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Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

Psychological research often builds on between-group comparisons of (measurements of) latent variables; for instance, to evaluate cross-cultural differences in neuroticism or mindfulness. A critical assumption in such comparative research is that the same latent variable(s) are measured in exactly the same way across all groups (i.e., measurement invariance). Otherwise, one would be comparing apples and oranges. Nowadays, measurement invariance is often tested across a large number of groups by means of multigroup factor analysis. When the assumption is untenable, one may compare group-specific measurement models to pinpoint sources of noninvariance, but the number of pairwise comparisons exponentially increases with the number of groups. This makes it hard to unravel invariances from noninvariances and for which groups they apply, and it elevates the chances of falsely detecting noninvariance. An intuitive solution is clustering the groups into a few clusters based on the measurement model parameters. Therefore, we present mixture multigroup factor analysis (MMG-FA) which clusters the groups according to a specific level of measurement invariance. Specifically, in this article, clusters of groups with metric invariance (i.e., equal factor loadings) are obtained by making the loadings cluster-specific, whereas other parameters (i.e., intercepts, factor (co)variances, residual variances) are still allowed to differ between groups within a cluster. MMG-FA was found to perform well in an extensive simulation study, but a larger sample size within groups is required for recovering more subtle loading differences. Its empirical value is illustrated for data on the social value of emotions and data on emotional acculturation. (PsycInfo Database Record (c) 2022 APA, all rights reserved). ispartof: Psychological Methods vol:27 issue:3 pages:281-306 ispartof: location:United States status: published

We propose a method for monitoring proportions when the in-control proportion and the sample sizes vary over time. Our approach is able to overcome some of the performance issues of other commonly used methods, as we demonstrate in this paper using analytical and numerical methods. The derivations and results are shown mainly for monitoring proportions, but we show how the method can be extended to the monitoring of count data. Published version

The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with ε adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.

Recent minimum sample size formula (Riley et al.) for developing clinical prediction models help ensure that development datasets are of sufficient size to minimise overfitting. While these criteria are known to avoid excessive overfitting on average, the extent of variability in overfitting at recommended sample sizes is unknown. We investigated this through a simulation study and empirical example to develop logistic regression clinical prediction models using unpenalised maximum likelihood estimation, and various post-estimation shrinkage or penalisation methods. While the mean calibration slope was close to the ideal value of one for all methods, penalisation further reduced the level of overfitting, on average, compared to unpenalised methods. This came at the cost of higher variability in predictive performance for penalisation methods in external data. We recommend that penalisation methods are used in data that meet, or surpass, minimum sample size requirements to further mitigate overfitting, and that the variability in predictive performance and any tuning parameters should always be examined as part of the model development process, since this provides additional information over average (optimism-adjusted) performance alone. Lower variability would give reassurance that the developed clinical prediction model will perform well in new individuals from the same population as was used for model development.

Background This research work is elaborated investigation of COVID-19 data for Weibull distribution under indeterminacy using time truncated repetitive sampling plan. The proposed design parameters like sample size, acceptance sample number and rejection sample number are obtained for known indeterminacy parameter. Methods The plan parameters and corresponding tables are developed for specified indeterminacy parametric values. The conclusion from the outcome of the proposed design is that when indeterminacy values increase the average sample number (ASN) reduces. Results The proposed repetitive sampling plan methodology application is given using COVID-19 data belong to Italy. The efficiency of the proposed sampling plan is compared with the existing sampling plans. Conclusions Using the tables and COVID-19 data illustration, it is concluded that the proposed plan required a smaller sample size as examined with the available sampling plans in the literature.

Background Numerous statistical methods can be used to calculate the confidence interval (CI) of risk differences. There is consensus in previous literature that the Wald method should be discouraged. We compared five statistical methods for estimating the CI of risk difference in terms of CI width and study conclusion in antibiotic non-inferiority trials. Methods In a secondary analysis of a systematic review, we included non-inferiority trials that compared different antibiotic regimens, reported risk differences for the primary outcome, and described the number of successes and/or failures as well as patients in each arm. For each study, we re-calculated the risk difference CI using the Wald, Agresti-Caffo, Newcombe, Miettinen-Nurminen, and skewness-corrected asymptotic score (SCAS) methods. The CIs by different statistical methods were compared in terms of CI width and conclusion on non-inferiority. A wider CI was considered to be more conservative. Results The analysis included 224 comparisons from 213 studies. The statistical method used to calculate CI was not reported in 134 (59.8%) cases. The median (interquartile range IQR) for CI width by Wald, Agresti-Caffo, Newcombe, Miettinen-Nurminen, and SCAS methods was 13.0% (10.8%, 17.4%), 13.3% (10.9%, 18.5%), 13.6% (11.1%, 18.9%), 13.6% (11.1% and 19.0%), and 13.4% (11.1%, 18.9%), respectively. In 216 comparisons that reported a non-inferiority margin, the conclusion on non-inferiority was the same across the five statistical methods in 211 (97.7%) cases. The differences in CI width were more in trials with a sample size of 100 or less in each group and treatment success rate above 90%. Of the 18 trials in this subgroup with a specified non-inferiority margin, non-inferiority was shown in 17 (94.4%), 16 (88.9%), 14 (77.8%), 14 (77.8%), and 15 (83.3%) cases based on CI by Wald, Agresti-Caffo, Newcombe, Miettinen-Nurminen, and SCAS methods, respectively. Conclusions The statistical method used to calculate CI was not reported in the majority of antibiotic non-inferiority trials. Different statistical methods for CI resulted in different conclusions on non-inferiority in 2.3% cases. The differences in CI widths were highest in trials with a sample size of 100 or less in each group and a treatment success rate above 90%. Trial registration PROSPERO CRD42020165040. April 28, 2020.

Background Accuracy can be improved by taking multiple synchronous samples from each subject in a study to estimate the endpoint of interest if sample values are not highly correlated. If feasible, it is useful to assess the value of this cluster approach when planning studies. Multiple assessments may be the only method to increase power to an acceptable level if the number of subjects is limited. Methods The main aim is to estimate the difference in outcome between groups of subjects by taking one or more synchronous primary outcome samples or measurements. A summary statistic from multiple samples per subject will typically have a lower sampling error. The number of subjects can be balanced against the number of synchronous samples to minimize the sampling error, subject to design constraints. This approach can include estimating the optimum number of samples given the cost per subject and the cost per sample. Results The accuracy improvement achieved by taking multiple samples depends on the intra-class correlation (ICC). The lower the ICC, the greater the benefit that can accrue. If the ICC is high, then a second sample will provide little additional information about the subject’s true value. If the ICC is very low, adding a sample can be equivalent to adding an extra subject. Benefits of multiple samples include the ability to reduce the number of subjects in a study and increase both the power and the available alpha. If, for example, the ICC is 35%, adding a second measurement can be equivalent to adding 48% more subjects to a single measurement study. Conclusion A study’s design can sometimes be improved by taking multiple synchronous samples. It is useful to evaluate this strategy as an extension of a single sample design. An Excel workbook is provided to allow researchers to explore the most appropriate number of samples to take in a given setting.

