Sample Size Determination

Extended  Abstract:

Aim: Construction of estimator - point as well as interval, hypothesis testing and methods relating to determination of sample size in the context of statistical inference of traffic intensity parameter of the M/M/1 queuing model.

Method: We construct the estimator by leveraging a trick wherein we have exploited the relationship between the Bernoulli process and the M/M/1 process. This method is preferable to other existing methods because of ease of data collection for each sample point, as it is only necessary to observe if the number of customers left behind by a departing customer is zero or greater than zero.

Novelty: Our point estimator is simple and unique in the sense that it possesses many of the desirable properties from the frequentist point of view. To the best of our knowledge, a similar estimator with such nice properties is not available in the literature. Method for interval estimation has also been outlined. Additionally, a method for testing hypothesis on traffic intensity is presented. Another novelty of the paper is a method for determining the sample size. This is rare in the domain of statistical inference in queuing theory. A practical illustration numerically demonstrates our theoretical results.

PS: A full text pdf version of the published paper is available for download from:
https://www.tandfonline.com/eprint/7PYHXBHJDSBG4UJMTBMQ/full?target=10.1080/17509653.2018.1436010

This article proposes 2 new approaches to test a nonzero population correlation (rho): the hypothesis-imposed univariate sampling bootstrap (HI) and the observed-imposed univariate sampling bootstrap (OI). The authors simulated correlated populations with various combinations of normal and skewed variates. With alpha set=.05, N> or =10, and rho< or =0.4, empirical Type I error rates of the parametric r and the conventional bivariate sampling bootstrap reached .168 and .081, respectively, whereas the largest error rates of the HI and the OI were .079 and .062. On the basis of these results, the authors suggest that the OI is preferable in alpha control to parametric approaches if the researcher believes the population is nonnormal and wishes to test for nonzero rhos of moderate size.

PURPOSE:
To investigate whether mesenchymal stem cells (MSCs) seeded in novel polyvinyl alcohol (PVA)-chitosan composite hydrogel can provide comparable or even further improve cartilage repair outcomes as compared to previously established alginate-transplanted models.
METHODS:
Medial femoral condyle defect was created in both knees of twenty-four mature New Zealand white rabbits, and the animals were divided into four groups containing six animals each. After 3 weeks, the right knees were transplanted with PVA-chitosan-MSC, PVA-chitosan scaffold alone, alginate-MSC construct or alginate alone. The left knee was kept as untreated control. Animals were killed at the end of 6 months after transplantation, and the cartilage repair was assessed through Brittberg morphological score, histological grading by O'Driscoll score and quantitative glycosaminoglycan analysis.
RESULTS:
Morphological and histological analyses showed significant (p < 0.05) tissue repair when treated with PVA-chitosan-MSC or alginate MSC as compared to the scaffold only and untreated control. In addition, safranin O staining and the glycosaminoglycan (GAG) content were significantly higher (p < 0.05) in MSC treatment groups than in scaffold-only or untreated control group. No significant difference was observed between the PVA-chitosan-MSC- and alginate-MSC-treated groups.
CONCLUSION:
PVA-chitosan hydrogel seeded with mesenchymal stem cells provides comparable treatment outcomes to that of previously established alginate-MSC construct implantation. This study supports the potential use of PVA-chitosan hydrogel seeded with MSCs for clinical use in cartilage repair such as traumatic injuries

This presentation describes the steps involved in per- forming sample size analyses for a variety of linear models, both univariate and multivariate. As an an- alyst you must gather and synthesize the information needed, but you should be able to rely on the ana- lytical tools to accommodate the numerous ways in which you can characterize and solve problems. Ex-

When the measurement of outcome is unreliable or the cost of obtaining an additional subject is relatively high compared to the cost of obtaining an additional measurement from the same subject, it may be desirable to consider taking more than one measurement per subject to increase power or to minimize the cost in a clinical trial. When each subject in two comparison groups has a fixed number of repeated measurements, this paper develops an asymptotic procedure to calculate the number of subjects per group required to achieve a given power for an α-level bioequivalence test. Furthermore, Monte Carlo simulation is used to evaluate the accuracy of the approximate sample size calculation procedure and a brief discussion on how to determine the optimal number of repeated measurements is included.

