Equivalent Sample Size Research Articles

On a Less Cumbersome Method of Estimation of Parameters of Type III Generalized Logistic Distribution by Order Statistics

In this work we have derived appropriate U-statistics from a sample of any size exceeding a specified integer to estimate the location and scale parameters of Type III generalized logistic distribution without the knowledge or by evaluation of the means, variances and co-variances of order statistics of an equivalent sample size arising from the corresponding standard form of distribution. The exact variances and the asymptotic variances of the estimators have been obtained. The efficiency of the obtained estimators relative to some of the standard estimators have been also obtained. An illustration describing the betterness of U-statistics estimation method over the classical maximum-likelihood method is also given.

Evolution of low flows in Czechia revisited

Abstract. Although a nationwide study focusing on the evolution of low flows in Czechia was conducted in the past, a need for the revision of the results has arisen. By means of the trend analysis, which specifically considers the presence of significant serial correlation at the first lag, the former study highlighted areas where 7-day low flows increase or decrease. However, taking into account only the lag-one autoregressive process might still have led to the detection of so-called pseudo-trends because, besides short-term persistence, also long-term persistence may adversely influence the variance of the test statistic when the independence among data is required. Therefore, one should carefully investigate the presence of persistence in time series. Before the trend analysis itself, the authors' previous studies aimed at the discrimination between short memory processes and long memory processes employing jointly the Phillips–Perron test and the Kwiatkowski–Phillips–Schmidt–Shin test. This analysis was accompanied by the Hurst exponent estimation. Here, the subsequent identification of trends is carried out using three modifications of the Mann–Kendall test that allow different kinds of persistence. These include the Bayley–Hammersley–Matalas–Langbein–Lettenmaier equivalent sample size approach, the trend-free pre-whitening approach and a block bootstrap with automatic selection of the block length, which was applied for the first time in hydrology. The general results are similar to those presented in the former study on trends. Nevertheless, the divergent minimum discharges evolution in the western part of Czechia is now much clear. Moreover, no significant increasing trend in series incorporating Julian days was found.

Learning extended tree augmented naive structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka. • New Bayesian network structure learning approach to extend the Tree Augmented Naive (TAN) classifier. • Efficient implementation of TAN and Extended-TAN using the Edmonds algorithm for directed weighted spanning trees. • Alternative approach to well-known classifiers such as TAN and AODE. • Missing data can be treated without the need of data imputation. • Easy-to-install Weka plugin.

Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models

Since sampling weights are not simply equal to the reciprocal of selection probabilities its always challenging to incorporate survey weights into likelihood-based analysis. These weights are always adjusted for various characteristics. In cases where logistic regression model is used to predict categorical outcomes with survey data, the sampling weights should be considered if the sampling design does not give each individual an equal chance of being selected in the sample. The weights are rescaled to sum to an equivalent sample size since original weights have small variances. The new weights are called the adjusted weights. Quasi-likelihood maximization is the method that is used to make estimation with the adjusted weights but the other new method that can be created is correct likelihood for logistic regression which included the adjusted weights. Adjusted weights are further used to adjust for both covariates and intercepts when the correct likelihood method was used. We also looked at the differences and similarities between the two methods. Analysis: Both binary logistic regression model and multinomial logistic regression model were used in parameter estimation and we applied the methods to body mass index data from Nairobi Hospital, which is in Nairobi County where a sample of 265 was used. R-software Version 3.0.2 was used in the analysis. Conclusion: The results from the study showed that there were some similarities and differences between the quasi-likelihood and correct likelihood methods in parameter estimates, standard errors and statistical p-values.

A minimum fluid volume of 75 mL is needed to ensure adequacy in a pleural effusion: a retrospective analysis of 2540 cases.

