bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of Random Coefficient Regression Model to Myopia Data: A Case Study
Authors: Möttonen Jyrki , Oja Hannu , Krause Ulf , Rantakallio Paula
Published: May 2007

A one‐year birth cohort from Northern Finland has been followed up since 1966. As a part of this study, we are in this paper concerned with analysing the progression of myopia (nearsightness) up to the age of 20 years. The random coefficient regression model was chosen for the analysis because of the large individual variation in the development of myopia. Maximum likelihood estimates for the parameters in the model were obtained via the expectation maximization (EM) algorithm. It is shown how the estimated model can be used to predict future observations for an individual using the previously recorded refractive error measurements as well as other relevant data on the patient in question.
Maximum Likelihood Estimation of Simultaneous Pairwise Linear Structural Relationships
Authors: Bolfarine Heleno , Rojas Manuel Galea
Published: May 2007

The problem of assessing the relative calibrations and relative accuracies of a set ofpinstruments, each designed to measure the same characteristic on a common group of individuals is considered by using the EM algorithm. As shown, the EM algorithm provides a general solution for this problem. Its implementation is simple and in its most general form requires no extra iterative procedures within the M step. One important feature of the algorithm in this set up is that the error variance estimates are always positive. Thus, it can be seen as a kind of restricted maximization procedure. The expected information matrix for the maximum likelihood estimators is derived, upon which the large sample estimated covariance matrix for the maximum likelihood estimators can be computed. The problem of testing hypothesis about the calibration lines can be approached by using the Wald statistics. The approach is illustrated by re‐analysing two data sets in the literature.
A Discrete Delta Method for Estimating Standard Errors for Estimators in Quantal Bioassay
Authors: Cobb E. Benton , Church J. D.
Published: May 2007

A nonparametric discrete delta method for estimating standard errors of percentile estimators in quantal bioassay is described. A simulation study of confidence intervals for EDx in probit analysis shows the discrete delta method compared favorably with intervals based on maximum likelihood and also some parametric bootstrap methods.
Weighted Concordance Analysis
Authors: Tricot Jean‐Marie , Lepage Yves
Published: May 2007

Using the variance stabilizing technique, a product multinomial model is introduced to generate a new statistic to test observers' uncertainty in a weighted concordance analysis. Distance matrices which follow some specific rules are obtained by linear combinations of hierarchical distance matrices whose elements are equal to 0 or 1 and unit diagonal. The new statistic is compared with the kappa statistic interpreted by considering the covariance matrix generated by the data. By rewriting the test statistic in a barycentric form, one demonstrates how to modify the barycentric coefficients to derive an adequate measure of the interobserver agreement. The methods are illustrated using two examples.
Raking Kappa: Describing Potential Impact of Marginal Distributions on Measures of Agreement
Authors: Agresti Alan , Ghosh Atalanta , Bini Matilde
Published: May 2007

Several authors have noted the dependence of kappa measures of inter‐rater agreement on the marginal distributions of contingency tables displaying the joint ratings. This paper introduces a smoothed version of kappa computed after raking the table to achieve pre‐specified marginal distributions. A comparison of kappa with raked kappa for various margins can indicate the extent of the dependence on the margins, and can indicate how much of the lack of agreement is due to marginal heterogeneity.
Optimal Unconditional Tables for Comparing Two Independent Proportions
Authors: Andrés, A. Martín , Sil Va Mato A.
Published: May 2007

Comparing two independent binomial proportions is quite a common problem in statistical practice. The unconditional method for doing so is more powerful than the conditional method (Fisher's exact test), but the computational difficulties of the former are much greater, and beyond the reach of most researchers. The solution adopted so far has been the publication of tables for critical regions, but the only ones that exist (MCDONALD et al., 1977; SUISSA and SHUSTER, 1985; and HABER, 1986) have certain limitations which prevent their general use (they are only valid for one‐tailed tests; they allow very limited values of sample size and α error, and they are not constructed using the most powerful version of the test). In this paper the authors present tables which do not contain these limitations and which are valid for α errors of 1%, 5% and 10% and for sample size of n1 ≦n2 ≦25 (beyond this figure, approximations may be used). They also illustrate the way to apply these tables (albeit in a conservative fashion) to the case of multinomial 2 × 2 trials.
Marked Point Process: Using Correlation Functions to Explore a Spatial Data Set
Authors: Goulard Michel , Pagès L. , Cabanettes A.
Published: May 2007

The relationship between the locations of the clumps of sprouts, some morphological characteristics of the clumps and the local soil environment in an old sweet chestnut coppice are studied. The theory of marked point process, which has not yet been used extensively in forestry studies, is shown to be adequate for the analysis of this type of spatial data. The marks correspond to morphological characteristics of the clumps: “diameter”, “number of sprouts”, “height at one year”, and “height at three years”. Several covariance functions are described which give a method for exploring the spatial relationships within the stand. Some of these functions are introduced for the first time in an actual statistical analysis.

