Size Of Sample Set Research Articles

Predicting two-year survival versus non-survival after first myocardial infarction using machine learning and Swedish national register data

BackgroundMachine learning algorithms hold potential for improved prediction of all-cause mortality in cardiovascular patients, yet have not previously been developed with high-quality population data. This study compared four popular machine learning algorithms trained on unselected, nation-wide population data from Sweden to solve the binary classification problem of predicting survival versus non-survival 2 years after first myocardial infarction (MI).MethodsThis prospective national registry study for prognostic accuracy validation of predictive models used data from 51,943 complete first MI cases as registered during 6 years (2006–2011) in the national quality register SWEDEHEART/RIKS-HIA (90% coverage of all MIs in Sweden) with follow-up in the Cause of Death register (> 99% coverage). Primary outcome was AUROC (C-statistic) performance of each model on the untouched test set (40% of cases) after model development on the training set (60% of cases) with the full (39) predictor set. Model AUROCs were bootstrapped and compared, correcting the P-values for multiple comparisons with the Bonferroni method. Secondary outcomes were derived when varying sample size (1–100% of total) and predictor sets (39, 10, and 5) for each model. Analyses were repeated on 79,869 completed cases after multivariable imputation of predictors.ResultsA Support Vector Machine with a radial basis kernel developed on 39 predictors had the highest complete cases performance on the test set (AUROC = 0.845, PPV = 0.280, NPV = 0.966) outperforming Boosted C5.0 (0.845 vs. 0.841, P = 0.028) but not significantly higher than Logistic Regression or Random Forest. Models converged to the point of algorithm indifference with increased sample size and predictors. Using the top five predictors also produced good classifiers. Imputed analyses had slightly higher performance.ConclusionsImproved mortality prediction at hospital discharge after first MI is important for identifying high-risk individuals eligible for intensified treatment and care. All models performed accurately and similarly and because of the superior national coverage, the best model can potentially be used to better differentiate new patients, allowing for improved targeting of limited resources. Future research should focus on further model development and investigate possibilities for implementation.

Examination of Different Item Response Theory Models on Tests Composed of Testlets

The purpose of this research is to first estimate the item and ability parameters and the standard error values related to those parameters obtained from Unidimensional Item Response Theory (UIRT), bifactor (BIF) and Testlet Response Theory models (TRT) in the tests including testlets, when the number of testlets, number of independent items, and sample size change, and then to compare the obtained results. Mathematic test in PISA 2012 was employed as the data collection tool, and 36 items were used to constitute six different data sets containing different numbers of testlets and independent items. Subsequently, from these constituted data sets, three different sample sizes of 250, 500 and 1000 persons were selected randomly. When the findings of the research were examined, it was determined that, generally the lowest mean error values were those obtained from UIRT, and TRT yielded a mean of error estimation lower than that of BIF. It was found that, under all conditions, models which take into consideration the local dependency have provided a better model-data compatibility than UIRT, generally there is no meaningful difference between BIF and TRT, and both models can be used for those data sets. It can be said that when there is a meaningful difference between those two models, generally BIF yields a better result. In addition, it has been determined that, in each sample size and data set, item and ability parameters and correlations of errors of the parameters are generally high.

URA/SISA Analysis for GPS and Galileo to Support ARAIM

This paper presents a User Range Accuracy (URA)/Signal-in-Space Accuracy (SISA) analysis to support ARAIM based on a time-dependent statistical characterization of orbit and clock error observations. By comparing precise orbits to broadcast ephemeris for each individual GPS and Galileo satellite, this work computes the Signal-in-Space Range Error (SISRE) that needs to be overbounded by the URA/SISA value included in the Integrity Support Message (ISM). Service data from January 2008 to February 2015 for GPS and from March to June 2015 for Galileo are processed, showing that range error is mainly driven by satellite's clock performance. In order for the ISM generation to account for the variation in error biases and standard deviation, GPS service history is broken down into monthly, quarterly, and yearly datasets. Results reveal that orbit and clock error distributions are non-zero mean on a monthly basis, although biases tend to reduce as sample set size increases.

Estimating higher-order structure functions from geophysical turbulence time series: Confronting the curse of the limited sample size.

Utilizing synthetically generated random variates and laboratory measurements, we document the inherent limitations of the conventional structure function approach in limited sample size settings. We demonstrate that an alternative approach, based on the principle of maximum likelihood, can provide nearly unbiased structure function estimates with far less uncertainty under such unfavorable conditions. The superiority of this approach over the conventional approach does not diminish even in the case of strongly correlated samples. Two entirely different types of probability distributions, which have been reported in the turbulence literature, are found to be compatible with the proposed approach.