No consensus exists regarding minimum fluid volume for adequacy of benign pleural effusion specimens. Although any volume is acceptable if cytologic findings are malignant, the distinction between the absence of disease and false-negativity is not straightforward in low-volume specimens. Recent literature has offered conflicting results regarding what minimum volume is necessary. Moreover, no studies to date have evaluated this issue across a large series of specimens with a wide distribution of volumes. The objective of the current study was to determine the minimum volume of pleural fluid necessary for optimal cytopathological diagnosis. The authors identified 2540 pleural fluid specimens received between January 2000 and December 2009 and retrospectively reviewed their diagnoses and characteristics. Because of the large range of volumes (1 mL-6500 mL), the cases were binned into 9 groups of roughly equivalent sample sizes. The malignancy fractions (percentage of cases with malignant diagnoses) were compared for each group. The current study specimens had a median volume of 200 mL and an overall malignancy fraction of 20.1%. The malignancy fraction increased from 10.1% (95% confidence interval, 8.1%-12.1%) for volumes < 5 mL to 23.3% (95% confidence interval, 20.0%-25.8%) for volumes between 50 mL and 75 mL (P = .009). Specimens with volumes ≥ 75 mL had malignancy fractions independent of volume. In addition, ratios of benign or malignant diagnoses versus nondiagnostic and atypical results continued to increase with volume. A fluid volume of ≥ 75 mL is required to eliminate the influence of specimen size on diagnostic adequacy. Although larger volumes do not appear to impact malignancy fraction, they do correlate with decreased nondiagnostic and atypical results.

A simple error estimation method for linear-regression-based thermal sharpening techniques with the consideration of scale difference

Thermal remote sensing imagery is helpful for land cover classification and related analysis. Unfortunately, the spatial resolution of thermal infrared (TIR) band is generally coarser than that of visual near-infrared band, which limits its more precise applications. Various thermal sharpening (TSP) techniques have been developed for improving the spatial resolution of the imagery of TIR band or land surface temperature (LST). However, there is no research on the theoretical estimation of TSP error till now, which implies that the error in sharpened LST imagery is unknown and the further analysis might be not reliable. In this paper, an error estimation method based on classical linear regression theory for the linear-regression-based TSP techniques was firstly introduced. However, the scale difference between the coarse resolution and fine resolution is not considered in this method. Therefore, we further developed an improved error estimation method with the consideration of the scale difference, which employs a novel term named equivalent random sample size to reflect the scale difference. A simulation study of modified TsHARP (a typical TSP technique) shows that the improved method estimated the TSP error more accurately than classical regression theory. Especially, the phenomena that TSP error increases with the increasing resolution gap between the initial and target resolutions can be successfully predicted by the proposed method.

Determination of paternal and maternal parentage in lodgepole pine seed: full versus partial pedigree reconstruction

Estimating seed orchards’ maternal and paternal gametic contributions is of importance in assessing the genetic quality of seed crops. The advantage of full over partial pedigree reconstruction in investigating the mating dynamics in a lodgepole pine (Pinus contorta Dougl. ex. Loud. ssp. latifolia Engelm.) seed orchard population (N = 74) was demonstrated using nuclear and chloroplast microsatellite markers. We analyzed offspring of equivalent sample sizes representing full (bulk seed with unknown maternal and paternal parentage (n = 635)) and partial (11 maternal family arrays (n = 619)) pedigree reconstruction methods. Small differences in selfing rate, gene flow, and male reproductive success were observed between the two methods; however, the full pedigree reconstruction enabled simultaneous estimation of female-related fertility parameters (female reproductive success and effective number of maternal parents) that partial pedigree reconstruction could not provide. The use of bulk random sample of seed from orchards’ crops is recommended when male and female fertility parameters, as well as selfing and contamination rates, are needed for seed orchards’ seed crops genetic rating.

Sample Size Determination in NT-Net Quasi-Monte Carlo Simulation

Monte Carlo (MC) technique prevails in probabilistic design simulation, such as in statistical tolerance analysis and synthesis. A quasi-Monte Carlo (e.g., number theoretic net method (NT-net)) with better computation efficiency over MC has recently attracted interests in application. In spite of a comprehensive case study (Huang et al., 2004, “Tolerance Analysis for Design of Multistage Manufacturing Processes Using Number-Theoretical Net Method (NT-net),” Int. J. Flexible Manuf. Syst., 16, pp. 65–90 and Zhou et al., 2001, “Sequential Algorithm Based on Number Theoretic Method for Tolerance Analysis and Synthesis,” ASME J. Manuf. Sci. Eng., 123(3), pp. 490–493) for comparison between NT-net and MC, a method for sample size determination of NT-net is still not available. Combinatorial theory and the solution of occupancy problem are used for estimating equivalent sample sizes of MC and NT-net, allowing the NT-net sample size determination in application. A multivariate Chebyshev polynomial with variant coefficients is used to represent generic design functions for validation. The results are verified by case studies.

