Use of sample size calculation in scientific research in Brazilian Physical Education journals

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Joint economic design of X̄ and R control charts for processes subject to two independent assignable causes

A model for the joint economic design of X̄ and R control charts is developed. This model assumes that the process is subject to two assignable causes. One assignable cause shifts the process mean; the other shifts the process variance. The occurrence of the assignable cause of one kind does not block the occurrence of the assignable cause of another kind. Consequently, a second process parameter can go out-of-control after the first process parameter has gone out-of-control. A numerical study of the cost surface to the model considered has revealed that it is convex, at least in the interest region.

The Endothelial Sample Size Analysis in Corneal Specular Microscopy Clinical Examinations

Purpose: To evaluate endothelial cell sample size and statistical error in corneal specular microscopy (CSM) examinations. Methods: One hundred twenty examinations were conducted with 4 types of corneal specular microscopes: 30 with each BioOptics, CSO, Konan, and Topcon corneal specular microscopes. All endothelial image data were analyzed by respective instrument software and also by the Cells Analyzer software with a method developed in our lab(US Patent). A reliability degree (RD) of 95% and a relative error (RE) of 0.05 were used as cut-off values to analyze images of the counted endothelial cells called samples. The sample size mean was the number of cells evaluated on the images obtained with each device. Only examinations with RE<0.05 were considered statistically correct and suitable for comparisons with future examinations. The Cells Analyzer software was used to calculate the RE and customized sample size for all examinations. Results: Bio-Optics: sample size, 97 +/- 22 cells; RE, 6.52 +/- 0.86; only 10% of the examinations had sufficient endothelial cell quantity (RE<0.05); customized sample size, 162 +/- 34 cells. CSO: sample size, 110 +/- 20 cells; RE, 5.98 +/- 0.98; only 16.6% of the examinations had sufficient endothelial cell quantity (RE<0.05); customized sample size, 157 +/- 45 cells. Konan: sample size, 80 +/- 27 cells; RE, 10.6 +/- 3.67; none of the examinations had sufficient endothelial cell quantity (RE>0.05); customized sample size, 336 +/- 131 cells. Topcon: sample size, 87 +/- 17 cells; RE, 10.1 +/- 2.52; none of the examinations had sufficient endothelial cell quantity (RE>0.05); customized sample size, 382 +/- 159 cells. Conclusions: A very high number of CSM examinations had sample errors based on Cells Analyzer software. The endothelial sample size (examinations) needs to include more cells to be reliable and reproducible. The Cells Analyzer tutorial routine will be useful for CSM examination reliability and reproducibility.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Sample size estimation: an overview with applications to orthodontic clinical trial designs

Proper sample size estimation is an important part of clinical trial methodology and closely related to the precision and power of the trial's results. Trials with sufficient sample sizes are scientifically and ethically justified and more credible compared with trials with insufficient sizes. Planning clinical trials with inadequate sample sizes might be considered as a waste of time and resources, as well as unethical, since patients might be enrolled in a study in which the expected results will not be trusted and are unlikely to have an impact on clinical practice. Because of the low emphasis of sample size calculation in clinical trials in orthodontics, it is the objective of this article to introduce the orthodontic clinician to the importance and the general principles of sample size calculations for randomized controlled trials to serve as guidance for study designs and as a tool for quality assessment when reviewing published clinical trials in our specialty. Examples of calculations are shown for 2-arm parallel trials applicable to orthodontics. The working examples are analyzed, and the implications of design or inherent complexities in each category are discussed.

COMPUTATIONAL ANALYSIS OF THE AEROELASTIC DYNAMICS OF A WIND TURBINE BLADE WITH VARIABLE-SPEED STALL CONTROL

The accuracy of simulating the aerodynamics and structural properties of the blades is crucial in the wind-turbine technology. Hence the models used to implement these features need to be very precise and their level of detailing needs to be high. With the variety of blade designs being developed the models should be versatile enough to adapt to the changes required by every design. We are going to implement a combination of numerical models which are associated with the structural and the aerodynamic part of the simulation using the computational power of a parallel HPC cluster. The structural part models the heterogeneous internal structure of the beam based on a novel implementation of the Generalized Timoshenko Beam Model Technique.. Using this technique the 3-D structure of the blade is reduced into a 1-D beam which is asymptotically equivalent. This reduces the computational cost of the model without compromising its accuracy. This structural model interacts with the Flow model which is a modified version of the Blade Element Momentum Theory. The modified version of the BEM accounts for the large deflections of the blade and also considers the pre-defined structure of the blade. The coning, sweeping of the blade, tilt of the nacelle and the twist of the sections along the blade length are all computed by the model which aren’t considered in the classical BEM theory. Each of these two models provides feedback to the other and the interactive computations lead to more accurate outputs. We successfully implemented the computational models to analyze and simulate the structural and aerodynamic aspects of the blades. The interactive nature of these models and their ability to recompute data using the feedback from each other makes this code more efficient than the commercial codes available. In this thesis we start off with the verification of these models by testing it on the well-known benchmark blade for the NREL-5MW Reference Wind Turbine, an alternative fixed-speed stall-controlled blade design proposed by Delft University, and a novel alternative design that we proposed for a variable-speed stall-controlled turbine, which offers the potential for more uniform power control and improved annual energy production.. To optimize the power output of the stall-controlled blade we modify the existing designs and study their behavior using the aforementioned aero elastic model.

