Sample size re-estimation without un-blinding for time-to-event outcomes in oncology clinical trials

Sample size re-estimation is essential in oncology studies. However, the use of blinded sample size reassessment for survival data has been rarely reported. Based on the density function of the exponential distribution, an expectation-maximization（EM） algorithm of the hazard ratio was derived, and several simulation studies were used to verify its applications. The method had obvious variation in the hazard ratio estimates and overestimation for the relatively small hazard ratios. Our studies showed that the stability of the EM estimation results directly correlated with the sample size, the convergence of the EM algorithm was impacted by the initial values, and a balanced design produced the best estimates. No reliable blinded sample size re-estimation inference can be made in our studies, but the results provide useful information to steer the practitioners in this field from repeating the same endeavor.

Research on aiming methods for small sample size shooting tests of two-dimensional trajectory correction fuse

The longitudinal dispersion of the projectile in shooting tests of two-dimensional trajectory corrections fused with fixed canards is extremely large that it sometimes exceeds the correction ability of the correction fuse actuator.The impact point easily deviates from the target,and thus the correction result cannot be readily evaluated.However,the cost of shooting tests is considerably high to conduct many tests for data collection.To address this issue,this study proposes an aiming method for shooting tests based on small sample size.The proposed method uses the Bootstrap method to expand the test data;repeatedly iterates and corrects the position of the simulated theoretical impact points through an improved compatibility test method;and dynamically adjusts the weight of the prior distribution of simulation results based on Kullback-Leibler divergence,which to some extent avoids the real data being"submerged"by the simulation data and achieves the fusion Bayesian estimation of the dispersion center.The experimental results show that when the simulation accuracy is sufficiently high,the proposed method yields a smaller mean-square deviation in estimating the dispersion center and higher shooting accuracy than those of the three comparison methods,which is more conducive to reflecting the effect of the control algorithm and facilitating test personnel to iterate their proposed structures and algorithms.;in addition,this study provides a knowledge base for further comprehensive studies in the future.

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.

Utility of Adaptive Sample Size Designs and A Review Example

Sample size can be a key design feature that not only affects the probability of a trial＇s success but also determines the duration and feasibility of a trial. If an investigational drug is expected to be effective and address unmet medical needs of an orphan disease, where the accrual period may require many years with a large sample size to detect a minimal clinically relevant treatment effect, a minimum sample size may be set to maintain nominal power. In limited situations such as this, there may be a need for flexibility in the initial and final sample sizes; thus, it is useful to consider the utility of adaptive sample size designs that use sample size re-estimation or group sequential design. In this paper, we propose a new adaptive performance measure to consider the utility of an adaptive sample size design in a trial simulation. Considering that previously proposed sample size re-estimation methods do not take into account errors in estimation based on interim results, we propose Bayesian sample size re-estimation criteria that take into account prior information on treatment effect, and then, we assess its operating characteristics in a simulation study. We also present a review example of sample size re-estimation mainly based on published paper and review report in Pharmaceuticals and Medical Devices Agency （PMDA）.

Spatial Interpolation and Sample Size Optimization for Soil Copper(Cu) Investigation in Cropland Soil at County Scale Using Cokriging

Knowledge on spatial distribution and sampling size optimization of soil copper （Cu） could lay solid foundations for environmetal quality survey of agricultural soils at county scale. In this investigation, cokriging method was used to conduct the interpolation of Cu concentraiton in cropland soil in Shuangliu County, Sichuan Province, China. Based on the original 623 physicochmically measured soil samples, 560, 498, and 432 sub-samples were randomly selected as target variable and soil organic matter （SOM） of the whole original samples as auxiliary variable. Interpolation results using Cokriging under different sampling numbers were evaluated for their applicability in estimating the spatial distribution of soil Cu at county sacle. The results showed that the root mean square error （RMSE） produced by Cokriging decreased from 0.9 to 7.77%, correlation coefficient between the predicted values and the measured increased from 1.76 to 9.76% in comparison with the ordinary Kriging under the corresponding sample sizes. The prediction accuracy using Cokriging was still higher than original 623 data using ordinary Kriging even as sample size reduced 10%, and their interpolation maps were highly in agreement. Therefore, Cokriging was proven to be a more accurate and economic method which could provide more information and benefit for the studies on spatial distribution of soil pollutants at county scale.

Strategies on Sample Size Determination and Qualitative and Quantitative Traits Integration to Construct Core Collection of Rice (Oryza sativa)

The development of a core collection could enhance the utilization of germplasm collections in crop improvement programs and simplify their management. Selection of an appropriate sampling strategy is an important prerequisite to construct a core collection with appropriate size in order to adequately represent the genetic spectrum and maximally capture the genetic diversity in available crop collections. The present study was initiated to construct nested core collections to determine the appropriate sample size to represent the genetic diversity of rice landrace collection based on 15 quantitative traits and 34 qualitative traits of 2 262 rice accessions. The results showed that 50-225 nested core collections, whose sampling rate was 2.2%-9.9%, were sufficient to maintain the maximum genetic diversity of the initial collections. Of these, 150 accessions （6.6%） could capture the maximal genetic diversity of the initial collection. Three data types, i.e. qualitative traits （QT1）, quantitative traits （QT2） and integrated qualitative and quantitative traits （QTT）, were compared for their efficiency in constructing core collections based on the weighted pair-group average method combined with stepwise clustering and preferred sampling on adjusted Euclidean distances. Every combining scheme constructed eight rice core collections （225, 200, 175, 150, 125, 100, 75 and 50）. The results showed that the QTT data was the best in constructing a core collection as indicated by the genetic diversity of core collections. A core collection constructed only on the information of QT1 could not represent the initial collection effectively. QTT should be used together to construct a productive core collection.