By using these functions, it is shown that the clumps are regularly distributed. The variables “diameter” and “number of sprouts” are strongly spatially negatively correlated, whereas the heights are slightly or not correlated. By categorising the individuals according to the mark values, it is shown that the small clumps tended to be aggregated in the gaps between medium and large clumps. Values of heights in the ties of the distribution are related as well as their spatial correlation to the local soil environment.
On Encoding Values for Data Recorded as X ≥ C
Authors: Lachenbruch Peter A. , Clements Philip J. , He Weizhong
Published: May 2007

In many medical and other contexts, an ordered variable is measured and the limits of measuring ability will be reached. In such cases, the data may be reported as X ≥ C. For example, in a cell count, a laboratory technician may report the data as “count ≥ 100.” If the data are a dependent variable, censored data methods are the standard techniques. However, if X is an independent variable, some methods need to be devised to handle the problem. A simple method is to encode the values X ≥ C to some value X0. A candidate for this is the conditional mean (or median) of X given X ≥ C. This paper gives some results, and examines some robustness questions for the proposed method.
Construction and Comparison of Two Receiver Operating Characteristic Curves Derived from the Same Samples
Authors: Le Chap T. , Lindgren Bruce R.
Published: May 2007

Receiver operating characteristic (ROC) curves are used to describe the performance of diagnostic procedures. This paper proposes a simple method for the statistical comparison of two ROC curves derived from the same set of patients and the same set of healthy subjects. Generalization to studies involving more than two screening factors is straightforward. This method does not require the calculation of variances of the areas or difference of areas under the curves.
Augmented Partial Diallel Design for Estimating Combining Ability of Parents
Authors: Jaggi Seema , Agarwal K. N.
Published: May 2007

The Augmented Partial Diallel Cross (APDC) represents an intermediate position between the Complete Diallel Cross (CDC) and the Partial Diallel Cross (PDC) in which one or more primary lines are crossed with all the other lines but the lines of secondary interest form a PDC system. The method of sampling adopted for crosses of secondary lines is from arrangement of secondary lines on circumference of a circle. The mathematics for analysis of such APDC has been given systematically. The efficiency of estimates of general combining ability (g.c.a.) effects obtained from APDC has been compared with that of Pederson's estimator and CDC. It is observed that there are four types of variances for g.c.a. effects where as for comparing specific combining ability (s.c.a.) effects there are large number of variances indicating that the design is totally unbalanced for s.c.a. comparisons.
A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3
Authors: Federer Walter T.
Published: May 2007

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency.

A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero‐one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.
Comparing Trials with Multiple Outcomes: The Multivariate One‐Sided Hypothesis with Unknown Covariances
Authors: Frick Hans
Published: May 2007

The paper deals with a problem arising for tests in clinical trials. The outcomes of a standard and a new treatment to be compared are multivariate normally distributed with common but unknown covariance matrix. Under the null hypothesis the means of the outcomes are equal, under the alternative the new treatment is assumed to be superior, i.e. the means are larger without further quantification. For known covariance matrix there is a variety of tests for this problem. Some of these procedures can be extended to the case of unknown covariances if one is willing to accept a bias. There is, however, also an efficient unbiased test. The paper contains some numerical comparisons of these different procedures and takes a look on the minimax properties of the unbiased test.
Use of Phase for the Detection of Hidden Periodicites
Authors: Reschenhofer Erhard
Published: May 2007

Standard tests for the detection of hidden periodicities in time series are largely ignored by applied workers. Various simple but inappropriate methods are used instead. Therefore a method is suggested which is both simple and appropriate but which requires the prior knowledge of certain characteristics of the suspected periodicity. For illustration, this method is applied to a set of data from a chronobiological study.
Confidence Intervals for the Risk Ratio in Cohort Studies under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

Three simple interval estimates for the risk ratio in inverse sampling are considered. The first two interval estimates are derived on the basis of Fieller's Theorem and the delta method with the logarithmic transformation, respectively. The third interval estimate is derived on the basis of an F‐test statistic proposed by BENNETT (1981) for testing equal probabilities of a disease between two comparison groups when the disease is rare. To evaluate the performance of these three methods, a Monte Carlo simulation is used to compare the actual coverage probability with the nominal confidence level for each method and to estimate the expected length of the corresponding confidence interval in a variety of situations. On the basis of the results found in the simulation, we have concluded that the method with the logarithmic transformation is either equivalent to or better than the other two methods for all situations considered here.
Indices of Disease Severity in Diseases that Cause Abscesses in Target Organs
Authors: Trajstman A.
Published: May 2007