Continuous monitoring of bovine spongiform encephalopathy rapid test performance by weak positive tissue controls and quality control charts

Bovine spongiform encephalopathy (BSE) rapid tests and routine BSE-testing laboratories underlie strict regulations for approval. Due to the lack of BSE-positive control samples, however, full assay validation at the level of individual test runs and continuous monitoring of test performance on-site is difficult. Most rapid tests use synthetic prion protein peptides, but it is not known to which extend they reflect the assay performance on field samples, and whether they are sufficient to indicate on-site assay quality problems. To address this question we compared the test scores of the provided kit peptide controls to those of standardized weak BSE-positive tissue samples in individual test runs as well as continuously over time by quality control charts in two widely used BSE rapid tests. Our results reveal only a weak correlation between the weak positive tissue control and the peptide control scores. We identified kit-lot related shifts in the assay performances that were not reflected by the peptide control scores. Vice versa, not all shifts indicated by the peptide control scores indeed reflected a shift in the assay performance. In conclusion these data highlight that the use of the kit peptide controls for continuous quality control purposes may result in unjustified rejection or acceptance of test runs. However, standardized weak positive tissue controls in combination with Shewhart-CUSUM control charts appear to be reliable in continuously monitoring assay performance on-site to identify undesired deviations.

Sample size in orthodontic randomized controlled trials: are numbers justified?

Sample size calculations are advocated by the Consolidated Standards of Reporting Trials (CONSORT) group to justify sample sizes in randomized controlled trials (RCTs). This study aimed to analyse the reporting of sample size calculations in trials published as RCTs in orthodontic speciality journals. The performance of sample size calculations was assessed and calculations verified where possible. Related aspects, including number of authors; parallel, split-mouth, or other design; single- or multi-centre study; region of publication; type of data analysis (intention-to-treat or per-protocol basis); and number of participants recruited and lost to follow-up, were considered. Of 139 RCTs identified, complete sample size calculations were reported in 41 studies (29.5 per cent). Parallel designs were typically adopted (n = 113; 81 per cent), with 80 per cent (n = 111) involving two arms and 16 per cent having three arms. Data analysis was conducted on an intention-to-treat (ITT) basis in a small minority of studies (n = 18; 13 per cent). According to the calculations presented, overall, a median of 46 participants were required to demonstrate sufficient power to highlight meaningful differences (typically at a power of 80 per cent). The median number of participants recruited was 60, with a median of 4 participants being lost to follow-up. Our finding indicates good agreement between projected numbers required and those verified (median discrepancy: 5.3 per cent), although only a minority of trials (29.5 per cent) could be examined. Although sample size calculations are often reported in trials published as RCTs in orthodontic speciality journals, presentation is suboptimal and in need of significant improvement.

Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

BACKGROUND The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID). METHODS We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size. RESULTS The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia. CONCLUSIONS Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Sample Size vs. Bias in Defect Prediction

Most empirical disciplines promote the reuse and sharing of datasets, as it leads to greater possibility of replication. While this is increasingly the case in Empirical Software Engineering, some of the most popular bug-fix datasets are now known to be biased. This raises two significants concerns: first, that sample bias may lead to underperforming prediction models, and second, that the external validity of the studies based on biased datasets may be suspect. This issue has raised considerable consternation in the ESE literature in recent years. However, there is a confounding factor of these datasets that has not been examined carefully: size. Biased datasets are sampling only some of the data that could be sampled, and doing so in a biased fashion; but biased samples could be smaller, or larger. Smaller data sets in general provide less reliable bases for estimating models, and thus could lead to inferior model performance. In this setting, we ask the question, what affects performance more? bias, or size? We conduct a detailed, large-scale meta-analysis, using simulated datasets sampled with bias from a high-quality dataset which is relatively free of bias. Our results suggest that size always matters just as much bias direction, and in fact much more than bias direction when considering information-retrieval measures such as AUC and F-score. This indicates that at least for prediction models, even when dealing with sampling bias, simply finding larger samples can sometimes be sufficient. Our analysis also exposes the complexity of the bias issue, and raises further issues to be explored in the future.