This paper considers the portfolio problem for high dimensional data when the dimension and size are both large. We analyze the traditional Markowitz mean-variance (MV) portfolio by large dimension matrix theory, and find the spectral distribution of the sample covariance is the main factor to make the expected return of the traditional MV portfolio overestimate the theoretical MV portfolio. A correction is suggested to the spectral construction of the sample covariance to be the sample spectrally corrected covariance, and to improve the traditional MV portfolio to be spectrally corrected. In the expressions of the expected return and risk on the MV portfolio, the population covariance matrix is always a quadratic form, which will direct MV portfolio estimation. We provide the limiting behavior of the quadratic form with the sample spectrally-corrected covariance matrix, and explain the superior performance to the sample covariance as the dimension increases to infinity proportionally with the sample size. Moreover, this paper deduces the limiting behavior of the expected return and risk on the spectrally-corrected MV portfolio, and illustrates the superior properties of the spectrally-corrected MV portfolio. In simulations, we compare the spectrally-corrected estimates with the traditional and bootstrap-corrected estimates, and show the performance of the spectrally-corrected estimates are the best in portfolio returns and portfolio risk. We also compare the performance of the new proposed estimation with deferent optimal portfolio estimates for real data from S&P 500. The empirical findings are consistent with the theory developed in the paper.

While novel statistical methods quantifying the shared heritability of traits and diseases between ancestral distinct populations have been recently proposed, a thorough evaluation of these approaches under differing circumstances remain elusive. Brown et al.2016 proposed the method Popcorn to estimate the shared heritability, i.e. genetic correlation, using only summary statistics. Here, we evaluate Popcorn under several parameters and circumstances: sample size, number of SNPs, sample size of external reference panel, various population pairs, inappropriate external reference panel, and admixed population involved. Our results determined the minimum sample size of the external reference panel, summary statistics, and number of SNPs required to accurately estimate both the genetic correlation and heritability. Moreover, the number of individuals and SNPs required to produce accurate and stable estimates was directly proportional with heritability in Popcorn. Misrepresentation of the reference panel overestimated the genetic correlation by 20% and heritability by 60%. Lastly, applying Popcorn to homogeneous (EUR) and admixed (ASW) populations underestimated the genetic correlation by 15%. Although statistical approaches estimating the shared heritability between ancestral populations will provide novel etiologic insight, caution is required ensuring results are based on the appropriate sample size, number of SNPs, and the generalizability of the reference panel to the discovery populations.

BackgroundNon-proportional hazards are common with time-to-event data but the majority of randomised clinical trials (RCTs) are designed and analysed using approaches which assume the treatment effect follows proportional hazards (PH). Recent advances in oncology treatments have identified two forms of non-PH of particular importance - a time lag until treatment becomes effective, and an early effect of treatment that ceases after a period of time. In sample size calculations for treatment effects on time-to-event outcomes where information is based on the number of events rather than the number of participants, there is crucial importance in correct specification of the baseline hazard rate amongst other considerations. Under PH, the shape of the baseline hazard has no effect on the resultant power and magnitude of treatment effects using standard analytical approaches. However, in a non-PH context the appropriateness of analytical approaches can depend on the shape of the underlying hazard.MethodsA simulation study was undertaken to assess the impact of clinically plausible non-constant baseline hazard rates on the power, magnitude and coverage of commonly utilized regression-based measures of treatment effect and tests of survival curve difference for these two forms of non-PH used in RCTs with time-to-event outcomes.ResultsIn the presence of even mild departures from PH, the power, average treatment effect size and coverage were adversely affected. Depending on the nature of the non-proportionality, non-constant event rates could further exacerbate or somewhat ameliorate the losses in power, treatment effect magnitude and coverage observed. No single summary measure of treatment effect was able to adequately describe the full extent of a potentially time-limited treatment benefit whilst maintaining power at nominal levels.ConclusionsOur results show the increased importance of considering plausible potentially non-constant event rates when non-proportionality of treatment effects could be anticipated. In planning clinical trials with the potential for non-PH, even modest departures from an assumed constant baseline hazard could appreciably impact the power to detect treatment effects depending on the nature of the non-PH. Comprehensive analysis plans may be required to accommodate the description of time-dependent treatment effects.

The receiver operating characteristic (ROC) and precision–recall (PR) plots have been widely used to evaluate the performance of species distribution models. Plotting the ROC/PR curves requires a traditional test set with both presence and absence data (namely PA approach), but species absence data are usually not available in reality. Plotting the ROC/PR curves from presence‐only data while treating background data as pseudo absence data (namely PO approach) may provide misleading results.In this study, we propose a new approach to calibrate the ROC/PR curves from presence and background data with user‐provided information on a constant c, namely PB approach. Here, c defines the probability that species occurrence is detected (labeled), and an estimate of c can also be derived from the PB‐based ROC/PR plots given that a model with good ability of discrimination is available. We used five virtual species and a real aerial photography to test the effectiveness of the proposed PB‐based ROC/PR plots. Different models (or classifiers) were trained from presence and background data with various sample sizes. The ROC/PR curves plotted by PA approach were used to benchmark the curves plotted by PO and PB approaches.Experimental results show that the curves and areas under curves by PB approach are more similar to that by PA approach as compared with PO approach. The PB‐based ROC/PR plots also provide highly accurate estimations of c in our experiment.We conclude that the proposed PB‐based ROC/PR plots can provide valuable complements to the existing model assessment methods, and they also provide an additional way to estimate the constant c (or species prevalence) from presence and background data., The receiver operating characteristic (ROC) and precision–recall (PR) plots have been widely used to evaluate the performances of species distribution models. We propose a new approach to calibrate the ROC/PR curves from presence and background data with user‐provided information on a constant c. An estimate of c can also be derived from the ROC/PR plots given that a model with good ability of discrimination is available.

There is some debate in the psychometric literature about item parameter estimation in multistage designs. It is occasionally argued that the conditional maximum likelihood (CML) method is superior to the marginal maximum likelihood method (MML) because no assumptions have to be made about the trait distribution. However, CML estimation in its original formulation leads to biased item parameter estimates. Zwitser and Maris (2015, Psychometrika) proposed a modified conditional maximum likelihood estimation method for multistage designs that provides practically unbiased item parameter estimates. In this article, the differences between different estimation approaches for multistage designs were investigated in a simulation study. Four different estimation conditions (CML, CML estimation with the consideration of the respective MST design, MML with the assumption of a normal distribution, and MML with log-linear smoothing) were examined using a simulation study, considering different multistage designs, number of items, sample size, and trait distributions. The results showed that in the case of the substantial violation of the normal distribution, the CML method seemed to be preferable to MML estimation employing a misspecified normal trait distribution, especially if the number of items and sample size increased. However, MML estimation using log-linear smoothing lea to results that were very similar to the CML method with the consideration of the respective MST design.