Some animal diseases cause variable numbers of abscesses of varying severity in target organs. In assessing the efficacy of vaccines developed to combat these diseases it is necessary to devise indices of disease severity that incorporate the number of abscesses in an animal and the severity scores of the abscesses. Three indices are defined and their relative merits are discussed. Some of the distributional properties of the indices are examined and their relevance to statistical analyses are discussed.
Statistical Tests for Signals in Categorial Temporal Data
Authors: Cannon Ann R. , Meeker William Q.
Published: May 2007

This paper describes methods for using categorical temporal data to detect differences in behavior between a treated group and a control group. The first‐level output from the data is typically a set of many different correlated test statistics comparing the two groups. In previous work, a decision was made by counting the number of significant individual tests and calibrating with bootstrap simulation. This article goes further, suggesting two possible alternative statistics: the sum of the squared individual test statistics and a Wald‐like combination of the individual test statistics. All three overall comparison statistics are defined and a method for computing critical values from simulated distributions using a bootstrap method is given. The use of all three methods is then demonstrated on each of three data sets. Finally, a simulated power study reveals that the Wald‐like statistic is much better than the other two, leading to the suggestion of its use in place of the other two statistics.
Modelling the Age‐Period‐Cohort Trend Surface
Authors: Lee Wen C. , Lin Ruey S.
Published: May 2007

Age‐period‐cohort analysis of incidence and/or mortality data has received much attention in the literature. Though several authors seem to offer solutions to the non‐identifiability problem inherent in this kind of analysis, the constraints imposed lack sound biological bases and the interpretability of the parameters is in doubt. By introducing the axes of ‘adjusted’ age, period, and cohort variables in the age‐period‐cohort trend surface, the authors find that separate effects from these variables can be estimated and can be clearly interpreted. The constraint behind the procedure is also found to be mathematically simple and elegant. Since the method still lacks a biological foundation, it is best viewed as an adjunct to the graphical trend‐surface analysis rather than as a solution to the non‐identifiability problem. Previously published mortality data of prostate cancer is used to illustrate the methodology.
Response to Selection and Inbreeding Depression in a Dynamic Population for Amount of Inbreeding
Authors: Nomura T.
Published: May 2007

A method for predicting response to selection and inbreeding depression in a dynamic population for amount of inbreeding was derived and illustrated with an example of selection under full‐sib mating.
Symmetry and Asymmetry Models for Rectangular Tables
Authors: Kateri M. , Papaioannou T.
Published: May 2007

The models of complete, quasi and conditional symmetry as well as marginal homogeneity and diagonal asymmetry, applicable to square contingency tables are extended to non‐square ones. Several properties of the models are investigated and estimation and test theory is presented. The utility of the new proposed models is discussed and illustrated by reanalyzing classical data sets.
Estimation, Testing and Adjustment of Transient Healthy Entrant Effects
Authors: Hoover D. R. , Muñoz A. , He Y. , Jacobson L. P.
Published: May 2007

At recruitment, cohorts often selectively exclude non‐healthy individuals with symtoms prodromal to the response. After a certain time from study entry, the health status of participants regresses towards the underlying population. Methods developed here estimate, test and adjust out this transient healthy entrant effect from survival function estimation. In the simplest case, each participant's time is divided into: Ω1‐ immediately after study entry while these transient healthy entrant effects are strong, and Ω2‐ later, after they have vanished or greatly diminished. Truncated Kaplan‐Meier models fit separately to risk sets in Ω1and Ω2quantify and remove the bias from transient healthy entrant effects and test for statistical significance. If sufficient data are available, these methods can be expanded to dividing the subjects' time into multiple subperiods or fitting specific models of attenuation for the transient healthy entrant effect. Examination of nickel refinery workers and an HIV‐1 infected cohort suggest that, without the adjustments proposed here, transient healthy entrant effects cause moderate overestimations of survival probability.
Estimating Pair Correlation Functions of Planar Cluster Processes
Authors: Stoyan Dietrich , Stoyan Helga
Published: May 2007

The pair correlation functiong(r)is an important tool in exploratory data analysis and model choice in point process statistics. In the case of cluster processes, the behaviour ofg(r)for smallris particularly interesting. But just these values ofg(r)can be estimated with difficulties only. This paper tries to show that kernel estimators yield reliable results. It is useful to work with variable band widths. An example where the points are positions of pines in a forest illustrates the application of the method.
A Note on Dilution Assays with Errors in Dilutions
Authors: Trajstman A. C.
Published: May 2007