Sample size effect on the dynamic torsional behaviour of the 2A12 aluminium alloy

In order to investigate the effect of sample size on the dynamic torsional behaviour of the 2A12 aluminium alloy. In this paper, torsional split Hopkinson bar tests are conducted on this alloy with different sample dimensions. It is found that with the decreasing gauge length and thickness, the tested yield strength increases. However, the sample innerlouter diameter has little effect on the dynamic torsional behaviour. Based on the finite element method, the stress states in the alloy with different sample sizes are analysed. Due to the effect of stress concentration zone （SCZ）, the shorter sample has a higher yield stress. Furthermore, the stress distributes more uniformly in the thinner sample, which leads to the higher tested yield stress. According to the experimental and simulation analysis, some suggestions on choosing the sample size are given as well.

Reliability Assessment for the Solenoid Valve of a High-Speed Train Braking System under Small Sample Size

Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data,which lead to large deviation under conditions of small sample size and zero?failure data. To improve this problem,a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high?speed train,the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time,a concave method is employed to obtain the relationships between accumulation failure prob?abilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation,and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally,the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system,which shows that the change in the reliability and failure rate among the di erent hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi?tions of small sample size and zero?failure data.

Metal Corrosion Rate Prediction of Small Samples Using an Ensemble Technique

Accurate prediction of the internal corrosion rates of oil and gas pipelines could be an effective way to prevent pipeline leaks.In this study,a proposed framework for predicting corrosion rates under a small sample of metal corrosion data in the laboratory was developed to provide a new perspective on how to solve the problem of pipeline corrosion under the condition of insufficient real samples.This approach employed the bagging algorithm to construct a strong learner by integrating several KNN learners.A total of 99 data were collected and split into training and test set with a 9:1 ratio.The training set was used to obtain the best hyperparameters by 10-fold cross-validation and grid search,and the test set was used to determine the performance of the model.The results showed that theMean Absolute Error(MAE)of this framework is 28.06%of the traditional model and outperforms other ensemblemethods.Therefore,the proposed framework is suitable formetal corrosion prediction under small sample conditions.

Empirical Determination of the Tolerable Sample Size for Ols Estimator in the Presence of Multicollinearity (<i>ρ</i>)

This paper investigates the tolerable sample size needed for Ordinary Least Square (OLS) Estimator to be used when there is presence of Multicollinearity among the exogenous variables of a linear regression model. A regression model with constant term (β0) and two independent variables (with β1 and β2 as their respective regression coefficients) that exhibit multicollinearity was considered. A Monte Carlo study of 1000 trials was conducted at eight levels of multicollinearity (0, 0.25, 0.5, 0.7, 0.75, 0.8, 0.9 and 0.99) and sample sizes (10, 20, 40, 80, 100, 150, 250 and 500). At each specification, the true regression coefficients were set at unity while 1.5, 2.0 and 2.5 were taken as the hypothesized value. The power value rate was obtained at every multicollinearity level for the aforementioned sample sizes. Therefore, whether the hypothesized values highly depart from the true values or not once the multicollinearity level is very high (i.e. 0.99), the sample size needed to work with in order to have an error free estimation or the inference result must be greater than five hundred.

Impacts of sample size for stomach content analysis on the estimation of ecosystem indices

This study used Ecopath model of the Jiaozhou Bay as an example to evaluate the effect of stomach sample size of three fish species on the projection of this model. The derived ecosystem indices were classified into three categories:(1) direct indices, like the trophic level of species, influenced by stomach sample size directly;(2)indirect indices, like ecology efficiency(EE) of invertebrates, influenced by the multiple prey-predator relationships;and(3) systemic indices, like total system throughout(TST), describing the status of the whole ecosystem. The influences of different stomach sample sizes on these indices were evaluated. The results suggest that systemic indices of the ecosystem model were robust to stomach sample sizes, whereas specific indices related to species were indicated to be with low accuracy and precision when stomach samples were insufficient.The indices became more uncertain when the stomach sample sizes varied for more species. This study enhances the understanding of how the quality of diet composition data influences ecosystem modeling outputs. The results can also guide the design of stomach content analysis for developing ecosystem models.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

Power Analysis and Sample Size Determination for Crossover Trials with Application to Bioequivalence Assessment of Topical Ophthalmic Drugs Using Serial Sampling Pharmacokinetic Data