Purpose State regulations require that CT radiation output be measured using a dosimeter after major service. The most common major service is tube replacement. We hypothesized that historical QC data could be used instead to determine if output measurements are necessary, potentially reducing the need for output measurements that require an on‐site visit by a qualified medical physicist. Methods Records of 65 original equipment manufacturer (OEM) tube replacements were reviewed to determine with what frequency output was outside the manufacturer's specifications. The previous 7 days of historical quality control (QC) data prior to a tube change was used to establish a baseline mean noise level and 95% inferential confidence intervals (ICIs) about the mean. This was compared to an ICI constructed using 7 days of QC data post‐tube change and the region of indifference. Different methods for acquiring samples of image noise were compared using a single factor analysis of variance (ANOVA). Results None of the 65 tube replacements reviewed in this study resulted in an output change that exceeded the manufacturer's specifications. In all but one case, the results of the ICI analysis matched the measured output results. In the single case where results were discordant, the mean image noise was slightly higher after the tube change, which may have indicated the need for a larger sample size or service unrelated to the X‐ray tube, for example, system calibration. The method used to sample image noise did not significantly affect the calculated mean noise. Conclusions This review of historical OEM tube replacement data indicated the likelihood of output falling outside manufacturer specifications is low. Considering this, it is likely that using QC data from programs required by regulation and the American College of Radiology (ACR), medical physicists can reliably verify radiation output stability remotely instead of making measurements using a dosimeter.

Context: In empirical software engineering, crossover designs are popular for experiments comparing software engineering techniques that must be undertaken by human participants. However, their value depends on the correlation ( r ) between the outcome measures on the same participants. Software engineering theory emphasizes the importance of individual skill differences, so we would expect the values of r to be relatively high. However, few researchers have reported the values of r . Goal: To investigate the values of r found in software engineering experiments. Method: We undertook simulation studies to investigate the theoretical and empirical properties of r . Then we investigated the values of r observed in 35 software engineering crossover experiments. Results: The level of r obtained by analysing our 35 crossover experiments was small. Estimates based on means, medians, and random effect analysis disagreed but were all between 0.2 and 0.3. As expected, our analyses found large variability among the individual r estimates for small sample sizes, but no indication that r estimates were larger for the experiments with larger sample sizes that exhibited smaller variability. Conclusions: Low observed r values cast doubts on the validity of crossover designs for software engineering experiments. However, if the cause of low r values relates to training limitations or toy tasks, this affects all Software Engineering (SE) experiments involving human participants. For all human-intensive SE experiments, we recommend more intensive training and then tracking the improvement of participants as they practice using specific techniques, before formally testing the effectiveness of the techniques.

Statistical correction for measurement error in epidemiologic studies is possible, provided that information about the measurement error model and its parameters are available. Such information is commonly obtained from a randomly sampled internal validation sample. It is however unknown whether randomly sampling the internal validation sample is the optimal sampling strategy. We conducted a simulation study to investigate various internal validation sampling strategies in conjunction with regression calibration. Our simulation study showed that for an internal validation study sample of 40% of the main study’s sample size, stratified random and extremes sampling had a small efficiency gain over random sampling (10% and 12% decrease on average over all scenarios, respectively). The efficiency gain was more pronounced in smaller validation samples of 10% of the main study’s sample size (i.e., a 31% and 36% decrease on average over all scenarios, for stratified random and extremes sampling, respectively). To mitigate the bias due to measurement error in epidemiologic studies, small efficiency gains can be achieved for internal validation sampling strategies other than random, but only when measurement error is nondifferential. For regression calibration, the gain in efficiency is, however, at the cost of a higher percentage bias and lower coverage.

Quality of research is determined by many factors and one such climacteric factor is sample size. Inability to use correct sample size in study might lead to fallacious results in the form of rejection of true findings or approval of false results. Too large sample size is wastage of resources and use of too small sample size might fail to answer the research question or provide imprecise results and may question the validity of study. Despite being such a paramount aspect of research, the knowledge about sample size calculation is sparse among researchers. Why is it important to calculate sample size; when to calculate it; how to calculate it and what details about sample size calculation should be reported in research protocols or articles; are the lesser known basics to majority of researchers. The present review is directed to address these aforementioned fundamentals about sample size. Sample size should be calculated during the initial phase of planning of study. Several components are required for sample size calculation such as effect size, type-1 error, type-2 error, and variance. Researchers must be aware that there are different formulas for calculating sample size for different types of study designs. The researcher must include details about sample size calculation in the methodology section, so that it can be justified and it also adds to the transparency of the study. The literature about calculation of sample size for different study designs is scattered over many textbooks and journals. Scrupulous literature search was conducted to find the passable information for this review. This paper presents the sample size calculation formulas in a single review in a simplified manner with relevant examples, so that researchers may adequately use them in their research.

In a recent review published in this journal, Coutts et al. (2019) compared nine different ways to estimate the maximum depositional age (MDA) of siliclastic rocks by means of detrital geochronology. Their results show that among these methods three are positively and six negatively biased. This paper investigates the cause of these biases and proposes a solution to it. A simple toy example shows that it is theoretically impossible for the reviewed methods to find the correct depositional age in even a best case scenario: the MDA estimates drift to ever smaller values with increasing sample size. The issue can be solved using a maximum likelihood model that was originally developed for fission track thermochronology by Galbraith and Laslett (1993). This approach parameterises the MDA estimation problem with a binary mixture of discrete and continuous distributions. The ‘Maximum Likelihood Age’ (MLA) algorithm converges to a unique MDA value, unlike the ad hoc methods reviewed by Coutts et al. (2019). It successfully recovers the depositional age for the toy example, and produces sensible results for realistic distributions. This is illustrated with an application to a published dataset of 13 sandstone samples that were analysed by both LA-ICPMS and CA-TIMS U–Pb geochronology. The ad hoc algorithms produce unrealistic MDA estimates that are systematically younger for the LA-ICPMS data than for the CA-TIMS data. The MLA algorithm does not suffer from this negative bias. The MLA method is a purely statistical approach to MDA estimation. Like the ad hoc methods, it does not readily accommodate geological complications such as post-depositional Pb-loss, or analytical issues causing erroneously young outliers. The best approach in such complex cases is to re-analyse the youngest grains using more accurate dating techniques. The results of the MLA method are best visualised on radial plots. Both the model and the plots have applications outside detrital geochronology, for example to determine volcanic eruption ages.

