confirms the existence of spatial conditional heteroscedasticity, i.e. dependency in the error variance. However, this spatial dependency is not a global phenomenon, but can be ascribed to spatial concentrations of apartments with a relatively high variance in a small number of the same neighborhoods. The analysis of spatial heteroscedasticity helps to improve the estimation efficiency and prediction accuracy. In addition, spatial differences can be used to account for idiosyncratic risk when conducting mass appraisal.

ULTRA-HIGH-PERFORMANCE FIBRE-REINFORCED CONCRETE UNDER HIGH-VELOCITY PROJECTILE IMPACT - PART 2. APPLICABILITY OF PREDICTION MODELS

Semi-infinite targets of Ultra-High-Performance Fibre-Reinforced Concrete with various fibre volume fractions were subjected to the high-velocity projectile impact using in-service bullets. In this study, a variety of empirical and semi-analytical models for prediction of the depth of penetration and mass ejection were evaluated with respect to the experimental results. Models for the depth of penetration and spalling mass ejection were revisited and applied both with deformable and nondeformable projectiles parameters. The applicability of the prediction models was assessed through a statistical comparison of values from models with experimental results. The evaluation of the applicability was made through the newly proposed measure of a relative prediction accuracy for model selection and model estimation, which was verified with established statistical accuracy evaluations, such as accuracy ratio, logarithmic standard deviation and correlation coefficient. The best fit to the experimental readings was provided by newer semi-analytical models, which are incorporating additional concrete parameters beside compressive strength while the majority of older models failed to provide sufficient accuracy.

Effect of Hidden Relatedness on Single-Step Genetic Evaluation in an Advanced Open-Pollinated Breeding Program.

Open-pollinated (OP) mating is frequently used in forest tree breeding due to the relative temporal and financial efficiency of the approach. The trade-off is the lower precision of the estimated genetic parameters. Pedigree/sib-ship reconstruction has been proven as a tool to correct and complete pedigree information and to improve the precision of genetic parameter estimates. Our study analyzed an advanced generation Eucalyptus population from an OP breeding program using single-step genetic evaluation. The relationship matrix inferred from sib-ship reconstruction was used to rescale the marker-based relationship matrix (G matrix). This was compared with a second scenario that used rescaling based on the documented pedigree. The proposed single-step model performed better with respect to both model fit and the theoretical accuracy of breeding values. We found that the prediction accuracy was superior when using the pedigree information only when compared with using a combination of the pedigree and genomic information. This pattern appeared to be mainly a result of accumulated unrecognized relatedness over several breeding cycles, resulting in breeding values being shrunk toward the population mean. Using biased, pedigree-based breeding values as the base with which to correlate predicted GEBVs, resulted in the underestimation of prediction accuracies. Using breeding values estimated on the basis of sib-ship reconstruction resulted in increased prediction accuracies of the genotyped individuals. Therefore, selection of the correct base for estimation of prediction accuracy is critical. The beneficial impact of sib-ship reconstruction using G matrix rescaling was profound, especially in traits with inbreeding depression, such as stem diameter.

Predicting Lung Function Following Lobectomy: A New Method to Adjust for Inherent Selection Bias

Background: Predictions that overestimate post-lobectomy lung function are more likely than underestimates to lead to lobectomy. Studies of post-lobectomy lung function have included only surgical patients, so overestimates are overrepresented. This selection bias has led to incorrect estimates of prediction bias, which has led to inaccurate threshold values for determining lobectomy eligibility. Objective: The objective of this study was to demonstrate and adjust for this selection bias in order to arrive at correct estimates of prediction bias, the 95% limits of agreement, and adjusted threshold values for determining when exercise testing is warranted. Methods: We conducted a retrospective study of patients evaluated for lobectomy. We used multiple imputations to determine postoperative results for patients who did not have surgery because their predicted postoperative values were low. We combined these results with surgical patients to adjust for selection bias. We used the Bland-Altman method and the bivariate normal distribution to determine threshold values for surgical eligibility. Results: Lobectomy evaluation was performed in 114 patients; 79 had lobectomy while 35 were ineligible based on predicted values. Prediction bias using the Bland-Altman method changed significantly after controlling for selection bias. To achieve a postoperative FEV1 > 30% and DLCO ≥30%, a predicted FEV1 > 46% and DLCO ≥53% were required. Compared to current guidelines, using these thresholds would change management in 17% of cases. Conclusion: The impact of selection bias on estimates of prediction accuracy was significant but can be corrected. Threshold values for determining surgical eligibility should be reassessed.