The mechanical strength of a ceramic porous hollow fiber

The mechanical strength of inorganic porous hollow fibers is a critical constraint that limits their wide scale application. Various methods, including 3-point bending, 4-point bending, and diametrical compression are used for the quantification of the mechanical strength. Here, we show that these methods cannot be used in an interchangeable manner. For large sets of alumina hollow fibers, the parameters describing the cumulative probability of failure functions depend on the type of measurement, i.e., 3 or 4-point, the span size, and the measurement geometry. This implies that reporting data on mechanical properties of inorganic hollow fibers requires that extensive information about the experimental details is provided, and that a direct quantitative comparison between datasets is unjustifiable. The mechanical strength of the alumina hollow fibers tends to follow a normal distribution, or log-normal distribution, instead of the often used Weibull distribution. Monte Carlo simulations demonstrate that, especially at small sample set sizes, it is difficult to accurately determine the shape of the probability distribution. However, detailed knowledge of the type and the shape of this distribution function is essential when mechanical strength values are to be used in further design.

Weak Convergence Analysis of Asymptotically Optimal Hypothesis Tests

In recent years, solutions to various hypothesis testing problems in the asymptotic setting have been proposed using the results from large deviation theory. Such tests are optimal in terms of appropriately defined error exponents. For the practitioner, however, error probabilities in the finite sample size setting are more important. In this paper, we show how results on weak convergence of the test statistic can be used to obtain better approximations for the error probabilities in the finite sample size setting. While this technique is popular among statisticians for common tests, we demonstrate its applicability for several recently proposed asymptotically optimal tests, including tests for robust goodness of fit, homogeneity tests, outlier hypothesis testing, and graphical model estimation.

Incorporating limited field operability and legacy soil samples in a hypercube sampling design for digital soil mapping

AbstractMost calibration sampling designs for Digital Soil Mapping (DSM) demarcate spatially distinct sample sites. In practical applications major challenges are often limited field accessibility and the question on how to integrate legacy soil samples to cope with usually scarce resources for field sampling and laboratory analysis. The study focuses on the development and application of an efficiency improved DSM sampling design that (1) applies an optimized sample set size, (2) compensates for limited field accessibility, and (3) enables the integration of legacy soil samples. The proposed sampling design represents a modification of conditioned Latin Hypercube Sampling (cLHS), which originally returns distinct sample sites to optimally cover a soil related covariate space and to preserve the correlation of the covariates in the sample set. The sample set size was determined by comparing multiple sample set sizes of original cLHS sets according to their representation of the covariate space. Limited field accessibility and the integration of legacy samples were incorporated by providing alternative sample sites to replace the original cLHS sites. We applied the modified cLHS design (cLHSadapt) in a small catchment (4.2 km2) in Central China to model topsoil sand fractions using Random Forest regression (RF). For evaluating the proposed approach, we compared cLHSadapt with the original cLHS design (cLHSorig). With an optimized sample set size n = 30, the results show a similar representation of the cLHS covariate space between cLHSadapt and cLHSorig, while the correlation between the covariates is preserved (r = 0.40 vs. r = 0.39). Furthermore, we doubled the sample set size of cLHSadapt by adding available legacy samples (cLHSadapt+) and compared the prediction accuracies. Based on an external validation set cLHSval (n = 20), the coefficient of determination (R2) of the cLHSadapt predictions range between 0.59 and 0.71 for topsoil sand fractions. The R2‐values of the RF predictions based on cLHSadapt+, using additional legacy samples, are marginally increased on average by 5%.

Computational performance optimization of support vector machine based on support vectors

The computational performance of support vector machine (SVM) mainly depends on the size and dimension of training sample set. Because of the importance of support vectors in the determination of SVM classification hyperplane, a kind of method for computational performance optimization of SVM based on support vectors is proposed. On one hand, at the same time of the selection of super-parameters of SVM, according to Karush-Kuhn-Tucker condition and on the precondition of no loss of potential support vectors, we eliminate non-support vectors from training sample set to reduce sample size and thereby to reduce the computation complexity of SVM. On the other hand, we propose a simple intrinsic dimension estimation method for SVM training sample set by analyzing the correlation between number of support vectors and intrinsic dimension. Comparative experimental results indicate the proposed method can effectively improve computational performance.

Nonparametric estimation of the finite time ruin probability in the classical risk model

In this paper, we consider the nonparametric estimation of the finite time ruin probability in the classical risk model. Suppose that the individual claim size distribution is unknown, but a random sample of claims is available. We construct the estimator by double Fourier transform. The asymptotic properties of the estimator are studied under large sample setting, and show that an almost convergence rate can be obtained. Some simulation examples are also provided to illustrate the performance of the estimator under finite sample size setting.