This study aimed at evaluating the effect of organizational culture on strategy implementation in Private chartered universities in Kenya. The objective of this study was to ascertain the effect of hierarchy culture on the strategy implementation in Private chartered universities in Kenya. A cross-sectional survey research design was adopted and it used both quantitative and qualitative data as it seeks the effect of organizational culture on the implementation of corporate strategy. The accessible population included University and students’ leaders. This study used both stratified random sampling and the target sample size was 194 employees. The statistical package for social sciences (SPSS) version 21 was used to describe the relationships between dependent and independent variables. The study used correlation and regression techniques as well as the analysis of variance (ANOVA) to test the study hypotheses. A multiple linear regression model was also used to derive inferential statistical indicators like the correlation, coefficient of determination, F-statistics, t-test statistic, and the p-value. In this research Pearson’s correlation analysis was used to test for the existence of multicollinearity. Normality testing was done to compare the cumulative distribution of the data. Factor analysis was also carried out on all items in each variable in order to reduce the measurable and observable variables. The key finding based on the tests conducted in the study was that the variable: Hierarchy culture had an effect on the dependent variable: Strategy implementation. The p-value published showed that there was a positive effect of hierarchy culture on strategy implementation in Private chartered universities in Kenya

Background: Despite the large burden of chronic kidney disease (CKD), it is challenging to conduct adequately powered clinical trials in this setting. Sound and efficient trials are needed to advance treatment. Various analysis strategies can be used to compare the efficacy of a parallel trial design with that of three two period trial designs. Methods: The type 1 error rates and powers of various trial designs were calculated using simulated data from models fit to two re cent CKD trials. In addition, we assessed the influences of a variety of analysis strategies and of the presence of a carryover effect. Results: The parallel and crossover designs (with analysis of change from baseline to the off treatment value) maintained the target type 1 error rate in all scenarios. In some scenarios, an open label design yielded inflated type 1 error rates. In many scenarios, the open label and delayed start designs had unacceptably low power and high type 1 error rates. Overall, the crossover design had the highest power by far, and always controlled the type 1 error rate. Conclusion: The recommended approach to a CKD trial is a two period design with an endpoint that is the rate of change in estimat ed glomerular filtration rate from pretreatment to off treatment. As compared to a parallel trial, a crossover study involves a consider ably smaller sample size and shorter total follow-up duration. A crossover design may also be preferable for patients, and facilitates recruitment of a sufficient number of subjects.

Background In a cluster randomised controlled trial (CRCT), randomisation units are “clusters” such as schools or GP practices. This has methodological implications for study design and statistical analysis, since clustering often leads to correlation between observations which, if not accounted for, can lead to spurious conclusions of efficacy/effectiveness. Bayesian methodology offers a flexible, intuitive framework to deal with such issues, but its use within CRCT design and analysis appears limited. This review aims to explore and quantify the use of Bayesian methodology in the design and analysis of CRCTs, and appraise the quality of reporting against CONSORT guidelines. Methods We sought to identify all reported/published CRCTs that incorporated Bayesian methodology and papers reporting development of new Bayesian methodology in this context, without restriction on publication date or location. We searched Medline and Embase and the Cochrane Central Register of Controlled Trials (CENTRAL). Reporting quality metrics according to the CONSORT extension for CRCTs were collected, as well as demographic data, type and nature of Bayesian methodology used, journal endorsement of CONSORT guidelines, and statistician involvement. Results Twenty-seven publications were included, six from an additional hand search. Eleven (40.7%) were reports of CRCT results: seven (25.9%) were primary results papers and four (14.8%) reported secondary results. Thirteen papers (48.1%) reported Bayesian methodological developments, the remaining three (11.1%) compared different methods. Four (57.1%) of the primary results papers described the method of sample size calculation; none clearly accounted for clustering. Six (85.7%) clearly accounted for clustering in the analysis. All results papers reported use of Bayesian methods in the analysis but none in the design or sample size calculation. Conclusions The popularity of the CRCT design has increased rapidly in the last twenty years but this has not been mirrored by an uptake of Bayesian methodology in this context. Of studies using Bayesian methodology, there were some differences in reporting quality compared to CRCTs in general, but this study provided insufficient data to draw firm conclusions. There is an opportunity to further develop Bayesian methodology for the design and analysis of CRCTs in order to expand the accessibility, availability, and, ultimately, use of this approach.

The purpose of this study was to determine the number of samples that should be used in independent treatment comparisons with different effect sizes (0.25-3.0), the number of treatments (2-5), and the power of the test (70% -95%) in single and multi-factor treatments. The material of the study was the random numbers drawn from the population that shows a normal distribution with N (0, 1) parameter. The power of the test was calculated by sampling with replacement from the population and after the differences between the treatments in terms of standard deviation were established, 10000 simulations were performed. This setup was carried out for experiments with one, two, and three factors. In the comparison of single factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 3 and 7. In the comparison of two-factor independent treatment means, when the effect size was larger than Δ = 2 and the test power was between 70% and 95%, the sample sizes varied between 2 and 3. In the comparison of three-factor independent treatment means, when the effect size was larger than Δ= 1.5 and the test power was between 70% and 95%, the sample size was 2. If all treatment comparisons were generalized; it was observed that when the effect size increased, and the power of the test decreased, the sample size decreased In the t-test and F tests used in independent treatment comparisons, a power analysis was performed under different situations, and the number of experimental units for each 5% power increment between 70% and 95% were presented in tables. These tables, may help researchers to determine the number of samples without power analysis in independent group comparisons.

The aim of this paper is to introduce basic concepts and methods for calculating sample size in animal studies. At the planning stage of clinical studies, the determination of the sample size is a very important process to show the validity, accuracy, and reliability of the study. However, not all studies require a sample size to be calculated. Before conducting the study, it is essential to determine whether the study objectives suggest a pilot and exploratory study, as well as the purpose of testing the hypothesis of interest. Since most animal experiments are pilot and exploratory studies, it would be more appropriate to review other considerations for conducting an experiment while maintaining scientific and qualitative levels rather than sample size estimation. Sample size is calculated in various situations in animal studies. Therefore, it can be estimated according to the situations and objectives through the methods of precision analysis, power analysis, and so on. In some cases, nonparametric methods can be employed if the assumptions of normality is not met or a small sample is available for the study.

In continuous test norming, the test score distribution is estimated as a continuous function of predictor(s). A flexible approach for norm estimation is the use of generalized additive models for location, scale, and shape. It is unknown how sensitive their estimates are to model flexibility and sample size. Generally, a flexible model that fits at the population level has smaller bias than its restricted nonfitting version, yet it has larger sampling variability. We investigated how model flexibility relates to bias, variance, and total variability in estimates of normalized z scores under empirically relevant conditions, involving the skew Student t and normal distributions as population distributions. We considered both transversal and longitudinal assumption violations. We found that models with too strict distributional assumptions yield biased estimates, whereas too flexible models yield increased variance. The skew Student t distribution, unlike the Box–Cox Power Exponential distribution, appeared problematic to estimate for normally distributed data. Recommendations for empirical norming practice are provided.

Continuous norming is an increasingly popular approach to establish norms when the performance on a test is dependent on age. However, current continuous norming methods rely on a number of assumptions that are quite restrictive and may introduce bias. In this study, quantile regression was introduced as more flexible alternative. Bias and precision of quantile regression-based norming were investigated with (age-)group as covariate, varying sample sizes and score distributions, and compared with bias and precision of two other norming methods: traditional norming and mean regression-based norming. Simulations showed the norms obtained using quantile regression to be most precise in almost all conditions. Norms were nevertheless biased when the score distributions reflected a ceiling effect. Quantile regression-based norming can thus be considered a promising alternative to traditional norming and mean regression-based norming, but only if the shape of the score distribution can be expected to be close to normal.

To interpret a person’s change score, one typically transforms the change score into, for example, a percentile, so that one knows a person’s location in a distribution of change scores. Transformed scores are referred to as norms and the construction of norms is referred to as norming. Two often-used norming methods for change scores are the regression-based change approach and the T Scores for Change method. In this article, we discuss the similarities and differences between these norming methods, and use a simulation study to systematically examine the precision of the two methods and to establish the minimum sample size requirements for satisfactory precision.