Dilution assays involve a number of steps in the preparation of the dilutions and the delivery of the diluent. These steps may give rise to dilution errors. If assays are treated as if the nominal dilutions have been used then under estimates of micro‐organism density may occur. In this paper models for dilution errors are introduced.
Modelling Cultivar Mixtures Using SEIR Compartmental Models
Authors: Goleniewski George
Published: May 2007

A SEIR (susceptible, exposed, infectious, removed) compartmental model is constructed to represent disease progress in a two cultivar mixture. The concept of the spore pool is the means by which inoculum exchange between the constituent cultivars is represented. Infection frequencies for each cultivar are permitted to vary with that cultivar's susceptible fraction according to a power‐law relationship. For each cultivar, new additions to the susceptible class balance deaths from the removed class so that the total leaf area of all four SEIR classes remains constant. It is shown that an equilibrium with non‐zero diseased classes exists in a certain parameter regime. A numerical stability analysis is performed using the model equations linearised about this equilibrium. The effects of changing induced resistance parameters within the model are demonstrated graphically. It is also demonstrated that the proportion of susceptibles as a function of mixture composition has an optimum in the regime where nontrivial equilibria exist, a feature of practical interest provided that equilibrium is reached within a growing season.
A Comparison of Generalized Poisson Distribution for Modeling Chromosome Aberrations
Authors: Lee Carl M.‐S. , Famoye Felix
Published: May 2007

Various models have been developed for modeling the distribution of chromosome aberrations in the literature (e. g. Consul, 1989). Generalized Poisson distribution is among the popular ones. The parameters of this distribution provide meaningful interpretation of the induction mechanism of the chromosome aberrations. In this article, we apply several estimation methods to estimate the generalized Poisson parameters for fitting the number of chromosome aberrations under different dosages of radiations. The methods compared are moment, maximum likelihood, minimum chi‐square, weighted discrepancy and empirically weighted rates of change. Our study suggests that the empirically weighted rates of change method results in smallest Mean Square Error and Mean Absolute Error for most dosages of radiations. The data used for this comparison are from Janardan and Schaeffer (1977).
A Complex Model for Gene Effects taking into Account Selection and Crossing Over
Authors: Hyánek Jaromir , Herrendörfer Günter
Published: May 2007

A general model for gene effects including the influence of selection and crossing over is presented. It is shown, how gene frequencies of alleles in two loci system are changed in selected populations in the presence of crossing over. This is used for estimation of gene effects.
An Exact Confidence Interval for the Ratio of Two Related Proportions
Authors: Parker R. A.
Published: May 2007

I propose an exact confidence interval for the ratio of two proportions when the proportions are not independent. One application is to estimate the population prevalence using a screening test with perfect specificity but imperfect sensitivity. The population prevalence is the ratio of the observed prevalence divided by the test's sensitivity. I describe a method to calculate exact confidence intervals for this problem and compare these results with approximate confidence intervals given previously.
Selecting the Best Population, Provided It Is Better than a Control: The Unequal Variance Case
Authors: Hsu Lifang , Chen Pinyuen
Published: May 2007

Bechhofer and Turnbull (1978) proposed two procedures to compare k normal means with a standard and the procedures guarantee that (1) with probability at least P0* (specified), no category is selected when the best experimental category is sufficiently worst than the standard, and (2) with probability at least P1* (specified), the best experimental category is selected when it is sufficiently better than the second best and the standard. For the case of common known variance, they studied a single‐stage procedure. For the case of common unknown variance, they studied a two‐stage procedure. Under the same formulation of Bechhofer and Turnbull (1978) and for the same selection goals (1) and (2) described above, Wilcox (1984a) proposed a procedure to the case of unknown and unequal variances, and supplied a table of the necessary constants to implement the procedure. This paper considers the case of unknown and unequal variances for the same formulation of Bechhofer and Turnbull, and Wilcox, but assumes that μ0 is an unknown control. A two‐stage procedure is proposed to solve the problem. A lower bound of the probability of a correct selection is derived and it takes the same form as the double integral appeared in Rinott (1978) which was used for the lower bound of the probability of a correct selection for a different selection goal.
Estimation of Finite and Closed Population Size: An Inverse Sampling Approach with Unequal Recapture Probability
Authors: Hossain Md. Forhad
Published: May 2007

Based on capture‐mark‐recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L ≥ 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.
On the Estimation of Intra‐Sire Regression Heritability Subject to Linear Constraint
Authors: Prabhakaran V. T. , Jaggi Seema
Published: May 2007

