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To prevent mistakes in psychological assessment, the precision of test norms is important. This can be achieved by drawing a large normative sample and using regression-based norming. Based on that norming method, a procedure for sample size planning to make inference on Z-scores and percentile rank scores is proposed. Sampling variance formulas for these norm statistics are derived and used to obtain the optimal design, that is, the optimal predictor distribution, for the normative sample, thereby maximizing precision of estimation. This is done under five regression models with a quantitative and a categorical predictor, differing in whether they allow for interaction and nonlinearity. Efficient robust designs are given in case of uncertainty about the regression model. Furthermore, formulas are provided to compute the normative sample size such that individuals' positions relative to the derived norms can be assessed with prespecified power and precision. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

COVID-19 is a worldwide public health threat. Diagnosis by RT-PCR has been employed as the standard method to confirm viral infection. Sample pooling testing can optimize the resources by reducing the workload and reagents shortage, and be useful in laboratories and countries with limited resources. This study aims to evaluate SARS-CoV-2 detection by sample pooling testing in comparison with individual sample testing.We created 210 pools out of 245 samples, varying from 4 to 10 samples per pool, each containing a positive sample. We conducted detection of SARS-CoV-2-specific RdRp/E target sites.Pooling of three samples for SARS-CoV-2 detection might be an efficient strategy to perform without losing RT-PCR sensitivity.Considering the positivity rate in Dominican Republic and that larger sample pools have higher probabilities of obtaining false negative results, the optimal sample size to perform a pooling strategy shall be three samples.La COVID-19 es una amenaza de salud pública mundial. La RT-PCR es el método estándar para confirmar la infección. La estrategia de pruebas de muestras agrupadas puede reducir la carga de trabajo y la escasez de reactivos, y ser útil en países con escasos recursos. Evaluamos la detección del SARS-CoV-2 mediante esta estrategia en comparación con pruebas individuales.Creamos 210 grupos de 245 muestras, de 4 a 10 muestras por grupo, cada uno con una muestra positiva. Realizamos extracción de ARN y qRT-PCR para detectar la presencia de la diana RdRp/E.La combinación de hasta 3 muestras para la detección del SARS-CoV-2 podría ser una estrategia eficaz sin perder la sensibilidad.Considerando la tasa de positividad en República Dominicana y que los grupos con más muestras tienen mayor probabilidad de obtener resultados falsos negativos, el tamaño óptimo para realizar esta estrategia es de 3 muestras.

This paper studies the optimality of matched-pair designs in randomized controlled trials (RCTs). Matched-pair designs are examples of stratified randomization, in which the researcher partitions a set of units into strata based on their observed covariates and assign a fraction of units in each stratum to treatment. A matched-pair design is such a procedure with two units per stratum. Despite the prevalence of stratified randomization in RCTs, implementations differ vastly. We provide an econometric framework in which, among all stratified randomization procedures, the optimal one in terms of the mean-squared error of the difference-in-means estimator is a matched-pair design that orders units according to a scalar function of their covariates and matches adjacent units. Our framework captures a leading motivation for stratifying in the sense that it shows that the proposed matched-pair design additionally minimizes the magnitude of the ex-post bias, i.e., the bias of the estimator conditional on realized treatment status. We then consider empirical counterparts to the optimal stratification using data from pilot experiments and provide two different procedures depending on whether the sample size of the pilot is large or small. For each procedure, we develop methods for testing the null hypothesis that the average treatment effect equals a prespecified value. Each test we provide is asymptotically exact in the sense that the limiting rejection probability under the null equals the nominal level. We run an experiment on the Amazon Mechanical Turk using one of the proposed procedures, replicating one of the treatment arms in Dellavigna and Pope (2018), and find the standard error decreases by 29%, so that only half of the sample size is required to attain the same standard error.