Objective To develop methods for determining a suitable sample size for bioequivalence assessment of generic topical ophthalmic drugs using crossover design with serial sampling schemes.Methods The power functions of the Fieller-type confidence interval and the asymptotic confidence interval in crossover designs with serial-sampling data are here derived.Simulation studies were conducted to evaluate the derived power functions.Results Simulation studies show that two power functions can provide precise power estimates when normality assumptions are satisfied and yield conservative estimates of power in cases when data are log-normally distributed.The intra-correlation showed a positive correlation with the power of the bioequivalence test.When the expected ratio of the AUCs was less than or equal to 1, the power of the Fieller-type confidence interval was larger than the asymptotic confidence interval.If the expected ratio of the AUCs was larger than 1, the asymptotic confidence interval had greater power.Sample size can be calculated through numerical iteration with the derived power functions.Conclusion The Fieller-type power function and the asymptotic power function can be used to determine sample sizes of crossover trials for bioequivalence assessment of topical ophthalmic drugs.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

A STATISTICAL INVESTIGATION OF FATIGUE CRACK INITIATION AND GROWTH PROCESS BASED UPON A LARGE SAMPLE SIZE EXPERIMENT

After finishing 102 replicate constant amplitude crack initiation and growth tests on Ly12-CZ aluminum alloy plate, a statistical investigation of the fatigue crack initiation and growth process is conducted in this paper. According to the post-mortem fractographic examination by scanning electron microscopy (SEM), some qualitative observations of the spacial correlation among fatigue striations are developed to reveal the statistical nature of material intrinsic inhomogeneity during the crack growth process. From the test data, an engineering division between crack initiation and growth is defined as the upper limit of small crack. The distributions of crack initiation life N-i, growth life N, and the statistical characteristics of crack growth rate da/dN are also investigated. It is hoped that the work will provide a solid test basis for the study of probabilistic fatigue, probabilistic fracture mechanics, fatigue reliability and its engineering applications.

A Proposed Method for Choice of Sample Size without Pre-Defining Error

Sample size is very important in statistical research because it is not too small or too large. Given significant level α, the sample size is calculated based on the z-value and pre-defined error. Such error is defined based on the previous experiment or other study or it can be determined subjectively by specialist, which may cause incorrect estimation. Therefore, this research proposes an objective method to estimate the sample size without pre-defining the error. Given an available sample X = {X1, X2, ..., Xn}, the error is calculated via the iterative process in which sample X is re-sampled many times. Moreover, after the sample size is estimated completely, it can be used to collect a new sample in order to estimate new sample size and so on.

Sample sizes based on three popular indices of risks

Sample size justification is a very crucial part in the design of clinical trials. In this paper, the authors derive a new formula to calculate the sample size for a binary outcome given one of the three popular indices of risk difference.The sample size based on the absolute difference is the fundamental one, which can be easily used to derive sample size given the risk ratio or OR.

Simulation Program to Determine Sample Size and Power for a Multiple Logistic Regression Model with Unspecified Covariate Distributions

Binary logistic regression models are commonly used to assess the association between outcomes and covariates. Many covariates are inherently continuous, and have a variety of distributions, including those that are heavily skewed to the left or right. Existing theoretical formulas, criteria, and simulation programs cannot accurately estimate the sample size and power of non-standard distributions. Therefore, we have developed a simulation program that uses Monte Carlo methods to estimate the exact power of a binary logistic regression model. This power calculation can be used for distributions of any shape and covariates of any type (continuous, ordinal, and nominal), and can account for nonlinear relationships between covariates and outcomes. For illustrative purposes, this simulation program is applied to real data obtained from a study on the influence of smoking on 90-day outcomes after acute atherothrombotic stroke. Our program is applicable to all effect sizes and makes it possible to apply various statistical methods, logistic regression and related simulations such as Bayesian inference with some modifications.

Sample Size Determination and Statistical Hypothesis Testing for Core Centration in Press Coated Tablets

A novel statistical approach to evaluate the manufacturing quality of press coated tablets in terms of the centering of their core is presented. We also provide a formula to determine the necessary sample size. This approach is applied to real data.

Size and Shape of Sample Units in Native Forests and Plantations

The size and form of sampling units-SU have always been variables considered in planning and structuring forest inventories, being performed in forests or in plantations. The experimental work outlined to deal with the problem was conducted in an area of araucaria forest, in Sao Joao de Triunfo, PR, Brazil. The forms of sampling units circle, square and rectangular were evaluated, whose areas ranged from 200 m2 to 1000 m2. Time was recorded using a stopwatch and computed separately for locomotion and measurement. The power model was used to adjust the relations of the times of locomotion and measurement, as well as a hyperbolic one for the coefficient of variation, all taking as function of the SUs sizes. To achieve the analytical solution for the optimum size of the SU, it was necessary simulating the behavior of the three functions until the size of 10,000 m2. By taking the derivative of the combined function it was found the maximum point, which allowed optimizing the size of the SU in 600 m2 for the structured experimental conditions. This result proved the formulated hypothesis, performing even a critical analysis of the inclusion of other relevant variables, such as size of the area to be inventoried, number of SUs performed in one day of work, average distance between the SUs, average speeds for locomotion between SUs and for taking all respective measurements.