The derivation of the restricted intra‐sire regression heritability estimator is provided. Procedures for obtaining a stable estimate of residual error variance σ2are outlined. A small illustration based on live data is given.
Estimation of Parameters for One‐Way Layout with Rank Set Sampling
Authors: Muttlak Hassen A.
Published: May 2007

Ranked set sampling (RSS) as suggested by McIntyre (1952) and independently by Takahasi and Wakimoto (1968) may be used to estimate the parameters of the one‐way layout. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random (SRS) method. Estimators of the populations (treatments) effect are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.
Estimating the Population Mean Using Extreme Ranked Set Sampling
Authors: Samawi Hani M. , Ahmed Mohammad S. , Abu‐Dayyeh Walid
Published: May 2007

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.
Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors
Authors: Barakat Ali S. , Quade Dana , Salama Ibrahim A.
Published: May 2007

Given independent multivariate random samples {Xij: j = 1, …, ni} from Fi, for i = 1,2, a test is desired for H0: F1 = F2 against general alternatives. Consider the k · (n1 + n2) possible ways of choosing one observation from the combined samples and then one of its k nearest neighbors, and let Sk be the proportion of these choices in which the point and neighbor are in the same sample. Schilling (1986) proposed Sk as a test statistic, but did not indicate how to determine k. We suggest as test statistic W = N Σ kSk, which we show is equivalent to a sum of N Wilcoxon rank sums, and also to a sum of two two‐sample U‐statistics of degrees (1, 2) and (2, 1). Simulation with multivariate normal data suggests that our test is generally more powerful than Schilling's test using k = 1, 2, or 3. We illustrate its use with Fisher's iris data.
Estimation of the Power of the Kruskal‐Wallis Test
Authors: Mahoney Michelle , Magel Rhonda
Published: May 2007

Power calculations of a statistical test require that the underlying population distribution(s) be completely specified. Statisticians, in practice, may not have complete knowledge of the entire nature of the underlying distribution(s) and are at a loss for calculating the exact power of the test. In such cases, an estimate of the power would provide a suitable substitute. In this paper, we are interested in estimating the power of the Kruskal‐Wallis one‐way analysis of variance by ranks test for a location shift.

We investigated an extension of a data‐based power estimation method presented by Collings and Hamilton (1988), which requires no prior knowledge of the underlying population distributions other than necessary to perform the Kruskal‐Wallis test for a location shift. This method utilizes bootstrapping techniques to produce a power estimate based on the empirical cumulative distribution functions of the sample data. We performed a simulation study of the extended power estimator under the conditions ofk= 3 andk= 5 samples of equal sizesm= 10 andm= 20, with four underlying continuous distributions that possessed various location configurations. Our simulation study demonstates that the Extended Average × & Y power estimation method is a reliable estimator of the power of the Kruskal‐Wallis test fork= 3 samples, and a more conservative to a mild overestimator of the true power fork= 5 samples.
Point Estimation on Relative Risk under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

When the underlying disease is rare, to control the coefficient of variation for the sample proportion of cases, we may wish to apply inverse sampling. In this paper, we derive the uniformly minimum variance unbiased estimator (UMVUE) of relative risk and its variance in closed form under inverse sampling. On the basis of a Monte Carlo simulation, we demonstrate that using the UMVUE of relative risk can substantially reduce the mean‐squared‐error of using the maximum likelihood estimator, especially when the number of index cases in both comparison samples is small. For a given fixed total cost, we include a program that can be used to find the optimal allocation for the number of index cases to minimize the variance of the UMVUE as well.
Notes in Case‐Control Studies with Matched Pairs under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

In case‐control studies with matched pairs, the traditional point estimator of odds ratio (OR) is well‐known to be biased with no exact finite variance under binomial sampling. In this paper, we consider use of inverse sampling in which we continue to sample subjects to form matched pairs until we obtain a pre‐determined number (>0) of index pairs with the case unexposed but the control exposed. In contrast to use of binomial sampling, we show that the uniformly minimum variance unbiased estimator (UMVUE) of OR does exist under inverse sampling. We further derive an exact confidence interval of OR in closed form. Finally, we develop an exact test and an asymptotic test for testing the null hypothesis H0: OR = 1, as well as discuss sample size determination on the minimum required number of index pairs for a desired power at α‐level.
A New Approach to Equivalence Assessment in Standard Comparative Bioavailability Trials by Means of the Mann‐Whitney Statistic
Authors: Wellek S.
Published: May 2007