Novel statistical methodology reveals that hip shape is associated with incident radiographic hip osteoarthritis among African American women

Hip shape is a risk factor for the development of hip osteoarthritis (OA), and current methods to assess hip shape from radiographs are limited; therefore this study explored current and novel methods to assess hip shape. Data from a prior case-control study nested in the Johnston County OA Project were used, including 382 hips (from 342 individuals). Hips were classified by radiographic hip OA (RHOA) status as RHOA cases (baseline Kellgren Lawrence grade [KLG] 0 or 1, follow-up [mean 6 years] KLG≥2) or controls (KLG=0 or 1at both baseline and follow-up). Proximal femur shape was assessed using a 60-point model as previously described. The current analysis explored commonly used principal component analysis (PCA), as well as novel statistical methodologies suited to high dimension low sample size settings (Distance Weighted Discrimination [DWD] and Distance Projection Permutation [DiProPerm] hypothesis testing) to assess differences between cases and controls. Using these novel methodologies, we were able to better characterize morphologic differences by sex and race. In particular, the proximal femurs of African American women demonstrated significantly different shapes between cases and controls, implying an important role for sex and race in the development of RHOA. Notably, discrimination was improved with the use of DWD and DiProPerm compared to PCA. DWD with DiProPerm significance testing provides improved discrimination of variation in hip morphology between groups, and enables subgroup analyses even under small sample sizes.

Survival Prognostic Factors of Male Breast Cancer in Southern Iran: a LASSO-Cox Regression Approach.

We used to LASSO-Cox method for determining prognostic factors of male breast cancer survival and showed the superiority of this method compared to Cox proportional hazard model in low sample size setting. In order to identify and estimate exactly the relative hazard of the most important factors effective for the survival duration of male breast cancer, the LASSO-Cox method has been used. Our data includes the information of male breast cancer patients in Fars province, south of Iran, from 1989 to 2008. Cox proportional hazard and LASSO-Cox models were fitted for 20 classified variables. To reduce the impact of missing data, the multiple imputation method was used 20 times through the Markov chain Mont Carlo method and the results were combined with Rubin's rules. In 50 patients, the age at diagnosis was 59.6 (SD=12.8) years with a minimum of 34 and maximum of 84 years and the mean of survival time was 62 months. Three, 5 and 10 year survival were 92%, 77% and 26%, respectively. Using the LASSO-Cox method led to eliminating 8 low effect variables and also decreased the standard error by 2.5 to 7 times. The relative efficiency of LASSO-Cox method compared with the Cox proportional hazard method was calculated as 22.39. The19 years follow of male breast cancer patients show that the age, having a history of alcohol use, nipple discharge, laterality, histological grade and duration of symptoms were the most important variables that have played an effective role in the patient's survival. In such situations, estimating the coefficients by LASSO-Cox method will be more efficient than the Cox's proportional hazard method.

Microarray Gene Expression Data Classification Using Feature Selection and Naïve Bayes Classifier

Microarrays are successful tools to predict cancer from DNA gene-expression data and are successfully used in cancer classification. However, they provide high-dimensional data which is not easy to get accurate results for classification algorithms. Moreover, small sample size and big feature set of microarray data brings the over-fitting problem for the classification algorithms. Therefore, feature-selection is necessary to select relevant genes from noisy dataset. This study presents a feature extraction approach with MK-SVM algorithm to improve classification accuracy. With the experimental results and Receiver Operating Characteristic Curve (ROC) values and prediction accuracy, we conclude that Naive Bayes classifier gives very high and compatible results by using relevant genes selected by MK-SVM.

Applying stability selection to consistently estimate sparse principal components in high-dimensional molecular data.

Motivation: Principal component analysis (PCA) is a basic tool often used in bioinformatics for visualization and dimension reduction. However, it is known that PCA may not consistently estimate the true direction of maximal variability in high-dimensional, low sample size settings, which are typical for molecular data. Assuming that the underlying signal is sparse, i.e. that only a fraction of features contribute to a principal component (PC), this estimation consistency can be retained. Most existing sparse PCA methods use L1-penalization, i.e. the lasso, to perform feature selection. But, the lasso is known to lack variable selection consistency in high dimensions and therefore a subsequent interpretation of selected features can give misleading results.Results: We present S4VDPCA, a sparse PCA method that incorporates a subsampling approach, namely stability selection. S4VDPCA can consistently select the truly relevant variables contributing to a sparse PC while also consistently estimate the direction of maximal variability. The performance of the S4VDPCA is assessed in a simulation study and compared to other PCA approaches, as well as to a hypothetical oracle PCA that ‘knows’ the truly relevant features in advance and thus finds optimal, unbiased sparse PCs. S4VDPCA is computationally efficient and performs best in simulations regarding parameter estimation consistency and feature selection consistency. Furthermore, S4VDPCA is applied to a publicly available gene expression data set of medulloblastoma brain tumors. Features contributing to the first two estimated sparse PCs represent genes significantly over-represented in pathways typically deregulated between molecular subgroups of medulloblastoma.Availability and implementation: Software is available at https://github.com/mwsill/s4vdpca.Contact: m.sill@dkfz.deSupplementary information: Supplementary data are available at Bioinformatics online.