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.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can occur even when the coefficients are sparse and the sample size is large and larger than the number of controls. Therefore, relying on the existing asymptotic inference theory can be problematic in empirical applications. We compare the Lasso-based inference methods to modern high-dimensional OLS-based methods and provide practical guidance., Comment: Final author version, accepted at The Review of Economics and Statistics

Recommender systems personalize content by recommending items to users. Item recommendation algorithms are evaluated by metrics that compare the positions of truly relevant items among the recommended items. To speed up the computation of metrics, recent work often uses sampled metrics where only a smaller set of random items and the relevant items are ranked. This paper investigates such sampled metrics in more detail and shows that they are inconsistent with their exact counterpart, in the sense that they do not persist relative statements, for example, recommender A is better than B , not even in expectation. Moreover, the smaller the sample size, the less difference there is between metrics, and for very small sample size, all metrics collapse to the AUC metric. We show that it is possible to improve the quality of the sampled metrics by applying a correction, obtained by minimizing different criteria. We conclude with an empirical evaluation of the naive sampled metrics and their corrected variants. To summarize, our work suggests that sampling should be avoided for metric calculation, however if an experimental study needs to sample, the proposed corrections can improve the quality of the estimate.

The key statistical properties of the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) estimators were derived in this study for zero mean symmetric error distributions. A density function, named the Approximate Root Normal Distribution (ARND), was developed to approximate the distribution of a square root of a normal random variable. This enabled approximating the distribution of the RMSE estimator. The theoretical derivations and the demonstrations on common distributions, a benchmark time series, and a real world data set (with prediction errors generated from ANN and ARIMA models) lead to the following practically useful findings. When comparing errors having the same distribution type, RMSE was shown to be preferred for platykurtic distributions, MAE for leptokurtic distributions, and either RMSE or MAE for mesokurtic distributions. For different distribution types, however, using the two estimators alone was shown to lead to erroneous conclusions. The revelation that the estimated RMSE/MSE ratio could identify whether the errors came from platykurtic/mesokurtic/leptokurtic distributions was a useful complementary result. Comparison of errors based on, error distributions, sample size and the standard errors of the estimators, was discussed. The proposed procedure for deriving the statistical properties of the two estimators has scope for extension for other distribution types.

Tradeoffs occur when deciding between improving forest inventory precision by increasing sample size or by augmenting cluster plot design factors like size or subplot separation distance. The nature of these tradeoffs changes with variation in type and scale of the spatial pattern of the attribute of interest. To understand the impacts of relationships between type and scale of spatial heterogeneity and cluster plot design efficiency, we constructed a factorial simulation experiment and analysed relationships among forest inventory cost, cluster plot design factors, and different spatial heterogeneity scenarios constructed via simulation. To calculate cost, we constructed a cost model that accounted for both on- and between-plot costs. We found that type and scale of heterogeneity have important implications for plot design choices. Homogeneous stands and landscapes are the least costly to inventory. Subplot area and count have stronger impacts than subplot separation on cost efficiency, particularly in landscapes with aggregated forest patterns and in stands with homogeneous tree patterns. We discuss results in the context of the physical interaction between cluster plot geometry and spatial patterns at different scales, provide computer code for simulations, and suggest principles that forest inventory cluster plot design specialists should consider when designing inventories.

Curbstoning, the willful fabrication of survey responses by outside data collectors, threatens the integrity of the inferences drawn from data. Researchers who outsource data collection to survey collection panels, field interviewers, or research assistants should validate whether each collection agent actually collected the data. Our review of the survey auditing literature demonstrates a consistent presence of curbstoning, even at professional levels. This study proposes several general simple survey questions that have statistical distributions known a priori, as a method to detect curbstoning. By exploiting common deficiencies in statistical understanding, survey collectors imputing data to these questions can leverage empirically known distributions to determine deviation from the expected distribution of responses. We examined both authentic and fabricated surveys that included these questions and we compared the observed distributions with the expected distributions. The majority of the proposed methods had Type I error rates near or below the specified alpha level (.05). The methods demonstrated the ability to detect false responses correctly 48%-90% of the time across two samples when surveying at least 50 participants. While the methods varied in effectiveness, combining these methods demonstrated the highest statistical power, with Type I error rates lower than 1%. Additionally, even in situations with smaller sample sizes (e.g., N = 30), combining these methods allows them to be effective in detecting curbstoning. These methods provide a simple and generalizable way for researchers not present during data collection to possess accurate data. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

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

Aim: Missing data cause problems through decreasing sample size and the potential for introducing bias. We tested four missing data methods on the Sequential Organ Failure Assessment (SOFA) score, an intensive care research severity adjuster. Methods: Simulation study using 2015–2017 electronic health record data, where the complete dataset was sampled, missing SOFA score elements imposed and performance examined of four missing data methods – complete case analysis, median imputation, zero imputation (recommended by SOFA score creators) and multiple imputation (MI) – on the outcome of in-hospital mortality. Results: MI performed well, whereas other methods introduced varying amounts of bias or decreased sample size. Conclusion: We recommend using MI in analyses where SOFA score component values are missing in administrative data research.