Genome prediction accuracy of common bean via Bayesian models

ABSTRACT: We aimed to apply genomic information based on SNP (single nucleotide polymorphism) markers for the genetic evaluation of the traits “stay-green” (SG), plant architecture (PA), grain aspect (GA) and grain yield (GY) in common bean through Bayesian models. These models were compared in terms of prediction accuracy and ability for heritability estimation for each one of the mentioned traits. A total of 80 cultivars were genotyped for 377 SNP markers, whose effects were estimated by five different Bayesian models: Bayes A (BA), B (BB), C (BC), LASSO (BL) e Ridge regression (BRR). Although, prediction accuracies calculated by means of cross-validation have been similar within each trait, the BB model stood out for the trait SG, whereas the BRR was indicated for the remaining traits. The heritability estimates for the traits SG, PA, GA and GY were 0.61, 0.28, 0.32 and 0.29, respectively. In summary, the Bayesian methods applied here were effective and ease to be implemented. The used SNP markers can help in the early selection of promising genotypes, since incorporating genomic information increase the prediction accuracy of the estimated genetic merit.

Genomic Prediction of Breeding Values Using a Subset of SNPs Identified by Three Machine Learning Methods.

The analysis of large genomic data is hampered by issues such as a small number of observations and a large number of predictive variables (commonly known as “large P small N”), high dimensionality or highly correlated data structures. Machine learning methods are renowned for dealing with these problems. To date machine learning methods have been applied in Genome-Wide Association Studies for identification of candidate genes, epistasis detection, gene network pathway analyses and genomic prediction of phenotypic values. However, the utility of two machine learning methods, Gradient Boosting Machine (GBM) and Extreme Gradient Boosting Method (XgBoost), in identifying a subset of SNP makers for genomic prediction of breeding values has never been explored before. In this study, using 38,082 SNP markers and body weight phenotypes from 2,093 Brahman cattle (1,097 bulls as a discovery population and 996 cows as a validation population), we examined the efficiency of three machine learning methods, namely Random Forests (RF), GBM and XgBoost, in (a) the identification of top 400, 1,000, and 3,000 ranked SNPs; (b) using the subsets of SNPs to construct genomic relationship matrices (GRMs) for the estimation of genomic breeding values (GEBVs). For comparison purposes, we also calculated the GEBVs from (1) 400, 1,000, and 3,000 SNPs that were randomly selected and evenly spaced across the genome, and (2) from all the SNPs. We found that RF and especially GBM are efficient methods in identifying a subset of SNPs with direct links to candidate genes affecting the growth trait. In comparison to the estimate of prediction accuracy of GEBVs from using all SNPs (0.43), the 3,000 top SNPs identified by RF (0.42) and GBM (0.46) had similar values to those of the whole SNP panel. The performance of the subsets of SNPs from RF and GBM was substantially better than that of evenly spaced subsets across the genome (0.18–0.29). Of the three methods, RF and GBM consistently outperformed the XgBoost in genomic prediction accuracy.