Saddlepoint-based bootstrap inference for the spatial dependence parameter in the lattice process

A saddlepoint-based bootstrap (SPBB) method for inference on the spatial dependence parameter in Gaussian lattice regression models is proposed. The method handles any estimator that is expressible as the root of a quadratic estimating equation (QEE), and includes common estimators like maximum likelihood (ML) and restricted ML (REML). Since the underlying QEE has a moment generating function in closed-form, this is inverted via the saddlepoint method to produce accurate approximations to the respective distributions of the estimators. Confidence intervals are then produced by pivoting the distribution function. The approach provides a unified perspective by viewing estimators in the simultaneous autoregressive (SAR), conditional autoregressive (CAR), and simultaneous moving average (SMA) models, through their underlying QEEs. The key assumption of monotonicity for the respective QEEs is verified, and results derived concerning their bias. Of importance for spatial modeling practitioners, is the finding that simulation studies show SPBB confidence intervals outperforming those based on standard (first-order) asymptotic theory in small to moderate sample size settings, and being orders of magnitude faster than computationally intensive approaches like the bootstrap. The methodology is illustrated on two classical lattice datasets.

Adjusted Supremum Score‐Type Statistics for Evaluating Non‐Standard Hypotheses

AbstractSupremum score test statistics are often used to evaluate hypotheses with unidentifiable nuisance parameters under the null hypothesis. Although these statistics provide an attractive framework to address non‐identifiability under the null hypothesis, little attention has been paid to their distributional properties in small to moderate sample size settings. In situations where there are identifiable nuisance parameters under the null hypothesis, these statistics may behave erratically in realistic samples as a result of a non‐negligible bias induced by substituting these nuisance parameters by their estimates under the null hypothesis. In this paper, we propose an adjustment to the supremum score statistics by subtracting the expected bias from the score processes and show that this adjustment does not alter the limiting null distribution of the supremum score statistics. Using a simple example from the class of zero‐inflated regression models for count data, we show empirically and theoretically that the adjusted tests are superior in terms of size and power. The practical utility of this methodology is illustrated using count data in HIV research.

Minimum-cost rapid-growing random trees for segmented assembly path planning

In this paper, the segmented assembly path-planning problem is proposed to reveal an integrated assembly path-planning task. We define the two phases of an assembly path-planning task and address their differences. A new method based on rapid-growing random trees (RRT) is presented for obtaining a minimum-cost path and making the total cost of the solution path remain constant for solving the same path-planning tasks in different iterations. The approach is also able to guarantee a solution with smooth rotation motions. We test this algorithm in various examples with good performance. And we also discuss the impact of the random sample set size of the algorithm in path optimization and execution time in various situations including segmented assembly path-planning task. Based on the results from the tests, suggestions for selecting a proper random sample set size are given.

A reshaped approach for protein nanocrystal structure analysis from XFELs

The size and quality of protein crystals are critical limiting factors in conventional X-ray crystallography structural studies. Serial femtosecond X-ray crystallography (SFX) presents new opportunities through the use of submicron and nano-scale crystal samples. SFX experiments with X-ray free-electron lasers have demonstrated success (Chapman, 2011). While new instances are arising for the study of poorly crystallizing proteins, fresh examination must also be made of their analysis. Significantly, the smallness of the crystal samples creates broad integrated intensity distributions that require careful consideration for the accurate reconstruction of high-resolution protein crystal structures. Structural imperfections are also expected to play significant roles in the formation of SFX diffraction patterns (Dilanian, 2013). We present preliminary results from a new approach for SFX data analysis. As motivation, it is observed that significant similarities lie between merged SFX data-sets and powder diffraction patterns. The merged Bragg peak-shape distributions in SFX diffraction patterns are characterised by the shape, size and disorder distributions of the large crystal sample set. Powder diffraction peak-shape distributions are formed similarly by a collection of independent scatterers of such varying characteristics. The presented method utilizes an established powder diffraction analysis tool, the Le Bail method (Le Bail, 1988), for extension and application to SFX data. It is shown here that the continuous whole-pattern fitting technique, combined with variable peak-shape functions, can be used to closely model simulated SFX patterns and to extract integrated intensities. The presented approach is posed as a new analysis method for SFX experiments in which both crystal size and structural disorder variations can be incorporated.