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

When designing a clinical trial, one key aspect of the design is the sample size calculation. The sample size calculation tends to rely on a target or expected difference. The expected difference can be based on the observed data from previous studies, which results in bias. It has been reported that large treatment effects observed in trials are often not replicated in subsequent trials. If these values are used to design subsequent studies, the sample sizes may be biased which results in an unethical study. Regression to the mean (RTM) is one explanation for this. If only health technologies which meet a particular continuation criterion (such as p

Phase II clinical trials in oncology are used to initially evaluate the therapeutic efficacy of a new treatment. In the past, the total response was a frequently used endpoint to access the effectiveness of the treatment. When the total response is modest, clinicians may also be interested in disease control (defined as the total response or stable disease) since it may better predict clinical outcomes. Thus, formally testing both the total response and disease control in a phase II trial has an important clinical implication. In this paper, we propose a new method to construct optimal subset designs for one-stage and two-stage phase II clinical trials with two binary endpoints, i.e. the total response and disease control. A new set of hypotheses under the framework of intersection-union tests is provided in which the treatment is considered promising if both the total response and disease control are good. We show that the power function for each test in a large family of tests is nondecreasing in both the total response rate and disease control rate; identify the parameter configurations at which the maximum Type I error rate and minimum power are achieved and derive level- α tests. We also provide optimal one-stage designs with the minimum sample size and optimal two-stage designs with the least expected total sample size.

This study proposes a new acceptance sampling scheme, namely mean ranked sampling scheme, for efficient decision of statistical quality control. The proposed scheme is based on ranked set sampling under exponential distribution for acceptance or rejection of a lot. Two-point method on operating characteristic function is used for the derivation of plan parameters assuming approximation of exponential to normal distribution. The minimum sample sizes and acceptance numbers are obtained satisfying producer’s and consumer’s risk at certain levels of acceptable (AQL) and tolerable quality (RQL). The main advantages of proposed scheme are (i) data is selected by using free cost sampling method from a large lot and (ii) all units of selected lot are used in making decision. The probability & distribution functions for proposed mean ranked set sampling plan are derived. The OC values comparison with simple random sampling is presented. It is shown that the tables presented here can be used if mean life of units are chosen as a criterion.

The cure fraction models are intended to analyze lifetime data from populations where some individuals are immune to the event under study, and allow a joint estimation of the distribution related to the cured and susceptible subjects, as opposed to the usual approach ignoring the cure rate. In situations involving small sample sizes with many censored times, the detection of nonfinite coefficients may arise via maximum likelihood. This phenomenon is commonly known as monotone likelihood (ML), occurring in the Cox and logistic regression models when many categorical and unbalanced covariates are present. An existing solution to prevent the issue is based on the Firth correction, originally developed to reduce the estimation bias. The method ensures finite estimates by penalizing the likelihood function. In the context of mixture cure models, the ML issue is rarely discussed in the literature; therefore, this topic can be seen as the first contribution of our paper. The second major contribution, not well addressed elsewhere, is the study of the ML issue in cure mixture modeling under the flexibility of a semiparametric framework to handle the baseline hazard. We derive the modified score function based on the Firth approach and explore finite sample size properties of the estimators via a Monte Carlo scheme. The simulation results indicate that the performance of coefficients related to the binary covariates are strongly affected to the imbalance degree. A real illustration, in the melanoma dataset, is discussed using a relatively novel data set collected in a Brazilian university hospital.

The goal of this research is to compare multiple linear regression coefficient estimations with multicollinearity. In order to quantify the effectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression method (MRR), and generalized Liu-Kejian method (LKM) are compared (AMSE). For this study, the simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation coefficient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rose, the AMSE decreased. The MRR and LKM both outperformed the LSM. At random error of variance 10, the MRR is the most suitable for all circumstances.