Stable nitrogen isotopes (δ15N) in bioindicators are increasingly employed to identify nitrogen sources in many ecosystems and biological characteristics of the eastern oyster (Crassostrea virginica) make it an appropriate species for this purpose. To assess nitrogen isotopic fractionation associated with assimilation and baseline variations in oyster mantle, gill, and muscle tissue δ15N, manipulative fieldwork in Chesapeake Bay and corresponding modeling exercises were conducted. This study (1) determined that five individuals represented an optimal sample size; (2) verified that δ15N in oysters from two locations converged after shared deployment to a new location reflecting a change in nitrogen sources; (3) identified required exposure time and temporal integration (four months for muscle, two to three months for gill and mantle); and (4) demonstrated seasonal δ15N increases in seston (summer) and oysters (winter). As bioindicators, oysters can be deployed for spatial interpolation of nitrogen sources, even in areas lacking extant populations.

Here, small area estimation is applied in the sense that we are &quot;borrowing strength&quot; from data outside of given subpopulations for which we are to publish estimated totals, or means, or ratios of totals. We will consider estimated totals for establishment surveys. A subpopulation for which we wish to estimate a total will be called a &quot;publication group&quot; (PG), and data that may be modeled together, using one regression, will be called an &quot;estimation group&quot; (EG). See Knaub(1999, 2001, 2003) regarding this for a more complex application. When a PG consists of a set of EGs, that is stratification. When an EG contains PGs, this is a simple form of small area estimation because we are using data outside of a given publication group to help estimate statistics/parameters for that model, used to estimate for each impacted PG. (In Knaub(1999, 2001), there are overlapping &#39;areas&#39; as well.) Here we consider very small areas (PGs), which may fall within a &...

The Fisher and Kullback- Liebler information measures were calculated from the approximation of a binomial distribution by both the Poisson and the normal distributions and are applied to the approximation of a Poisson distribution by a normal distribution. In this paper the concept of relative loss in information due to approximating the distribution of a random variable Xn by the distribution of another random variable Yn is introduced, and this concept is used to determine the value of the sample size for which the relative loss in information measure is less than a given level epsilon.

XR5000 is a tricyclic carboxamide-based cytotoxic agent that binds to DNA by intercalation and stimulates DNA cleavage by inhibition of both topoisomerase I and II. The aim of this study was to evaluate the antitumoral activity and safety profile of XR5000 given as second-line chemotherapy in patients with advanced non-small cell lung cancer (NSCLC). Patients received XR5000 at the dose

We present a bootstrap Monte Carlo algorithm for computing the power function of the generalized correlation coefficient. The proposed method makes no assumptions about the form of the underlying probability distribution and may be used with observed data to approximate the power function and pilot data for sample size determination. In particular, the bootstrap power functions of the Pearson product moment correlation and the Spearman rank correlation are examined. Monte Carlo experiments indicate that the proposed algorithm is reliable and compares well with the asymptotic values. An example which demonstrates how this method can be used for sample size determination and power calculations is provided.

This article proposes 2 new approaches to test a nonzero population correlation (rho): the hypothesis-imposed univariate sampling bootstrap (HI) and the observed-imposed univariate sampling bootstrap (OI). The authors simulated correlated populations with various combinations of normal and skewed variates. With alpha set=.05, N&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; or =10, and rho&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; or =0.4, empirical Type I error rates of the parametric r and the conventional bivariate sampling bootstrap reached .168 and .081, respectively, whereas the largest error rates of the HI and the OI were .079 and .062. On the basis of these results, the authors suggest that the OI is preferable in alpha control to parametric approaches if the researcher believes the population is nonnormal and wishes to test for nonzero rhos of moderate size.

SUMMARY The sample mean difference ∆ is an unbiased estimator of Gini’s mean difference ∆. It is well known that ∆ ˆ is asymptotically normally distributed (Hoeffding, 1948). In order to obtain confidence intervals for ∆, ∆ ˆ must be standardized and hence its variance Var( ∆ ˆ ) must be estimated. In this paper we study the effective coverage of the confidence intervals for ∆, when using a specific unbiased estimator ) ˆ ( ar V ˆ ∆ for the variance of ∆ ˆ , in a non-parametric framework. The empirical determination of the minimum sample size required to reach a good approximation of the nominal coverage is analyzed through a new approach. The reported results show that this threshold is critically related to the asymmetry and the tail heaviness in the underlying distribution.

The problem of sample size estimation is important in the medical applications, especially in the cases of expensive measurements of immune biomarkers. The papers describes the problem of logistic regression analysis including model feature selection and includes the sample size determination algorithms, namely methods of univariate statistics, logistics regression, cross-validation and Bayesian inference. The authors, treating the regression model parameters as the multivariate variable, propose to estimate sample size using the distance between parameter distribution functions on cross-validated data sets.

Sample size determination for survival time studies is discussed, taking into account stratification. We present formulas and tables which also apply in the case of multicenter clinical trials. In addition, the same method is used to estimate the sample size requirement when a covariate is grouped into strata. Simulation studies compare the results to covariate adjustment by the Cox proportional hazards model.