Genetic parameters, predictions, and rankings for semen production traits in a Thailand multi-breed dairy population using genomic-polygenic and polygenic models

The objectives were to compare estimates of variance components, genetic parameters, prediction accuracies, and rankings of bulls for semen volume (VOL), number of sperm (NS), and motility (MOT) using genomic-polygenic (GPRM) and polygenic repeatability models (PRM). The dataset comprised 13,535 VOL, 12,773 NS, and 12,660 MOT from 131 bulls collected from 2001 to 2017 in the Semen Production and Dairy Genetic Evaluation Center of the Dairy Farming Promotion Organization of Thailand. Genotypic data encompassed 76,519 actual and imputed SNP from 72 animals. The three-trait GPRM and PRM included the fixed effects of contemporary group, ejaculate order, age of bull, ambient temperature, and heterosis. Random effects were animal additive genetic, permanent environmental, and residual. Variance components and genetic parameters were estimated using AIREMLF90. GPRM heritabilities were slightly greater than PRM for MOT (0.27 compared with 0.24), and slightly less for VOL (0.11 compared with 0.12), and NS (0.17 compared with 0.19). Repeatabilities were slightly less for GPRM than PRM (0.44 compared with 0.45 for MOT, 0.26 compared with 0.28 for NS, and 0.20 compared with 0.21 for VOL). Additive genetic correlations were high between NS and MOT (GPRM: 0.76, PRM: 0.78), moderate between VOL and NS (GPRM: 0.43, PRM: 0.55), and near zero between VOL and MOT (GPRM: -0.13, PRM: 0.04). Rank correlations between GPRM and PRM estimated breeding values (EBV) were high for all traits. The similarity between GPRM and PRM results suggested that SNP data from the small number of genotyped animals had a minimal impact on genetic predictions in this population.

Age estimation of Hispanic children using the London Atlas

PurposeTo test the accuracy of the London Atlas for age estimation of Hispanic children and to determine if there is any difference in age accuracy between Hispanic males and females. MethodsThe London Atlas was used to estimate age from panoramic radiographs of 17 males and 17 females for each year of age from six to 15.99 years, using the electronic patient database of a dental school. Exclusion criteria included gross pathology, hypodontia, hyperdontia, and previous orthodontic treatment. ResultsThere were 332 panoramic radiographs evaluated. In all age groups, 34 radiographs (from 17 males and 17 females) were reviewed, except for the age bracket 6–6.99 years, for which only 26 radiographs were available. The mean age estimated of the entire sample by the London Atlas (11.44 years) was greater than the mean chronological age (11.09 years), which was statistically significant (P<.001). The mean difference between chronological and estimated ages for males was .30 years and for females was .40 years, but the difference between sexes was not significant (P=.324). One hundred sixty-two radiographs (49%) were estimated to the exact age interval while 45 (14%) were under-estimated and 125 (38%) were over-estimated. Two hundred and forty radiographs (72%) were estimated to a value within one year of the actual age. ConclusionThere was no difference in age estimation prediction accuracy between Hispanic males and females but an age overestimation of three percent in the cohort was seen. The London Atlas accuracy is suitable for use in forensic investigation.

Modelling of biochemical oxygen demand from limited water quality variable by ANFIS using two partition methods

Abstract This paper aims to: (1) develop models based on adaptive neuro-fuzzy inference system (ANFIS) able to predict five-day biochemical oxygen demand (BOD5) in Ouizert reservoir; (2) demonstrate the capability of the ANFIS in the practical issues of water quality management; (3) choose the optimal combination of input variables to improve the model performance; (4) compare two ANFIS partition methods, namely subtractive clustering called ANFIS-SC and grid partitioning, called ANFIS-GP. The models were developed using experimental data which were gathered during a ten-year period, at a mean monthly time step (scale). The input data used are total inorganic nitrogen, chemical oxygen demand (COD), total dissolved solid, dissolved oxygen and phosphate; the output is five-day biochemical oxygen demand (BOD5). Results reveal that ANFIS-SC models gave a higher correlation coefficient, a lower root mean square errors (RMSE) and mean absolute errors than the corresponding ANFIS-GP models. We can conclude that ANFIS-SC has supremacy over ANFIS-GP in terms of performance criteria and prediction accuracy for BOD5 estimation. The results showed that COD is the more effective variable for BOD5 estimating than other parameters, hence COD is the major driving factor for BOD5 modelling through ANFIS.