Of 25% of randomised controlled trials (RCTs) on interventions for inflammatory bowel disease (IBD) have no power calculation. To systematically review RCTs reporting interventions for the management of IBD and to produce data for minimum sample sizes that would achieve appropriate power using the actual clinical data. We included RCTs retrieved from Cochrane IBD specialised Trial register and CENTRAL investigating any form of therapy for either induction or maintenance of remission against control, placebo, or no intervention of IBD in patients of any age. The relevant data was extracted, and the studies were grouped according to the intervention used. We recalculated sample size and the achieved difference, as well as minimum sample sizes needed in the future. A total of 105 trials were included. There was a large discrepancy between the estimated figure for the minimal clinically important difference used for the calculations (15% group differences observed 30% used for calculation) explaining substantial actual sample size deficits. The minimum sample sizes indicated for future trials based on the 25 years of trial data were calculated and grouped by the intervention. A third of intervention studies in IBD within the last 25 years are underpowered, with large variations in the calculation of sample sizes. The authors present a sample size estimate resource constructed on the published evidence base for future researchers and key stakeholders within the IBD trial field. [Abstract copyright: ©The Author(s) 2021. Published by Baishideng Publishing Group Inc. All rights reserved.]

Small area estimation (SAE) methods can provide information that conventional direct survey estimation methods cannot. The use of small area estimates based on linear and generalized linear mixed models is still very limited, possibly because of the perceived complexity of estimating the root mean square errors (RMSEs) of the estimates. This paper outlines a study used to determine the conditions under which the estimated RMSEs, produced as part of statistical output (‘plug-in’ estimates of RMSEs) could be considered appropriate for a practical application of SAE methods where one of the main requirements was to use SAS software. We first show that the estimated RMSEs created using an EBLUP model in SAS and those obtained using a parametric bootstrap are similar to the published estimated RMSEs for the corn data in the seminal paper by Battese, Harter and Fuller. We then compare plug-in estimates of RMSEs from SAS procedures used to create EBLUP and EBP estimators against estimates of RMSEs obtained from a parametric bootstrap. For this comparison we created estimates of current smoking in males for 153 local government areas (LGAs) using data from the NSW Population Health Survey in Australia. Demographic variables from the survey data were included as covariates, with LGA-level population proportions, obtained mainly from the Australian Census used for prediction. For the EBLUP, the estimated plug-in estimates of RMSEs can be used, provided the sample size for the small area is more than seven. For the EBP, the plug-in estimates of RMSEs are suitable for all in-sample areas, out-of-sample areas need to use estimated RMSEs that use the parametric bootstrap.

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.

Existing procedures for testing measurement invariance focus mainly on group-level comparisons rather than individual comparisons (i.e., the main conclusion typically concerns the question of comparability of group means). We propose a set of intuitive graphical displays called Person-Level Assessment of Measurement Invariance (PLAMI), which attempt to provide information about the effect of the lack of measurement invariance on the level of person scores. This information complements the group-level information contained in model fit indices and overall effect size indices, and should be especially useful for practitioners using tests for individual diagnostics. PLAMI uses results from the multiple-group factor analysis to estimate and visualize score distortions in terms of expected score difference between members of different groups and the probability of an unacceptably high score difference, conditional for the value of latent trait. The stability of the results can be evaluated by means of resampling. Simulation can be used for an a priori evaluation of the sample size adequacy. We illustrate the proposed plots on two real examples involving testing measurement invariance of the Machiavellianism scale, and we demonstrate the added value of PLAMI compared to the use of fit indices alone.

Modeling the relationship between some climatic determinants in the wet or cropping season of Makurdi, Benue State, Nigeria requires data aggregation. The consequence of this aggregation is the reduction in data sample size. This poses serious challenge of lack of model-fit when the Classical Linear Regression Modeling Approach is employed. The Bayesian Normal Regression Modeling Approach was therefore employed in surmounting this problem. Three Bayesian Normal Regression Models were fitted namely; the Solar radiation, Total Rainfall Amount and the Number of Dry Days model. Each model result was compared with that of its Classical model counterpart. The discrepancies observed were blamed on the sample size reduction. The results of the Bayesian models revealed that; Solar radiation increases by 0.791 MJ/m2 for each unit increase in the natural logarithm of Relative humidity. While it increases by 0.895 MJ/m2 for each unit increase in the natural logarithm of Wind speed. Total Rainfall Amount increases by 66.280 mm for each unit increase in the natural logarithm of the Number of Dry Days while it increases by 2.912 mm for each unit increase in the natural logarithm of the Number of Wet Days. Furthermore, the Number of Dry Days decreases by 6.905 days for each unit increase in the natural logarithm of Number of Wet days, while it increases by 2.028 days for each unit increase in the natural logarithm of Total Rainfall Amount. The study affirmed that the cropping season climate of Makurdi is becoming