Background The disease burden of SARS-CoV-2 as measured by tests from various localities, and at different time points present varying estimates of infection and fatality rates. Models based on these acquired data may suffer from systematic errors and large estimation variances due to the biases associated with testing. An unbiased randomized testing to estimate the true fatality rate is still missing. Methods Here, we characterize the effect of incidental sampling bias in the estimation of epidemic dynamics. Towards this, we explicitly modeled for sampling bias in an augmented compartment model to predict epidemic dynamics. We further calculate the bias from differences in disease prediction from biased, and randomized sampling, proposing a strategy to obtain unbiased estimates. Results Our simulations demonstrate that sampling biases in favor of patients with higher disease manifestation could significantly affect direct estimates of infection and fatality rates calculated from the numbers of confirmed cases and deaths, and serological testing can partially mitigate these biased estimates. Conclusions The augmented compartmental model allows the explicit modeling of different testing policies and their effects on disease estimates. Our calculations for the dependence of expected confidence on a randomized sample sizes, show that relatively small sample sizes can provide statistically significant estimates for SARS-CoV-2 related death rates.

Factor analysis is ubiquitously applied in behavioral sciences for capturing covariances of observed variables by latent variables (factors). When factor-analyzing data from many groups of subjects, mixture simultaneous factor analysis (MSFA) determines which groups have the same factor model by clustering them based on their factor loadings, factor (co)variances and residual variances. Two Monte Carlo simulations are performed to investigate the power and type I error of Wald tests for factor loading differences in MSFA, as affected by characteristics of the data (sample size in terms of number and size of groups), factor models (item communality levels, sizes and types of loading differences) and clustering (cluster size, classification error and uncertainty). The results were better in case of equal cluster sizes, strongly overdetermined factors, high communalities, and larger primary loading differences.

Background Growth Mixture Modeling (GMM) is commonly used to group individuals on their development over time, but convergence issues and impossible values are common. This can result in unreliable model estimates. Constraining variance parameters across classes or over time can solve these issues, but can also seriously bias estimates if variances differ. We aimed to determine which variance parameters can best be constrained in Growth Mixture Modeling. Methods To identify the variance constraints that lead to the best performance for different sample sizes, we conducted a simulation study and next verified our results with the TRacking Adolescent Individuals’ Lives Survey (TRAILS) cohort. Results If variance parameters differed across classes and over time, fitting a model without constraints led to the best results. No constrained model consistently performed well. However, the model that constrained the random effect variance and residual variances across classes consistently performed very poorly. For a small sample size (N = 100) all models showed issues. In TRAILS, the same model showed substantially different results from the other models and performed poorly in terms of model fit. Conclusions If possible, a Growth Mixture Model should be fit without any constraints on variance parameters. If not, we recommend to try different variance specifications and to not solely rely on the default model, which constrains random effect variances and residual variances across classes. The variance structure must always be reported Researchers should carefully follow the GRoLTS-Checklist when analyzing and reporting trajectory analyses.

Introduction In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions. Methods We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel–Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed). Results Mantel–Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues. Discussion Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel–Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method.

This study aims to analyze the contribution of industrial work practice and academic ability towards students' perceptions of readiness to enter the world of work in class III of the Office Administration Department of SMKN 1 Jambi. This study used a quantitative method with a sample size of 84 respondents. The research data were obtained by distributing questionnaires to students, then were analyzed by inferential statistics using simple regression and multiple regression data analysis techniques. Based on the results of the study, it was known that the contribution of X1 to Y was 22.7% with the regression equation Y = 50.962 + 0.942 X, which means that there was a positive effect of X1 on Y. Furthermore, the contribution of X2 to Y was 32.8% with the regression equation Y = 46.074 + 0.867 X, which means that X2 had a positive effect on Y. Then, the contribution of X1 and X2 to Y was 42.4% with the regression equation Y = 29.026 + 0.691 X1 + 0.727 X2. This means that the effect of industrial work practices (X1) and academic ability (X2) together (simultaneously) on readiness to enter the world of work (Y) was 42.4%, the remaining 57.6% was influenced by other factors. Thus, it can be concluded that industrial work practices and academic abilities contribute to students' perceptions of readiness to enter the world of work.

Background In order to correctly assess the effect of intervention from stratified cluster randomized trials (CRTs), it is necessary to adjust for both clustering and stratification, as failure to do so leads to misleading conclusions about the intervention effect. We have conducted a systematic survey to examine the current practices about analysis and reporting of stratified CRTs. Method We used the search terms to identify the stratified CRTs from MEDLINE since the inception to July 2019. In phase 1, we screened the title and abstract for English-only studies and selected, including the main results paper of the identified protocols, for the next phase. In phase 2, we screened the full text and selected studies for data abstraction. The data abstraction form was piloted and developed using the REDCap. We abstracted data on multiple design and methodological aspects of the study including whether the primary method adjusted for both clustering and stratification, reporting of sample size, randomization, and results. Results We screened 2686 studies in the phase 1 and selected 286 studies for phase 2—among them 185 studies were selected for data abstraction. Most of the selected studies were two-arm 140/185 (76%) and parallel-group 165/185 (89%) trials. Among these 185 studies, 27 (15%) of them did not provide any sample size or power calculation, while 105 (57%) studies did not mention any method used for randomization within each stratum. Further, 43 (23%) and 150 (81%) of 185 studies did not provide the definition of all the strata, while more than 60% of the studies did not include all the stratification variable(s) in the flow chart or baseline characteristics table. More than half 114/185 (62%) of the studies did not adjust the primary method for both clustering and stratification. Conclusion Stratification helps to achieve the balance among intervention groups. However, to correctly assess the intervention effect from stratified CRTs, it is important to adjust the primary analysis for both stratification and clustering. There are significant deficiencies in the reporting of methodological aspects of stratified CRTs, which require substantial improvements in several areas including definition of strata, inclusion of stratification variable(s) in the flow chart or baseline characteristics table, and reporting the stratum-specific number of clusters and individuals in the intervention groups.

This study develops a nearly unbiased estimator of the ratio of the contemporary effective mother size to the census size in a population, as a proxy of the ratio of contemporary effective size (or effective breeding size) to census size (Ne/N or Nb/N). The proposed estimator is based on both known mother–offspring (MO) and maternal‐sibling (MS) relationships observed within the same cohort, in which sampled individuals in the cohort probably share MO relationships with sampled mothers. The rationale is that the frequency of MO and MS pairs contains information regarding the contemporary effective mother size and the (mature) census size, respectively. Therefore, the estimator can be obtained only from genetic data. We also evaluate the performance of the estimator by running an individual‐based model. The results of this study provide the following: (a) parameter range for satisfying the unbiasedness, and (b) guidance for sample sizes to ensure the required accuracy and precision, especially when the order of the ratio is available. Furthermore, the results demonstrate the usefulness of a sibship assignment method for genetic monitoring, providing insights for interpreting environmental and/or anthropological factors fluctuating Ne/N (or Nb/N), especially in the context of conservation biology and wildlife management., We developed a nearly unbiased estimator of the ratio of the contemporary effective mother size to the census size in a population, as a proxy of Ne/N. The proposed estimator is based on a known mother–offspring (MO) relationship and on a known maternal‐sibling (MS) relationship found within the same cohort, in which sampled individuals in the cohort potentially share MO relationships with sampled mothers.