Functional gene-set analysis does not support a major role for synaptic function in attention deficit/hyperactivity disorder (ADHD).

Attention Deficit/Hyperactivity Disorder (ADHD) is one of the most common childhood-onset neuropsychiatric disorders. Despite high heritability estimates, genome-wide association studies (GWAS) have failed to find significant genetic associations, likely due to the polygenic character of ADHD. Nevertheless, genetic studies suggested the involvement of several processes important for synaptic function. Therefore, we applied a functional gene-set analysis to formally test whether synaptic functions are associated with ADHD. Gene-set analysis tests the joint effect of multiple genetic variants in groups of functionally related genes. This method provides increased statistical power compared to conventional GWAS. We used data from the Psychiatric Genomics Consortium including 896 ADHD cases and 2455 controls, and 2064 parent-affected offspring trios, providing sufficient statistical power to detect gene sets representing a genotype relative risk of at least 1.17. Although all synaptic genes together showed a significant association with ADHD, this association was not stronger than that of randomly generated gene sets matched for same number of genes. Further analyses showed no association of specific synaptic function categories with ADHD after correction for multiple testing. Given current sample size and gene sets based on current knowledge of genes related to synaptic function, our results do not support a major role for common genetic variants in synaptic genes in the etiology of ADHD.

A comparison of calibration sampling schemes at the field scale

High-resolution digital soil sensing and mapping is an important and emerging new technology that helps meet the strong and growing global demand for high-resolution soil property data. However, the combination of geophysical sensing and pedometrical techniques to produce soil property maps is complex and requires a well-structured design, from the initial steps of data collection right through to final model validation. In this study, we compare different sampling design strategies – an extension of conditioned Latin hypercube sampling, fuzzy k-means sampling and response surface sampling – as a basis for predicting soil texture, soil organic carbon and soil pH-value at two soil depth intervals using electromagnetic induction (EM38DD and EM31) and gamma spectroscopy (U, K, Th) data. Two different sample set sizes, two different regression approaches (multiple linear least squares and random forests), as well as several resampling and independent validation approaches are compared. In addition to these real-world datasets, we also compared the investigated methods for two comparable simulated datasets.Our accuracy estimation results reveal that an optimal combination of Latin hypercube sampling and random forest regression should be adopted. This is the case for both the real world examples as well as the two synthetic datasets. The analysis conducted indicates that this stems from optimized spread within the state space of the sensors.Iterative LHS subsampling with increasing sample set sizes may potentially be a successful approach for incrementally analyzing and validating the model and thus can help reduce laboratory costs when a certain desired accuracy level is achieved.Comparison between the different validation approaches reveals their complexity and highlights the necessity for adequate independent validation approaches. However, based on the findings of our study, we recommend ‘leave-group-out’ cross-validation and ‘.632 bootstrapping’ as the best estimates to use.Finally, this study shows that there are complex interactions between sampling design, regression approaches and validation approaches, which can greatly influence the final soil property maps and their accuracy estimates.Future work should focus on detailed analysis of Latin hypercube sampling and why it outperformed the other approaches. Therefore, comparisons with other sampling approaches should be conducted, as well as specific ‘sampling-for-validation’ approaches. Therefore we provide the simulated datasets as Supplementary reference material for future comparative analysis.

ShrinkBayes: a versatile R-package for analysis of count-based sequencing data in complex study designs.

BackgroundComplex designs are common in (observational) clinical studies. Sequencing data for such studies are produced more and more often, implying challenges for the analysis, such as excess of zeros, presence of random effects and multi-parameter inference. Moreover, when sample sizes are small, inference is likely to be too liberal when, in a Bayesian setting, applying a non-appropriate prior or to lack power when not carefully borrowing information across features.ResultsWe show on microRNA sequencing data from a clinical cancer study how our software ShrinkBayes tackles the aforementioned challenges. In addition, we illustrate its comparatively good performance on multi-parameter inference for groups using a data-based simulation. Finally, in the small sample size setting, we demonstrate its high power and improved FDR estimation by use of Gaussian mixture priors that include a point mass.ConclusionShrinkBayes is a versatile software package for the analysis of count-based sequencing data, which is particularly useful for studies with small sample sizes or complex designs.