Objective:The fragility index is a clinically interpretable metric increasingly used to interpret the robustness of clinical trials results that is generally not incorporated in sample size calculation and applied post-hoc. In this manuscript, we propose to base the sample size calculation on the fragility index in a way that supplements the classical prefixed alpha and power cutoffs and we provide a dedicated R software package for the design and analysis tools. Study design and setting:This approach follows from a novel hypothesis testing framework that is based on the fragility index and builds on the classical testing approach. As case studies, we re-analyse the design of two important trials in cardiovascular medicine, the FAME and FAMOUS-NSTEMI trials. Results:The analyses show that approach returns sample sizes which results in a higher power for the P value based test and most importantly a lower and context dependent Type I error rate for the fragility index based test compared to standard tests. Conclusion:Our method allows clinicians to control for the fragility index during clinical trial design.

In planning randomized clinical trials (RCTs) for diseases such as Alzheimer's disease (AD), researchers frequently rely on the use of existing data obtained from only two time points to estimate sample size via the subtraction of baseline from follow-up measurements in each subject. However, the inadequacy of this method has not been reported. The aim of this study is to discuss the limitation of sample size estimation based on the subtraction of available data from only two time points for RCTs. Mathematical equations are derived to demonstrate the condition under which the obtained data pairs with variable time intervals could be used to adequately estimate sample size. The MRI-based hippocampal volume measurements from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Monte Carlo simulations (MCS) were used to illustrate the existing bias and variability of estimates. MCS results support the theoretically derived condition under which the subtraction approach may work. MCS also show the systematically under- or over-estimated sample sizes by up to 32.27 % bias. Not used properly, such subtraction approach outputs the same sample size regardless of trial durations partly due to the way measurement errors are handled. Estimating sample size by subtracting two measurements should be treated with caution. Such estimates can be biased, the magnitude of which depends on the planned RCT duration. To estimate sample sizes, we recommend using more than two measurements and more comprehensive approaches such as linear mixed effect models.

Each cluster consists of multiple subunits from which outcome data are collected. In a subunit randomization trial, subunits are randomized into different intervention arms. Observations from subunits within each cluster tend to be positively correlated due to the shared common frailties, so that the outcome data from a subunit randomization trial have dependency between arms as well as within each arm. For subunit randomization trials with a survival endpoint, few methods have been proposed for sample size calculation showing the clear relationship between the joint survival distribution between subunits and the sample size, especially when the number of subunits from each cluster is variable. In this paper, we propose a closed form sample size formula for weighted rank test to compare the marginal survival distributions between intervention arms under subunit randomization, possibly with variable number of subunits among clusters. We conduct extensive simulations to evaluate the performance of our formula under various design settings, and demonstrate our sample size calculation method with some real clinical trials.

Introduction Magnitudes of change in endothelial function research can be articulated using effect size statistics. Effect sizes are commonly used in reference to Cohen’s seminal guidelines of small (d = 0.2), medium (d = 0.5), and large (d = 0.8). Quantitative analyses of effect size distributions across various research disciplines have revealed values differing from Cohen’s original recommendations. Here we examine effect size distributions in human endothelial function research, and the magnitude of small, medium, and large effects for macro and microvascular endothelial function. Methods Effect sizes reported as standardized mean differences were extracted from meta research available for endothelial function. A frequency distribution was constructed to sort effect sizes. The 25th, 50th, and 75th percentiles were used to derive small, medium, and large effects. Group sample sizes and publication year from primary studies were also extracted to observe any potential trends, related to these factors, in effect size reporting in endothelial function research. Results Seven hundred fifty-two effect sizes were extracted from eligible meta-analyses. We determined small (d = 0.28), medium (d = 0.69), and large (d = 1.21) effects for endothelial function that corresponded to the 25th, 50th, and 75th percentile of the data distribution. Conclusion Our data indicate that direct application of Cohen’s guidelines would underestimate the magnitude of effects in human endothelial function research. This investigation facilitates future a priori power analyses, provides a practical guiding benchmark for the contextualization of an effect when no other information is available, and further encourages the reporting of effect sizes in endothelial function research.