Development of a methodology to estimate error in the on-line measurements of blend uniformity in a continuous powder mixing process

Abstract In this paper, a multi-point fiber optic based NIR system was implemented to monitor API concentration at the discharge of a continuous mixer. The sample size being interrogated by NIR was determined by measuring the velocity of the powder on the chute, which allowed selection of the number of scans to be averaged. A methodology was developed that allows quantification of the error associated with the in-line measurements. Comparison of in-line and off-line measurements was made at equivalent sample sizes. Mathematical model fitting for the in-line as well as off-line data revealed that the contribution of the analytical method error was negligible. A baseline RSD of 0.02 in the in-line measurements persists because of the inherent non-uniform nature of powder material. These results are useful towards achieving Real-Time-Release (RTR) of continuously manufactured drug product.

Monolithic 3D titania with ultrathin nanoshell structures for enhanced photocatalytic activity and recyclability

Titania has attracted considerable interest for use in water purification applications due to its excellent photocatalytic activity. To further improve the efficiency of photocatalysis, numerous nanostructures (i.e. nanoparticles, nanotubes, and nanowires) have been proposed to increase the surface area of titania. Despite the high photocatalytic performance of the nanostructured titania, subsequent difficulties encountered in recollection and reuse of titania inhibit the practical application for water purification systems. Here we successfully fabricate monolithic, three dimensional (3D) nanoshell titania with high uniformity over large areas (~1 × 1 inch(2)) through proximity field nanopatterning (PnP) and low-temperature atomic layer deposition (ALD) techniques. The higher surface area of 3D nanoshell titania increases the photocatalytic performance more than three-fold relative to that of a thin film of equivalent sample size. Also, the monolithic form of titania enables it to be reused without any degradation of photocatalytic activity. The newly developed nanomaterials in this study can serve as an efficient and reusable photocatalyst for water purification systems.

Locally averaged Bayesian Dirichlet metrics for learning the structure and the parameters of Bayesian networks

The marginal likelihood of the data computed using Bayesian score metrics is at the core of score+search methods when learning Bayesian networks from data. However, common formulations of those Bayesian score metrics rely on free parameters which are hard to assess. Recent theoretical and experimental works have also shown that the commonly employed BDe score metric is strongly biased by the particular assignments of its free parameter known as the equivalent sample size. This sensitivity means that poor choices of this parameter lead to inferred BN models whose structure and parameters do not properly represent the distribution generating the data even for large sample sizes. In this paper we argue that the problem is that the BDe metric is based on assumptions about the BN model parameters distribution assumed to generate the data which are too strict and do not hold in real settings. To overcome this issue we introduce here an approach that tries to marginalize the meta-parameter locally, aiming to embrace a wider set of assumptions about these parameters. It is shown experimentally that this approach offers a robust performance, as good as that of the standard BDe metric with an optimum selection of its free parameter and, in consequence, this method prevents the choice of wrong settings for this widely applied Bayesian score metric.

Measuring longitudinal change in the hippocampal formation from in vivo high-resolution T2-weighted MRI

The hippocampal formation (HF) is a brain structure of great interest because of its central role in learning and memory, and its associated vulnerability to several neurological disorders. In vivo oblique coronal T2-weighted MRI with high in-plane resolution (~0.5 mm × 0.5 mm), thick slices (~2.0 mm), and a field of view tailored to imaging the hippocampal formation (denoted HF-MRI in this paper) has been advanced as a useful imaging modality for detailed hippocampal morphometry. Cross-sectional analysis of volume measurements derived from HF-MRI has shown the modality's promise to yield sensitive imaging-based biomarker for neurological disorders such as Alzheimer's disease. However, the utility of this modality for making measurements of longitudinal change has not yet been demonstrated. In this paper, using an unbiased deformation-based morphometry (DBM) pipeline, we examine the suitability of HF-MRI for estimating longitudinal change by comparing atrophy rates measured in the whole hippocampus from this modality with those measured from more common isotropic (~1 mm³) T1-weighted MRI in the same set of individuals, in a cohort of healthy controls and patients with cognitive impairment. While measurements obtained from HF-MRI were largely consistent with those obtained from T1-MRI, HF-MRI yielded slightly larger group effect of greater atrophy rates in patients than in controls. The estimated minimum sample size required for detecting a 25% change in patients' atrophy rate in the hippocampus compared to the control group with a statistical power β=0.8 was N=269. For T1-MRI, the equivalent sample size was N=325. Using a dataset of test-retest scans, we show that the measurements were free of additive bias. We also demonstrate that these results were not a confound of certain methodological choices made in the DBM pipeline to address the challenges of making longitudinal measurements from HF-MRI, using a region of interest (ROI) around the HF to globally align serial images, followed by slice-by-slice deformable registration to measure local volume change. Additionally, we present a preliminary study of atrophy rate measurements within hippocampal subfields using HF-MRI. Cross-sectional differences in atrophy rates were detected in several subfields.