By a suitable transformation of the pairs of observations obtained in the successive periods of the trial, bioequivalence assessment in a standard comparative bioavailability study reduces to testing for equivalence of two continuous distributions from which unrelated samples are available. Let the two distribution functions be given by F(x) = P[X ≤ x], G(y) = P[Y ≤ y] with (X, Y) denoting an independent pair of real‐valued random variables. An intuitively appealing way of putting the notion of equivalence of F and G into nonparametric terms can be based on the distance of the functional P[X > Y] from the value it takes if F and G coincide. This leads to the problem of testing the null hypothesis Ho P[X > Y] ≤ 1/2 ‐ ε1 or P[X > Y] ≥ 1/2 + ε2 versus H1 : 1/2 − ε1 < P[X > Y] < 1/2 + ∈2, with sufficiently small ε1, ε2 ∈ (0, 1/2). The testing procedure we derive for (0, H1) and propose to term Mann‐Whitney test for equivalence, consists of carrying out in terms of the U‐statistics estimator of P[X > Y] the uniformly most powerful level a test for an interval hypothesis about the mean of a Gaussian distribution with fixed variance. The test is shown to be asymptotically distribution‐free with respect to the significance level. In addition, results of an extensive simulation study are presented which suggest that the new test controls the level even with sample sizes as small as 10. For normally distributed data, the loss in power as against the optimal parametric procedure is found to be almost as small as in comparisons between the Mann‐Whitney and the t‐statistic in the conventional one or two‐sided setting, provided the power of the parametric test does not fall short of 80%.
Normal Approximation of a Discrete Distribution on Exact Test of Uniform Association in a 2 × 3 Table
Authors: Tomizawa Sadao , Seo Takashi , Kikuchi Seiji
Published: May 2007

For the analysis of 2 × 3 tables, TOMIZAWA (1993) considered an exact test of uniform association, which is an extension of independence, and then derived a discrete distribution. This paper gives a normal approximation of the discrete distribution and describes that the normalized statistic can test a one‐sided hypothesis on the uniform association. Also it points out that the square of the normalized test statistic is equal to the Pearson's chi‐squared statistic for testing the uniform association.
A Two‐Stage Test for Distinguishing Random, Pseudo‐Random and Nonrandom Mating Populations
Authors: Tai J. J. , Liu Joumiao
Published: May 2007

There is no such an implication that a population in Hardy‐Weinberg equilibrium must have undergone random mating. Therefore, it is unequivocal that the usual tests for “Hardy‐Weinberg equilibrium” are indeed tests for “random union of gametes” but not for “random mating”. In this paper, utilizing population characteristics expressed in equilibrium state (equilibrium or disequilibrium) and mating behavior (random or nonrandom), a two‐stage testing procedure for distinguishing random, pseudo‐random and nonrandom mating populations is proposed. At the first stage, a population is tested for Hardy‐Weinberg equilibrium. If insignificant result (i.e., in equilibrium) is obtained, then to a second stage the population is further tested for mating behavior. Random mating‐pairs data are needed here for analysis instead of random individuals for usual Hardy‐Weinberg equilibrium tests. Since distinguishing the three types of mating populations depends on the combined results of two stages, the probability of correct determination of the two‐stage tests is discussed by simulation studies.
Universal Optimality of Nearest Neighbour Balanced Block Designs using Second Order Correlated Models
Authors: Santharam C. , Ponnusamy K. N. , Chandrasekar B.
Published: May 2007

Block designs for observations correlated in one dimension are investigated. Santharam and Ponnusamy (1995) investigated the universal optimality of Nearest Neighbour balanced block designs (NNBD) using first order correlated models (AR(1), MA(1) and ARMA(1,1)). In this article we have investigated the universal optimality of NNBD using second order correlated models (ar(2), and MA (2)).
Estimation of Ratio Using Rank Set Sampling
Authors: Samawi Hani M. , Muttlak Hassen A.
Published: May 2007

Ranked set sampling (RSS) as suggested by McIntyre (1952) and developed by Takahasi and Wakimoto (1968) is used to estimate the ratio. It is proved that by using RSS method the efficiency of the estimator relative to the simple random sampling (SRS) method has increased. Computer simulated results are given. An example using real data is presented to illustrate the computations.
Testing Equality of Regressions When Error Variances are Heterogeneous to Study the Production Differentials of Rice in Bangladesh
Authors: Bhuyan K. C. , Majumder A. K.
Published: May 2007

Method to test the equality of p sets of regression coefficients in presence of heterogeneous error variances is suggested. The sets of regression coefficients are obtained from a sample where the sample observations are classified into p classes. The test statistic to test the significance of the regression is also suggested.