Background The size of the margin strongly influences the required sample size in non-inferiority and equivalence trials. What is sometimes ignored, however, is that for trials with binary outcomes, the scale of the margin – risk difference, risk ratio or odds ratio – also has a large impact on power and thus on sample size requirement. When considering several scales at the design stage of a trial, these sample size consequences should be taken into account. Sometimes, changing the scale may be needed at a later stage of a trial, for example, when the event proportion in the control arm turns out different from expected. Also after completion of a trial, a switch to another scale is sometimes made, for example, when using a regression model in a secondary analysis or when combining study results in a meta-analysis that requires unifying scales. The exact consequences of such switches are currently unknown. Methods and Results This article first outlines sample size consequences for different choices of analysis scale at the design stage of a trial. We add a new result on sample size requirement comparing the risk difference scale with the risk ratio scale. Then, we study two different approaches to changing the analysis scale after the trial has commenced: (1) mapping the original non-inferiority margin using the event proportion in the control arm that was anticipated at the design stage or (2) mapping the original non-inferiority margin using the observed event proportion in the control arm. We use simulations to illustrate consequences on type I and type II error rates. Methods are illustrated on the INES trial, a non-inferiority trial that compared single birth rates in subfertile couples after different fertility treatments. Our results demonstrate large differences in required sample size when choosing between risk difference, risk ratio and odds ratio scales at the design stage of non-inferiority trials. In some cases, the sample size requirement is twice as large on one scale compared with another. Changing the scale after commencing the trial using anticipated proportions mainly impacts type II error rate, whereas switching using observed proportions is not advised due to not maintaining type I error rate. Differences were more pronounced with larger margins. Conclusions Trialists should be aware that the analysis scale can have large impact on type I and type II error rates in non-inferiority trials.

One of the key aspects of designing a clinical trial is sample size estimation. While the statistical power improves with the increased sample size, one has to be considerate about the ethical, sci...

We consider the General Linear Model (GLM) which includes multivariate analysis of variance (MANOVA) and multiple linear regression as special cases. In practice, there are several widely used criteria for GLM: Wilks’ lambda, Bartlett–Nanda–Pillai test, Lawley–Hotelling test, and Roy maximum root test. Limiting distributions for the first three mentioned tests are known under different asymptotic settings. In the present paper, we obtain computable error bounds for the normal approximation of the Lawley–Hotelling statistic when the dimension grows proportionally to the sample size. This result enables us to get more precise calculations of the p-values in applications of multivariate analysis. In practice, more and more often analysts encounter situations where the number of factors is large and comparable with the sample size. Examples include medicine, biology (i.e., DNA microarray studies), and finance.

Spatial effects are often simultaneously investigated with non-linear effects of continuous covariates and the usual linear effect. In this work the performance of models with and without spatial dependence in partitioned (PM) and non-partitioned models (NPM) for four (4) censoring percentages, three(3) levels of Weibull baseline variances (WBV), and sample sizes 100, 500 & 1000 were investigated. Hazard models were adapted to the generalized additive predictors and analyses were carried out via MCMC simulation technique. The performances of the models were again assessed when fitted to the diabetic data set. Results suggest that; partition models outperformed the non-partition ones. Models with spatial dependence perform better than models without spatial dependence in denser event times and when WBVs are low. The partition models perform better with spatial dependence than the Non-partitioned models. For the diabetic data set, it is seen that covariates Age and Blood Sugar level (BSL) violates the proportionality assumptions upon test. Further assessment from the graph of coefficient against time; suggest that Age be put to cut-points while BSL was estimated for models with and without Penalized splines for the sake of comparison, since the graph shows just a slight deviation from proportionality. Hazard rates for the time varying Age; indicate that as the time of study rolls by, the hazard of experiencing the event death from the disease increases steadily between intervals but constant within each time interval. A unit change in hazard rate for BSL indicates a decrease for PM implemented for with and without penalized splines. The model without penalized splines was however, seen to be better with smaller DIC (Deviance Information Criteria) value. Marriage is seen to be significant in the management of the disease in comparison to single patients. In addition patients are advised to visit their physicians on a regular basis to run a routine check to keep their BSL in good range. The study provides a means of moving out of non-linear ruts in survival data analysis. Intervals increase sample sizes (pseudoobservations), which in turn improves the modified Partitioned model when they are with or without spatial dependence.