Estimation of genomic prediction accuracy from reference populations with varying degrees of relationship.

Genomic prediction is emerging in a wide range of fields including animal and plant breeding, risk prediction in human precision medicine and forensic. It is desirable to establish a theoretical framework for genomic prediction accuracy when the reference data consists of information sources with varying degrees of relationship to the target individuals. A reference set can contain both close and distant relatives as well as ‘unrelated’ individuals from the wider population in the genomic prediction. The various sources of information were modeled as different populations with different effective population sizes (Ne). Both the effective number of chromosome segments (Me) and Ne are considered to be a function of the data used for prediction. We validate our theory with analyses of simulated as well as real data, and illustrate that the variation in genomic relationships with the target is a predictor of the information content of the reference set. With a similar amount of data available for each source, we show that close relatives can have a substantially larger effect on genomic prediction accuracy than lesser related individuals. We also illustrate that when prediction relies on closer relatives, there is less improvement in prediction accuracy with an increase in training data or marker panel density. We release software that can estimate the expected prediction accuracy and power when combining different reference sources with various degrees of relationship to the target, which is useful when planning genomic prediction (before or after collecting data) in animal, plant and human genetics.

Effect of Trait Heritability, Training Population Size and Marker Density on Genomic Prediction Accuracy Estimation in 22 bi-parental Tropical Maize Populations.

Genomic selection is being used increasingly in plant breeding to accelerate genetic gain per unit time. One of the most important applications of genomic selection in maize breeding is to predict and select the best un-phenotyped lines in bi-parental populations based on genomic estimated breeding values. In the present study, 22 bi-parental tropical maize populations genotyped with low density SNPs were used to evaluate the genomic prediction accuracy (rMG) of the six trait-environment combinations under various levels of training population size (TPS) and marker density (MD), and assess the effect of trait heritability (h2), TPS and MD on rMG estimation. Our results showed that: (1) moderate rMG values were obtained for different trait-environment combinations, when 50% of the total genotypes was used as training population and ~200 SNPs were used for prediction; (2) rMG increased with an increase in h2, TPS and MD, both correlation and variance analyses showed that h2 is the most important factor and MD is the least important factor on rMG estimation for most of the trait-environment combinations; (3) predictions between pairwise half-sib populations showed that the rMG values for all the six trait-environment combinations were centered around zero, 49% predictions had rMG values above zero; (4) the trend observed in rMG differed with the trend observed in rMG/h, and h is the square root of heritability of the predicted trait, it indicated that both rMG and rMG/h values should be presented in GS study to show the accuracy of genomic selection and the relative accuracy of genomic selection compared with phenotypic selection, respectively. This study provides useful information to maize breeders to design genomic selection workflow in their breeding programs.

Instance Selection for Classifier Performance Estimation in Meta Learning

Building an accurate prediction model is challenging and requires appropriate model selection. This process is very time consuming but can be accelerated with meta-learning–automatic model recommendation by estimating the performances of given prediction models without training them. Meta-learning utilizes metadata extracted from the dataset to effectively estimate the accuracy of the model in question. To achieve that goal, metadata descriptors must be gathered efficiently and must be informative to allow the precise estimation of prediction accuracy. In this paper, a new type of metadata descriptors is analyzed. These descriptors are based on the compression level obtained from the instance selection methods at the data-preprocessing stage. To verify their suitability, two types of experiments on real-world datasets have been conducted. In the first one, 11 instance selection methods were examined in order to validate the compression–accuracy relation for three classifiers: k-nearest neighbors (kNN), support vector machine (SVM), and random forest. From this analysis, two methods are recommended (instance-based learning type 2 (IB2), and edited nearest neighbor (ENN)) which are then compared with the state-of-the-art metaset descriptors. The obtained results confirm that the two suggested compression-based meta-features help to predict accuracy of the base model much more accurately than the state-of-the-art solution.