As an application of the method, the equality of production functions of boro rice produced in different districts of Bangladesh in two different periods is tested.
Assessing Local Influence in Measurement Error Models
Authors: Lee Andy H. , Zhao Yuejen
Published: May 2007

We consider the assessment of local influence for generalized linear models when the covariates are measured with errors. We show how to evaluate the effect that perturbations to the data, case weights, and model assumptions may have on the parameter estimates. Based on the likelihood displacement functions, some useful influence diagnostics are derived. Two examples illustrate application of the proposed diagnostics and assessment of the measurement error assumptions.
Modeling Exposure Intensity and Susceptibility‐Latency Effect from Retrospective Cohort Data ‐ Application to Lung Cancer Mortality in Blackfoot Disease Endemic Area in Taiwan
Authors: Lee Wen‐Chung , Lin Ruey‐Shiung
Published: May 2007

It is challenge in epidemiology to characterize the temperol aspect of exposure‐disease association. The authors propose a stochastic model to deal with exposures that are time‐dependent and exhibit susceptibility and latency effects. The model is applied to a retrospective cohort data on lung cancer mortality in the blackfoot disease endemic area in Taiwan. The authors compare the proposed model with the multistage model, the back‐calculation model, the catalytic model, and the age‐period‐cohort models.
Correcting for Confounding in Analyzing Receiver Operating Characteristic Curves
Authors: Smith P. J. , Thompson T. J.
Published: May 2007

A method is described for modeling a receiver operating curve as a function of confounding covariates when the outcome of the screening test is a continuous variate. A parametric survival model is proposed for modeling the distribution of the screening test outcome as a function of true disease status and other confounding covariates. The sensitivity and specificity of the screening test at any “cut‐point” along the range of the screening test outcome may be estimated easily from the estimated survival distribution. Confidence intervals and an estimate of the area under the curve are derived.
Construction of Prediction Intervals in Location‐Scale Families
Authors: Kushary Debashis
Published: May 2007

Let x1≤x2≤x3… ≤xrbe thersmallest observations out ofnobservations from a location‐scale family with density\documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{\sigma}f\left({\frac{{x - \mu}}{\sigma}} \right) $\end{document}where μ and σ are the location and the scale parameters respectively. The goal is to construct a prediction interval of the form\documentclass{article}\pagestyle{empty}\begin{document}$ \left({\hat \mu + k_1 \hat \sigma,\,\hat \mu + k_2 \hat \sigma} \right) $\end{document}for a location‐scale invariant function,T(Y) = T(Y1, …, Ym), ofmfuture observations from the same distribution. Given any invariant estimators\documentclass{article}\pagestyle{empty}\begin{document}$ \hat \mu $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma $\end{document}, we have developed a general procedure for how to compute the values ofk1andk2. The two attractive features of the procedure are that it does not require any distributional knowledge of the joint distribution of the estimators beyond their first two raw moments and\documentclass{article}\pagestyle{empty}\begin{document}$ \hat \mu $\end{document}and\documentclass{article}\pagestyle{empty}\begin{document}$ \hat \sigma $\end{document}can be any invariant estimators of μ and σ. Examples with real data have been given and extensive simulation study showing the performance of the procedure is also offered.
On Variograms in Point Process Statistics
Authors: Wälder Olga , Stoyan Dietrich
Published: May 2007

Variograms, which are frequently used in geostatistics, are of value also in the statistics of marked point processes. When the marks come from a random field which is independent of the point process, ideas of geostatistics suffice for the interpretation of point process variograms. When this model is not appropriate, interactions between the points lead to point process variograms having forms which are unusual in geostcistics. This is shown by three theoretical examples and one from forestry.
The Determination of Axis Lengths ofDunaliellafrom the Image Analysis of TEM Sections through Randomly Orientated Cells
Authors: Roessler Jochen , Jones Tim , Bérubé Kelly Ann
Published: May 2007

We present a method which improves the determination of geometric parameters of unicellular organisms with prolate ellipsoid geometry, such asDunaliella. Approximately determined axis lenghts were obtained from transmission electron micrographs of ultrathin sections of microalgae. The density functions generated by these ‘axis lengths’ have poles which can be used to determine the short half axis length and ratio of axis lengths of the ellipsoid in order to determine the true cell volume.
Sensitivity Profiles of Diversity Indices
Authors: Izsák János
Published: May 2007

The author previously described special sensitivity measures for diversity indices. These measures make possible on analytical treatment of the index sensitivity. In the article a detailed analysis of sensitivity properties of the Hurlbert indices is presented. In the first step the abundances nk were sequenced in an increasing order. Plotting the sensitivity against nk or log nk, essential sensitivity properties can be observed. For example, one can study the sensitivities to changes in the dominant and subdominant abundances, the site of the “nearly neutral” abundance and the site of local sensitivity maxima in the domain of the relatively rare categories. The observations are supported by mathematical reasoning.
On the Properties of GEE Estimators in the Presence of Invariant Covariates
Authors: Spiess Martin , Hamerle Alfred
Published: May 2007