Author(s): Zheng, Bang Quan | Advisor(s): Bentler, Peter M | Abstract: Does Reweighted Least Squares (RLS) perform better in small samples than maximum likelihood (ML) for mean and covariance structure? ML statistics in covariance structure analysis are based on the asymptotic normality assumption; however, actual applications of structural equation modeling (SEM) in social and behavioral science research usually involve small samples. It has been found that chi-square tests often incorrectly over-reject the null hypothesis: Σ=Σ(θ), because when sample is small the sample covariance matrix becomes ill-conditioned and entails unstable estimates. In certain SEM models, the vector of parameter must contain both means, variances and covariances. Yet, whether RLS also works in mean and covariance structure remains unexamined. This research is an extended examination of reweighted least squares in mean and covariance structure. Specifically, we replace biased covariance matrix in traditional GLS function (Browne, 1974) with the unbiased sample covariance matrix that derives from ML estimation. Moreover, under the assumption of multivariate normality, a Monte Carlo simulation study was carried out to examine the statistical performance as compared with ML methods in different sample sizes. Based on empirical rejection frequencies and empirical averages of test statistic, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small.

PurposeAs an alternative to the standard p and np charts along with their various modifications, beta control charts are used in the literature for monitoring proportion data. These charts in general use average of proportions to set up the control limits assuming in-control parameters known. The purpose of the paper is to propose a control chart for detecting shift(s) in the percentiles of a beta distributed process monitoring scheme when in-control parameters are unknown. Such situations arise when specific percentile of proportion of conforming or non-conforming units is the quality parameter of interest.Design/methodology/approachParametric bootstrap method is used to develop the control chart for monitoring percentiles of a beta distributed process when in-control parameters are unknown. Extensive Monte Carlo simulations are conducted for various combinations of percentiles, false-alarm rates and sample sizes to evaluate the in-control performance of the proposed bootstrap control charts in terms of average run lengths (ARL). The out-of-control behavior and performance of the proposed bootstrap percentile chart is thoroughly investigated for several choices of shifts in the parameters of beta distribution. The proposed chart is finally applied to two skewed data sets for illustration.FindingsThe simulated values of in-control ARL are found to be closer to the theoretical results implying that the proposed chart for percentiles performs well with both positively and negatively skewed data. Also, the out-of-control ARL values for the percentiles decrease sharply with both downward and upward small, medium and large shifts in the parameters. The phenomenon indicates that the chart is effective in detecting shifts in the parameters. However, the speed of detection of shifts varies depending on the type of shift, the parameters and the percentile being considered. The proposed chart is found to be effective in comparison to the Shewhart-type chart and bootstrap-based unit gamma chart.Originality/valueIt is worthwhile to mention that the beta control charts proposed in the literature use average of proportion to set up the control limits. However, in practice, specific percentile of proportion of conforming or non-conforming items should be more useful as the quality parameter of interest than average. To the best of our knowledge, no research addresses beta control chart for percentiles of proportion in the literature. Moreover, the proposed control chart assumes in-control parameters to be unknown, and hence captures additional variability introduced into the monitoring scheme through parameter estimation. In this sense, the proposed chart is original and unique.

Whereas the theory of confirmatory adaptive designs is well understood for uncensored data, implementation of adaptive designs in the context of survival trials remains challenging. Commonly used adaptive survival tests are based on the independent increments structure of the log-rank statistic. This implies some relevant limitations: On the one hand, essentially only the interim log-rank statistic may be used for design modifications (such as data-dependent sample size recalculation). Furthermore, the treatment arm allocation ratio in these classical methods is assumed to be constant throughout the trial period. Here, we propose an extension of the independent increments approach to adaptive survival tests that addresses some of these limitations. We present a confirmatory adaptive two-sample log-rank test that allows rejection regions and sample size recalculation rules to be based not only on the interim log-rank statistic, but also on point-wise survival rate estimates, simultaneously. In addition, the possibility is opened to adapt the treatment arm allocation ratio after each interim analysis in a data-dependent way. The ability to include point-wise survival rate estimators in the rejection region of a test for comparing survival curves might be attractive, e.g., for seamless phase II/III designs. Data-dependent adaptation of the allocation ratio could be helpful in multi-arm trials in order to successively steer recruitment into the study arms with the greatest chances of success. The methodology is motivated by the LOGGIC Europe Trial from pediatric oncology. Distributional properties are derived using martingale techniques in the large sample limit. Small sample properties are studied by simulation.