COMPARISON OF ADJACENCY AND DISTANCE-BASED APPROACHES FOR SPATIAL ANALYSIS OF MULTIMODAL TRAFFIC CRASH DATA

Abstract. Many studies have utilized the spatial correlations among traffic crash data to develop crash prediction models with the aim to investigate the influential factors or predict crash counts at different sites. The spatial correlation have been observed to account for heterogeneity in different forms of weight matrices which improves the estimation performance of models. But very rarely have the weight matrices been compared for the prediction accuracy for estimation of crash counts. This study was targeted at the comparison of two different approaches for modelling the spatial correlations among crash data at macro-level (County). Multivariate Full Bayesian crash prediction models were developed using Decay-50 (distance-based) and Queen-1 (adjacency-based) weight matrices for simultaneous estimation crash counts of four different modes: vehicle, motorcycle, bike, and pedestrian. The goodness-of-fit and different criteria for accuracy at prediction of crash count reveled the superiority of Decay-50 over Queen-1. Decay-50 was essentially different from Queen-1 with the selection of neighbors and more robust spatial weight structure which rendered the flexibility to accommodate the spatially correlated crash data. The consistently better performance of Decay-50 at prediction accuracy further bolstered its superiority. Although the data collection efforts to gather centroid distance among counties for Decay-50 may appear to be a downside, but the model has a significant edge to fit the crash data without losing the simplicity of computation of estimated crash count.

Structure–reactivity modeling using mixture-based representation of chemical reactions

We describe a novel approach of reaction representation as a combination of two mixtures: a mixture of reactants and a mixture of products. In turn, each mixture can be encoded using an earlier reported approach involving simplex descriptors (SiRMS). The feature vector representing these two mixtures results from either concatenated product and reactant descriptors or the difference between descriptors of products and reactants. This reaction representation doesn't need an explicit labeling of a reaction center. The rigorous "product-out" cross-validation (CV) strategy has been suggested. Unlike the naïve "reaction-out" CV approach based on a random selection of items, the proposed one provides with more realistic estimation of prediction accuracy for reactions resulting in novel products. The new methodology has been applied to model rate constants of E2 reactions. It has been demonstrated that the use of the fragment control domain applicability approach significantly increases prediction accuracy of the models. The models obtained with new "mixture" approach performed better than those required either explicit (Condensed Graph of Reaction) or implicit (reaction fingerprints) reaction center labeling.

Sequence statistics of tertiary structural motifs reflect protein stability.

The Protein Data Bank (PDB) has been a key resource for learning general rules of sequence-structure relationships in proteins. Quantitative insights have been gained by defining geometric descriptors of structure (e.g., distances, dihedral angles, solvent exposure, etc.) and observing their distributions and sequence preferences. Here we argue that as the PDB continues to grow, it may become unnecessary to reduce structure into a set of elementary descriptors. Instead, it could be possible to deduce quantitative sequence-structure relationships in the context of precisely-defined complex structural motifs by mining the PDB for closely matching backbone geometries. To validate this idea, we turned to the the task of predicting changes in protein stability upon amino-acid substitution—a difficult problem of broad significance. We defined non-contiguous tertiary motifs (TERMs) around a protein site of interest and extracted sequence preferences from ensembles of closely-matching substructures in the PDB to predict mutational stability changes at the site, ΔΔGm. We demonstrate that these ensemble statistics predict ΔΔGm on par with state-of-the-art statistical and machine-learning methods on large thermodynamic datasets, and outperform these, along with a leading structure-based modeling approach, when tested in the context of unbiased diverse mutations. Further, we show that the performance of the TERM-based method is directly related to the amount of available relevant structural data, automatically improving with the growing PDB. This enables a means of estimating prediction accuracy. Our results clearly demonstrate that: 1) statistics of non-contiguous structural motifs in the PDB encode fundamental sequence-structure relationships related to protein thermodynamic stability, and 2) the PDB is now large enough that such statistics are already useful in practice, with their accuracy expected to continue increasing as the database grows. These observations suggest new ways of using structural data towards addressing problems of computational structural biology.