Since Liang and Zeger (1986) proposed the ‘generalized estimating equations’ approach for the estimation of regression parameters in models with correlated discrete responses, a lot of work has been devoted to the investigation of the properties of the corresponding GEE estimators. However, the effects of different kinds of covariates have often been overlooked. In this paper it is shown that the use of non‐singular block invariant matrices of covariates, as e.g. a design matrix in an analysis of variance model, leads to GEE estimators which are identical regardless of the ‘working’ correlation matrix used. Moreover, they are efficient (McCullagh, 1983). If on the other hand only covariates are used which are invariant within blocks, the efficiency gain in choosing the ‘correct’ vs. an ‘incorrect’ correlation structure is shown to be negligible. The results of a simple simulation study suggest that although different GEE estimators are not identical and are not as efficient as a ML estimator, the differences are still negligible if both types of invariant covariates are present.
On the Use of the Upper Confidence Limit for the Variance from a Pilot Sample for Sample Size Determination
Authors: Kieser Meinhard , Wassmer Gernot
Published: May 2007

In a recent paper, Browne (1995) investigated the use of a pilot sample for sample size calculation. Monte Carlo simulations indicated that using a 100 · (1 — γ) per cent upper one‐sided confidence limit on the population varíance σ2 leads to a sample size that guarantees the planned power with a probability of at least 1 − γ. The purpose of this paper is to get further insight into the results of Browne by analytical considerations. Furthermore, the expected power is investigated when applying the strategy and recommendations for the choice of the pilot sample size are given.
Efficient Utilization of Auxiliary Information at Estimation Stage
Authors: Bedi P. K.
Published: May 2007

Modified ratio or product estimators are suggested by making use of a very simple linear transformation on the auxiliary variable, which allows for a wider applicability of the modified estimators than that of customary ratio and product estimators.
The Multiple Poisson Distribution, Its Characteristics and a Variety of Forms
Authors: Wimmer Gejza , Altmann Gabriel
Published: May 2007

The multiple Poisson distribution, known under different names, such as generalized Poisson, compound Poisson, composed Poisson, stuttering Poisson, Poisson power series, Poisson‐stopped sum distribution, etc., plays an important role in discrete distribution theory. Here we want to show its basic characteristics, the variety of its forms and specify the generalizing distributions.
Use of Generalised Linear Mixed Models for the Analysis of Clustered Survival Data
Authors: Yau K. K. W. , McGilchrist C. A.
Published: May 2007

Data from a litter matched tumorigenesis experiment are analysed using a generalised linear mixed model (GLMM) approach to the analysis of clustered survival data in which there is a dependence of failure time observations within the same litter. Maximum likelihood (ML) and residual maximum likelihood (REML) estimates of risk variable parameters, variance component parameters and the prediction of random effects are given. Estimation of treatment effect parameter (carcinogen effect) has good agreement with previous analyses obtained in the literature though the dependence structure within a litter is modelled in different ways. The variance component estimation provides the estimated dispersion of the random effects. The prediction of random effects, is useful, for instance, in identifying high risk litters and individuals. The present analysis illustrates its wider application to detecting increased risk of occurrence of disease in particular families of a study population.
Some Tests on a Single Change in Independent Copies of Short Sequences: A Cancer Diagnostic Study
Authors: Faupel M. , Hsu Y. S. , Jin J. , Long D.
Published: May 2007

Testing a single change in mean or variance when the observations arenindependent short sequences has not been fully researched in the literature. Two statistical tests, maxtand modified likelihood radtio, are used in this study. Power comparisons and examples are also given. As expected the modified likelihood ratio test yields the largest power. However, with the assumptions we have in the examples, the maxtmight be the optimal method to use. The maxtmay prove useful in assessing departures from the steady state in which the data are short sequences of diagnostic information.
Parameter Estimation of the Gompertz Population
Authors: Chen Zhenmin
Published: May 2007

The Gompertz distribution has been used to model human mortality and fit actuarial tables. In the recent years, this distribution has been studied by some authors. The MLE estimates for the parameters of the Gompertz distribution were disucssed by GARG, RAO and REDMOND (1970). The purpose of this paper is to develop an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution.
Shrinkage Pre‐Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student‐t Errors
Authors: Khan Shahjahan , Md. Ehsanes Saleh A. K.
Published: May 2007

In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student‐t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.