We consider a random censoring model for survival analysis, allowing the possibility that only a proportion of individuals in the population are susceptible to death or failure, and the remainder are immune or cured. Susceptibles suffer the event under study eventually, but the time at which this occurs may not be observed due to censoring. Immune individuals have infinite lifetimes which are always censored in the sample. Assuming that the distribution of the susceptibles’ lifetimes as well as the censoring distribution have infinite right endpoints and are in the domain of attraction of the Gumbel distribution, we obtain asymptotic distributions, as sample size tends to infinity, of statistics relevant to testing for the possible existence of immunes in the population.

The extrapolation of quantiles beyond or below the largest or smallest observation plays an important role in hydrological practice, design of hydraulic structures, water resources management, or risk assessment. Traditionally, extreme quantiles are obtained using parametric methods that require to make an a priori assumption about the distribution that generated the data. This approach has several limitations mainly when applied to the tails of the distribution. Semiparametric or nonparametric methods, on the other hand, allow more flexibility and they may overcome the problems of the parametric approach. Therefore, we present here a comparison between three selected semi/nonparametric methods, namely the methods of Hutson (Stat and Comput, 12(4):331–338, 2002) and Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) and kernel density estimation. While the first and third methods have already applications in hydrology, Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) is proposed in this context for the first time. After describing the methods and their applications in hydrology, we compare their performance for different sample lengths and return periods. We use synthetic samples extracted from four distributions whose maxima belong to the Gumbel, Weibull, and Fréchet domain of attraction. Then, the same methods are applied to a real precipitation dataset and compared with a parametric approach. Eventually, a detailed discussion of the results is presented to guide researchers in the choice of the most suitable method. None of the three methods, in fact, outperforms the others; performances, instead, vary greatly with distribution type, return period, and sample size.

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.

Seemingly unrelated mixed-effects models were used to model biomass models for Larix olgensis, Pinus koraiensis, and Pinus sylvestris, and the developed models considered multiple variables to enhance the practicality of the models. Korean larch (Larix olgensis), Korean pine (Pinus koraiensis), and Mongolian pine (Pinus sylvestris) are important coniferous species in the northeastern area of the P.R. China; hence, accurate biomass estimates of these species are meaningful for evaluating forest health and calculating carbon storage. Based on the tree variables of diameter at breast height ( $$DBH$$ ), tree height ( $$H$$ ), age, live crown length and crown width, three log-transformed species-specific biomass functions were developed using linear seemingly unrelated regression (SUR) since the error structures of the component biomass model (stem, branches, foliage and roots) were proven to be multiplicative. Furthermore, the plot-level random effect was introduced into the SUR model, namely the SURM model, to achieve more accurate biomass estimates. The results showed that the SURM model has a better fitting performance than the SUR models for three species and model types. The determination coefficient, $${R}^{2}$$ , was always larger for the SURM models than for the corresponding SUR models, while the root mean square error, $${\text{RMSE}}$$ , was always smaller for the SURM models. By leave-one-out validation, the SURM models were proven to provide more accurate predictions because the mean prediction percent error ( $${\text{MPE}}$$ ) was close to 0 and the mean absolute percentage error ( $${\text{MAPE}}$$ ) was smaller than that of the corresponding SUR models across species and model types. In addition, the size and design of the sample used to calibrate for random effects were assessed using the $${\text{MAPE}}$$ statistical index, $${\text{MAPE}}$$ . The calibration of the SURM showed a decreasing pattern of bias as the sample size increased, indicating that more available sampled trees improved the prediction accuracy of SURM models, while only slight differences existed across sampling designs. Overall, the newly developed biomass models have advantages in various data structures, and will be meaningful and useful in terms of accurately predicting the biomass of three important species in Northeast China.

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.