The beta-binomial model that is generated by a simple mixture model has been commonly applied in the health, physical, and social sciences. In clinical and public health, overdispersion occurs due to biological variation between the subjects of interest. Both the binomial and beta-binomial models are applied to different problems occurring in rational test theory. In this study, we focused on modeling overdispersion for binomial distribution. The main aim was to show a complete and extensive understanding of the beta-binomial model and updated form by broaden its practical applications in the field of breast cancer with hormone medication. It is observed in different independent Bernoulli trials yes/no (xi=1, 0) experiments with success probabilities 0

An important step when designing an empirical study is to justify the sample size that will be collected. The key aim of a sample size justification for such studies is to explain how the collected data is expected to provide valuable information given the inferential goals of the researcher. In this overview article six approaches are discussed to justify the sample size in a quantitative empirical study: 1) collecting data from (almost) the entire population, 2) choosing a sample size based on resource constraints, 3) performing an a-priori power analysis, 4) planning for a desired accuracy, 5) using heuristics, or 6) explicitly acknowledging the absence of a justification. An important question to consider when justifying sample sizes is which effect sizes are deemed interesting, and the extent to which the data that is collected informs inferences about these effect sizes. Depending on the sample size justification chosen, researchers could consider 1) what the smallest effect size of interest is, 2) which minimal effect size will be statistically significant, 3) which effect sizes they expect (and what they base these expectations on), 4) which effect sizes would be rejected based on a confidence interval around the effect size, 5) which ranges of effects a study has sufficient power to detect based on a sensitivity power analysis, and 6) which effect sizes are expected in a specific research area. Researchers can use the guidelines presented in this article, for example by using the interactive form in the accompanying online Shiny app, to improve their sample size justification, and hopefully, align the informational value of a study with their inferential goals.

The problem of poor reproducibility of scientific findings has received much attention over recent years, in a variety of fields including psychology and neuroscience. The problem has been partly attributed to publication bias and unwanted practices such as p‐hacking. Low statistical power in individual studies is also understood to be an important factor. In a recent multisite collaborative study, we mapped brain anatomical left–right asymmetries for regional measures of surface area and cortical thickness, in 99 MRI datasets from around the world, for a total of over 17,000 participants. In the present study, we revisited these hemispheric effects from the perspective of reproducibility. Within each dataset, we considered that an effect had been reproduced when it matched the meta‐analytic effect from the 98 other datasets, in terms of effect direction and significance threshold. In this sense, the results within each dataset were viewed as coming from separate studies in an “ideal publishing environment,” that is, free from selective reporting and p hacking. We found an average reproducibility rate of 63.2% (SD = 22.9%, min = 22.2%, max = 97.0%). As expected, reproducibility was higher for larger effects and in larger datasets. Reproducibility was not obviously related to the age of participants, scanner field strength, FreeSurfer software version, cortical regional measurement reliability, or regional size. These findings constitute an empirical illustration of reproducibility in the absence of publication bias or p hacking, when assessing realistic biological effects in heterogeneous neuroscience data, and given typically‐used sample sizes., Region‐wise effect sizes and reproducibility rates of hemispheric asymmetry effects. In general, effects with higher effect sizes showed higher reproducibility, given the same conditions (e.g., sample size and data heterogeneity).

Objective Stillbirth is a potentially preventable complication of pregnancy. Identifying women at high risk of stillbirth can guide decisions on the need for closer surveillance and timing of delivery in order to prevent fetal death. Prognostic models have been developed to predict the risk of stillbirth, but none has yet been validated externally. In this study, we externally validated published prediction models for stillbirth using individual participant data (IPD) meta-analysis to assess their predictive performance. Methods MEDLINE, EMBASE, DH-DATA and AMED databases were searched from inception to December 2020 to identify studies reporting stillbirth prediction models. Studies that developed or updated prediction models for stillbirth for use at any time during pregnancy were included. IPD from cohorts within the International Prediction of Pregnancy Complications (IPPIC) Network were used to validate externally the identified prediction models whose individual variables were available in the IPD. The risk of bias of the models and cohorts was assessed using the Prediction study Risk Of Bias ASsessment Tool (PROBAST). The discriminative performance of the models was evaluated using the C-statistic, and calibration was assessed using calibration plots, calibration slope and calibration-in-the-large. Performance measures were estimated separately in each cohort, as well as summarized across cohorts using random-effects meta-analysis. Clinical utility was assessed using net benefit. Results Seventeen studies reporting the development of 40 prognostic models for stillbirth were identified. None of the models had been previously validated externally, and the full model equation was reported for only one-fifth (20%, 8/40) of the models. External validation was possible for three of these models, using IPD from 19 cohorts (491 201 pregnant women) within the IPPIC Network database. Based on evaluation of the model development studies, all three models had an overall high risk of bias, according to PROBAST. In the IPD meta-analysis, the models had summary C-statistics ranging from 0.53 to 0.65 and summary calibration slopes ranging from 0.40 to 0.88, with risk predictions that were generally too extreme compared with the observed risks. The models had little to no clinical utility, as assessed by net benefit. However, there remained uncertainty in the performance of some models due to small available sample sizes. Conclusions The three validated stillbirth prediction models showed generally poor and uncertain predictive performance in new data, with limited evidence to support their clinical application. The findings suggest methodological shortcomings in their development, including overfitting. Further research is needed to further validate these and other models, identify stronger prognostic factors and develop more robust prediction models. (c) 2021 The Authors. Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

Objectives: This study aimed to provide detailed guidance on modeling approaches for implementing competing events in discrete event simulations based on censored individual patient data (IPD). Methods: The event-specific distributions (ESDs) approach sampled times from event-specific time-to-event distributions and simulated the first event to occur. The unimodal distribution and regression approach sampled a time from a combined unimodal time-to-event distribution, representing all events, and used a (multinomial) logistic regression model to select the event to be simulated. A simulation study assessed performance in terms of relative absolute event incidence difference and relative entropy of time-to-event distributions for different types and levels of right censoring, numbers of events, distribution overlap, and sample sizes. Differences in cost-effectiveness estimates were illustrated in a colorectal cancer case study. Results: Increased levels of censoring negatively affected the modeling approaches’ performance. A lower number of competing events and higher overlap of distributions improved performance. When IPD were censored at random times, ESD performed best. When censoring occurred owing to a maximum follow-up time for 2 events, ESD performed better for a low level of censoring (ie, 10%). For 3 or 4 competing events, ESD better represented the probabilities of events, whereas unimodal distribution and regression better represented the time to events. Differences in cost-effectiveness estimates, both compared with no censoring and between approaches, increased with increasing censoring levels. Conclusions: Modelers should be aware of the different modeling approaches available and that selection between approaches may be informed by data characteristics. Performing and reporting extensive validation efforts remains essential to ensure IPD are appropriately represented.