Digging into the extremes: a useful approach for the analysis of rare variants with continuous traits?

The common disease/rare variant hypothesis predicts that rare variants with large effects will have a strong impact on corresponding phenotypes. Therefore it is assumed that rare functional variants are enriched in the extremes of the phenotype distribution. In this analysis of the Genetic Analysis Workshop 17 data set, my aim is to detect genes with rare variants that are associated with quantitative traits using two general approaches: analyzing the association with the complete distribution of values by means of linear regression and using statistical tests based on the tails of the distribution (bottom 10% of values versus top 10%). Three methods are used for this extreme phenotype approach: Fisher’s exact test, weighted-sum method, and beta method. Rare variants were collapsed on the gene level. Linear regression including all values provided the highest power to detect rare variants. Of the three methods used in the extreme phenotype approach, the beta method performed best. Furthermore, the sample size was enriched in this approach by adding additional samples with extreme phenotype values. Doubling the sample size using this approach, which corresponds to only 40% of sample size of the original continuous trait, yielded a comparable or even higher power than linear regression. If samples are selected primarily for sequencing, enriching the analysis by gathering a greater proportion of individuals with extreme values in the phenotype of interest rather than in the general population leads to a higher power to detect rare variants compared to analyzing a population-based sample with equivalent sample size.

Variations in the friction coefficients of tablet lubricants and relationship to their physicochemical properties.

A previously described modified annular shear cell (MASC) has been used to measure the friction coefficients of some powdered tablet lubricants on a steel surface. Commonly used lubricants, as well as others belonging to the stearate group, differed in their friction coefficients at equivalent sample sizes and in the degree of their ability to reduce friction with increasing amounts when evaluated by the apparatus. In all comparisons, magnesium stearate had the lowest friction coefficient. Divalent salts of stearic acid appeared to be better than the other lubricants tested, and among themselves differed only in the extent of their ability to decrease friction. The lubricants also differed in their physical and chemical properties. On evaluation by stepwise regression analysis, such physical properties as projected surface area of lubricant particles, Martin's diameter and bulk density accounted for most of the variation in friction coefficients of the lubricants rather than moisture content or melting point. It could therefore be suggested that particle size and/or surface area parameters be incorporated in product specifications to ensure reproducible functionality.

Sequential methods for pharmacogenetic studies

A study or experiment can be described as sequential if its design includes one or more interim analyses at which it is possible to stop the study, having reached a definitive conclusion concerning the primary question of interest. The potential of the sequential study to terminate earlier than the equivalent fixed sample size study means that, typically, there are ethical and economic advantages to be gained from using a sequential design. These advantages have secured a place for the methodology in the conduct of many clinical trials of novel therapies. Recently, there has been increasing interest in pharmacogenetics: the study of how DNA variation in the human genome affects the safety and efficacy of drugs. The potential for using sequential methodology in pharmacogenetic studies is considered and the conduct of candidate gene association studies, family-based designs and genome-wide association studies within the sequential setting is explored. The objective is to provide a unified framework for the conduct of these types of studies as sequential designs and hence allow experimenters to consider using sequential methodology in their future pharmacogenetic studies.

When should one adjust for measurement error in baseline variables in observational studies?

Previously, we showed that in randomised experiments, correction for measurement error in a baseline variable induces bias in the estimated treatment effect, and conversely that ignoring measurement error avoids bias. In observational studies, non-zero baseline covariate differences between treatment groups may be anticipated. Using a graphical approach, we argue intuitively that if baseline differences are large, failing to correct for measurement error leads to a biased estimate of the treatment effect. In contrast, correction eliminates bias if the true and observed baseline differences are equal. If this equality is not satisfied, the corrected estimator is also biased, but typically less so than the uncorrected estimator. Contrasting these findings, we conclude that there must be a threshold for the true baseline difference, above which correction is worthwhile. We derive expressions for the bias of the corrected and uncorrected estimators, as functions of the correlation of the baseline variable with the study outcome, its reliability, the true baseline difference, and the sample sizes. Comparison of these expressions defines a theoretical decision threshold about whether to correct for measurement error. The results show that correction is usually preferred in large studies, and also in small studies with moderate baseline differences. If the group sample sizes are very disparate, correction is less advantageous. If the equivalent balanced sample size is less than about 25 per group, one should correct for measurement error if the true baseline difference is expected to exceed 0.2-0.3 standard deviation units. These results are illustrated with data from a cohort study of atherosclerosis.