Highlights • Sample Size Determination (SSD) is a crucial step in sampling design. • Bayesian, mixed Bayesian-likelihood (MBL) and frequentist SSD approaches compared. • Bayesian and MBL SSD approach account for uncertainty about design parameters. • Various SSD criteria derived from probability distribution of credible intervals . • Legacy data on Zn concentration in soil used for postulating prior distributions., A crucial decision in designing a spatial sample for soil survey is the number of sampling locations required to answer, with sufficient accuracy and precision, the questions posed by decision makers at different levels of geographic aggregation. In the Indian Soil Health Card (SHC) scheme, many thousands of locations are sampled per district. In this paper the SHC data are used to estimate the mean of a soil property within a defined study area, e.g., a district, or the areal fraction of the study area where some condition is satisfied, e.g., exceedence of a critical level. The central question is whether this large sample size is needed for this aim. The sample size required for a given maximum length of a confidence interval can be computed with formulas from classical sampling theory, using a prior estimate of the variance of the property of interest within the study area. Similarly, for the areal fraction a prior estimate of this fraction is required. In practice we are uncertain about these prior estimates, and our uncertainty is not accounted for in classical sample size determination (SSD). This deficiency can be overcome with a Bayesian approach, in which the prior estimate of the variance or areal fraction is replaced by a prior distribution. Once new data from the sample are available, this prior distribution is updated to a posterior distribution using Bayes’ rule. The apparent problem with a Bayesian approach prior to a sampling campaign is that the data are not yet available. This dilemma can be solved by computing, for a given sample size, the predictive distribution of the data, given a prior distribution on the population and design parameter. Thus we do not have a single vector with data values, but a finite or infinite set of possible data vectors. As a consequence, we have as many posterior distribution functions as we have data vectors. This leads to a probability distribution of lengths or coverages of Bayesian credible intervals, from which various criteria for SSD can be derived. Besides the fully Bayesian approach, a mixed Bayesian-likelihood approach for SSD is available. This is of interest when, after the data have been collected, we prefer to estimate the mean from these data only, using the frequentist approach, ignoring the prior distribution. The fully Bayesian and mixed Bayesian-likelihood approach are illustrated for estimating the mean of log-transformed Zn and the areal fraction with Zn-deficiency, defined as Zn concentration

To estimate the mean of a quantitative variable in a hierarchical population, it is logistically convenient to sample in two stages (two-stage sampling), i.e. selecting first clusters, and then individuals from the sampled clusters. Allowing cluster size to vary in the population and to be related to the mean of the outcome variable of interest (informative cluster size), the following competing sampling designs are considered: sampling clusters with probability proportional to cluster size, and then the same number of individuals per cluster; drawing clusters with equal probability, and then the same percentage of individuals per cluster; and selecting clusters with equal probability, and then the same number of individuals per cluster. For each design, optimal sample sizes are derived under a budget constraint. The three optimal two-stage sampling designs are compared, in terms of efficiency, with each other and with simple random sampling of individuals. Sampling clusters with probability proportional to size is recommended. To overcome the dependency of the optimal design on unknown nuisance parameters, maximin designs are derived. The results are illustrated, assuming probability proportional to size sampling of clusters, with the planning of a hypothetical survey to compare adolescent alcohol consumption between France and Italy.

The consideration of a patient's treatment preference may be essential in determining how a patient will respond to a particular treatment. While traditional clinical trials are unable to capture these effects, the two-stage randomized preference design provides an important tool for researchers seeking to understand the role of patient preferences. In addition to the treatment effect, these designs seek to estimate the role of preferences through testing of selection and preference effects. The R package preference facilitates the use of two-stage clinical trials by providing the necessary tools to design and analyze these studies. To aid in the design, functions are provided to estimate the required sample size and to estimate the study power when a sample size is fixed. In addition, analysis functions are provided to determine the significance of each effect using either raw data or summary statistics. The package is able to incorporate either an unstratified or stratified preference design. The functionality of the package is demonstrated using data from a study evaluating two management methods in women found to have an atypical Pap smear.

Limited statistical power due to small sample sizes is a problem in fMRI research. Most of the work to date has examined the impact of sample size on task‐related activation, with less attention paid to the influence of sample size on brain‐behavior correlations, especially in actual experimental fMRI data. We addressed this issue using two large data sets (a working memory task, N = 171, and a relational processing task, N = 865) and both univariate and multivariate approaches to voxel‐wise correlations. We created subsamples of different sizes and calculated correlations between task‐related activity at each voxel and task performance. Across both data sets the magnitude of the brain‐behavior correlations decreased and similarity across spatial maps increased with larger sample sizes. The multivariate technique identified more extensive correlated areas and more similarity across spatial maps, suggesting that a multivariate approach would provide a consistent advantage over univariate approaches in the stability of brain‐behavior correlations. In addition, the multivariate analyses showed that a sample size of roughly 80 or more participants would be needed for stable estimates of correlation magnitude in these data sets. Importantly, a number of additional factors would likely influence the choice of sample size for assessing such correlations in any given experiment, including the cognitive task of interest and the amount of data collected per participant. Our results provide novel experimental evidence in two independent data sets that the sample size commonly used in fMRI studies of 20–30 participants is very unlikely to be sufficient for obtaining reproducible brain‐behavior correlations, regardless of analytic approach., Limited statistical power due to small sample sizes is a problem in fMRI research. Most of the work to date has examined the impact of sample size on task‐related activation, with less attention paid to the influence of sample size on brain‐behavior correlations, especially in actual experimental fMRI data. Our results provide novel experimental evidence in two independent data sets that the sample size commonly used in fMRI studies of 20–30 participants is very unlikely to be sufficient for obtaining reproducible brain‐behavior correlations, regardless of whether a univariate or multivariate approach is used.

This paper presents the Bayesian inference of the 3-component Kumaraswamy mixture distribution. The paper formulates the 3-component model, provides Bayesian estimates and their respective posterior risks assuming non-informative prior under type-I censoring. Since the Bayes estimates are not in closed form, the paper provides a comparative analysis of the estimates and their respective risks derived under quadrature method and importance sampling using different loss functions, assuming different sample sizes, test termination times and mixture probabilities. Finally, the proposed 3 component mixture model is then applied to the real life data to assess its validity. The convergence of the estimates under importance sampling is rapidly observed as compared to quadrature methods.

Background As the barriers to incorporating RNA sequencing (RNA-Seq) into biomedical studies continue to decrease, the complexity and size of RNA-Seq experiments are rapidly growing. Paired, longitudinal, and other correlated designs are becoming commonplace, and these studies offer immense potential for understanding how transcriptional changes within an individual over time differ depending on treatment or environmental conditions. While several methods have been proposed for dealing with repeated measures within RNA-Seq analyses, they are either restricted to handling only paired measurements, can only test for differences between two groups, and/or have issues with maintaining nominal false positive and false discovery rates. In this work, we propose a Bayesian hierarchical negative binomial generalized linear mixed model framework that can flexibly model RNA-Seq counts from studies with arbitrarily many repeated observations, can include covariates, and also maintains nominal false positive and false discovery rates in its posterior inference. Results In simulation studies, we showed that our proposed method (MCMSeq) best combines high statistical power (i.e. sensitivity or recall) with maintenance of nominal false positive and false discovery rates compared the other available strategies, especially at the smaller sample sizes investigated. This behavior was then replicated in an application to real RNA-Seq data where MCMSeq was able to find previously reported genes associated with tuberculosis infection in a cohort with longitudinal measurements. Conclusions Failing to account for repeated measurements when analyzing RNA-Seq experiments can result in significantly inflated false positive and false discovery rates. Of the methods we investigated, whether they model RNA-Seq counts directly or worked on transformed values, the Bayesian hierarchical model implemented in the mcmseq R package (available at https://github.com/stop-pre16/mcmseq) best combined sensitivity and nominal error rate control.

Background Forensic DNA phenotyping has gained momentum in the recent past due to the prediction of externally visible characters (EVCs) from the biological sample. The most common phenotypes like eye, hair, and skin color are predicted from the biological samples using a web-based system called IrisPlex. Based on six genetic SNPs, the IrisPlex system is developed and validated for its prediction accuracy in diverse ethnic groups worldwide. In previous studies, this system proved to have significant prediction accuracy. The EVCs vary substantially based on different geographical locations. Hence, the objective of this study was to validate the accuracy of the IrisPlex system in predicting the eye colors in the Iraqi population. Methods Six genetic single-nucleotide polymorphisms SNPs (HERC2-rs12913832, OCA2- rs1800407, SLC24A4-rs12896399, SLC45A2- rs16891982, TYR-rs1393350, and IRF4- rs12203592) in 58 Iraqi subjects were performed using Sequenom MassARRAY Genotyping. According to Liu et al., a predicted probability of 0.7 was considered as the threshold. Results Participants in this study of brown color were observed in 44.83%, intermediate in 43.1%, and blue in 12.07%. Completely predictive accuracy is obtained in 1; we observed the AUC at threshold 0.7 was 0.91 for brown, 0.79 for blue, and 0.60 for intermediate eye color. The sensitivity was 42.85% for blue, 0% for intermediate eye color, and 100% for brown-colored eye. Specificity was 100% for blue, 100% for intermediate, and 78.13% for brown eye color. Conclusion Hence, it was concluded that the prediction accuracy of the IrisPlex system for blue and brown color eye in the Iraqi population is significant in the studied population size. However, a pivotal study with larger sample size is required to represent the prediction accuracy of the IrisPlex system in the whole Iraqi population.

Close‐kin mark–recapture (CKMR) is a method for estimating abundance and vital rates from kinship relationships observed in genetic samples. CKMR inference only requires animals to be sampled once (e.g., lethally), potentially widening the scope of population‐level inference relative to traditional monitoring programs.One assumption of CKMR is that, conditional on individual covariates like age, all animals have an equal probability of being sampled. However, if genetic data are collected opportunistically (e.g., via hunters or fishers), there is potential for spatial variation in sampling probability that can bias CKMR estimators, particularly when genetically related individuals stay in close proximity.We used individual‐based simulation to investigate consequences of dispersal limitation and spatially biased sampling on performance of naive (nonspatial) CKMR estimators of abundance, fecundity, and adult survival. Population dynamics approximated that of a long‐lived mammal species subject to lethal sampling.Naive CKMR abundance estimators were relatively unbiased when dispersal was unconstrained (i.e., complete mixing) or when sampling was random or subject to moderate levels of spatial variation. When dispersal was limited, extreme variation in spatial sampling probabilities negatively biased abundance estimates. Reproductive schedules and survival were well estimated, except for survival when adults could emigrate out of the sampled area. Incomplete mixing was readily detected using Kolmogorov–Smirnov tests.Although CKMR appears promising for estimating abundance and vital rates with opportunistically collected genetic data, care is needed when dispersal limitation is coupled with spatially biased sampling. Fortunately, incomplete mixing is easily detected with adequate sample sizes. In principle, it is possible to devise and fit spatially explicit CKMR models to avoid bias under dispersal limitation, but development of such models necessitates additional complexity (and possibly additional data). We suggest using simulation studies to examine potential bias and precision of proposed modeling approaches prior to implementing a CKMR program., We examined the robustness of close‐kin mark–recapture (CKMR) estimators of abundance, survival, and recruitment under dispersal limitation and nonrandom sampling. We found that CKMR provides reasonably unbiased estimates when (a) dispersal is population‐wide or (b) when sampling is close to random. Abundance estimates are negatively biased when sampling is spatially restricted and there is dispersal limitation.

Purpose: This research was conducted at BRI Syariah KCP Muara Bungo, this was done because the researchers wanted to find out the influence of customer preferences using qardh and muarabah products with sharia system variables, products, services, places / locations and promotions to customer preferences at BRI Syariah KCP Muara Bungo.Design/Method/Approach:. This study uses a descriptive analysis approach and quantitative methods with the aim of examining the influence between variables studied through hypothesis testing. This study uses the Slovin formula to obtain sample sizes, for data analysis methods using multiple linear regression equation models. The assistance used is the SPSS statistical data processing program version 21.00. windows.Findings: The results showed that overall (simultaneous) there was a significant influence between variables consisting of sharia system variables, products, services, places / locations and promotions to customer preferences in BRI Syariah Muara Bungo KCP. While the variable that has the most influence is promotion (X5), because it has the highest regression coefficient.Originality/Values: Novelty of the study identified from issue studied constitently, and also place of where the study researched.

We consider longitudinal data and the problem of prediction of subpopulation (domain) characteristics that can be written as a linear combination of the variable of interest, including cases of small or zero sample sizes in the domain and time period of interest. We consider the empirical version of the predictor proposed by Royall (1976) showing that it is a generalization of the empirical version of the predictor presented by Henderson (1950). We propose a parametric bootstrap MSE estimator of the predictor. We prove its asymptotic unbiasedness and derive the order of its bias. Considerations are supported by Monte Carlo simulation analyses to compare its accuracy (not only the bias) with other MSE estimators, including jackknife and weighted jackknife MSE estimators that we adapt for the considered predictor.

We consider mice experiments where tumour cells are injected so that a tumour starts to grow. When the tumour reaches a certain volume, mice are randomized into treatment groups. Tumour volume is measured repeatedly until the mouse dies or is sacrificed. Tumour growth rates are compared between groups. We propose and evaluate linear regression for analysis accounting for the correlation among repeated measurements per mouse. More specifically, we examined five models with three different variance-covariance structures in order to recommend the least complex method for small to moderate sample sizes encountered in animal experiments. We performed a simulation study based on data from three previous experiments to investigate the properties of estimates of the difference between treatment groups. Models were estimated via marginal modelling using generalized least squares and restricted maximum likelihood estimation. A model with an autoregressive (AR-1) covariance structure was efficient and unbiased retaining nominal coverage and type I error when the AR-1 variance-covariance matrix correctly specified the association between repeated measurements. When the variance-covariance was misspecified, that model was still unbiased but the type I error and the coverage rates were affected depending on the degree of misspecification. A linear regression model with an autoregressive (AR-1) covariance structure is an adequate model to analyse experiments that compare tumour growth rates between treatment groups.