Using Generalised Dissimilarity Models and many small samples to improve the efficiency of regional and landscape scale invertebrate sampling

It is rarely cost-effective to survey invertebrates for use in systematic conservation planning activities. The efficiency of sampling methods needs to be improved, and this is especially important at landscape and regional scales. We investigated two methods that could be used to improve regional scale sampling efficiency using a case study of ants, beetles, flies, bugs, spiders and wasps from the semi-arid Pilbara region of Western Australia. First, Generalised Dissimilarity Models (GDMs) were used to divide the region into landscapes with relatively homogeneous communities and environmental conditions. We found that some of these landscapes were large, and a low sampling density could be employed in these areas due to the low spatial turnover in species. Other landscapes were 1–2 orders of magnitude smaller, and a higher sampling density should be employed to capture the high species turnover and unique species in these areas. Variation of sampling density based on landscape dimensions could vastly improve survey efficiency. Second, we investigated whether one large sample or five small samples were a more efficient method to estimate the species composition of each landscape. We found that five small samples captured a higher proportion of landscape scale species richness for a fixed sampling effort, and was therefore a more efficient method to determine the species composition of the landscape. Combining five small samples also resulted in less sample variability than one large sample, which increases statistical power to detect changes. We concluded that GDM was an effective method to increase sampling efficiency, because it allowed sampling density to vary according to the spatial turnover in species. Using many small samples is a more efficient method to capture the species composition of landscapes than a single large sample with an equivalent sample size.

Effects of anthropogenic habitat disturbance on local pollinator diversity and species turnover across a precipitation gradient

Anthropogenic habitat disturbance can have profound effects on multiple components of forest biotas including pollinator assemblages. We assessed the effect of small-scale disturbance on local richness, abundance, diversity and evenness of insect pollinator fauna; and how habitat disturbance affected species turnover across the landscape and overall diversity along a precipitation gradient in NW Patagonia (Argentina). We evaluated the effect of disturbance on overall pollinator fauna and then separately for bees (i.e. Apoidea) and non-bee pollinators. Locally, disturbed habitats had significantly higher pollinator species richness and abundances than undisturbed habitats for the whole pollinator assemblage, but not for bees or non-bees separately. However, significant differences in species richness between habitats vanished after accounting for differences in abundance between habitat types. At a local scale Shannon–Weaver diversity and evenness did not vary with disturbance. A β diversity index indicated that, across forest types, species turnover was lower between disturbed habitats than between undisturbed habitats. In addition, rarefaction curves showed that disturbed habitats as a whole accumulated fewer species than undisturbed habitats at equivalent sample sizes. We concluded that small patches of disturbed habitat have a negligible effect on local pollinator diversity; however, habitat disturbance reduced β diversity through a homogenization of the pollinator fauna (in particular of bees) across the landscape.

On the Use of Bootstrapped Topologies in Coalescent-Based Bayesian MCMC Inference: A Comparison of Estimation and Computational Efficiencies

Coalescent-based Bayesian Markov chain Monte Carlo (MCMC) inference generates estimates of evolutionary parameters and their posterior probability distributions. As the number of sequences increases, the length of time taken to complete an MCMC analysis increases as well. Here, we investigate an approach to distribute the MCMC analysis across a cluster of computers. To do this, we use bootstrapped topologies as fixed genealogies, perform a single MCMC analysis on each genealogy without topological rearrangements, and pool the results across all MCMC analyses. We show, through simulations, that although the standard MCMC performs better than the bootstrap-MCMC at estimating the effective population size (scaled by mutation rate), the bootstrap-MCMC returns better estimates of growth rates. Additionally, we find that our bootstrap-MCMC analyses are, on average, 37 times faster for equivalent effective sample sizes.

Exploring the Statistical Advantages of Nondestructive Evaluation Over Destructive Testing

In this paper, we propose a framework for exploring the statistical advantages of nondestructive evaluation (NDE) over destructive testing (DT). Two cases are considered: (1) 0–1 or pass/fail data, and (2) continuous measurement data. While NDE data are less expensive to collect, they are less precise than DT data. However, taking more NDE data provides more precision. The proposed framework provides a way to calculate equivalent sample sizes of NDE data for given sample sizes of DT data. We illustrate the proposed framework with a radiographic example.