bluuebunny/crossref_metadata_2025 huggingface dataset:
A Complete Analysis of Variability for Estimates of Absolute Risk from a Population‐Based Case‐Control Study on Breast Cancer
Authors: Benichou Jacques
Published: May 2007

The absolute risk is the probability of developing a given disease over a specified time interval given age and risk factors. GAIL et al. (1989) obtained point estimates for the absolute risk of breast cancer from a population‐based case‐control study, the Breast Cancer Detection and Demonstration Project (BCDDP). They combined relative risk estimates obtained from the case‐control data and based on four risk factors and age, and composite hazard estimates from the cohort data. In this paper, we present a complete analysis of variability for breast cancer absolute risk estimates. Our proposed variance estimator takes into account all components of variability, namely the variances of relative risk estimates and of baseline hazard estimates as well as the covariance between the two, the latter terms being based on implicit delta‐method arguments (BENICHOU and GAIL, 1989). Our variance estimator also takes into account the specifics of the BCDDP study, namely the subsampling of cases and controls. We provide full details of the variance calculations because we anticipate that, in future studies, subsampling will also occur. We also present numerical illustration based on the BCDDP data. These calculations have been used in a recently developed program that computes point estimates and confidence intervals for the absolute risk of breast cancer based on the BCDDP data (BENICHOU, 1993).
Sample Size Calculation for Intraclass Correlation in the Presence of Random Loss of Sampled Patients
Authors: Lui Kung‐Jong
Published: May 2007

When a trial involves an invasive laboratory test procedure or requires patients to make a commitment to follow a restrictive test schedule, we can often lose a great proportion of our sampled patients due to refusal of participation into our study. Therefore, incorporating the possible loss of patients into sample size calculation is certainly important in the planning stage of a study. In this paper, we have generalized the sample size calculation procedure for intraclass correlation by accounting for the random loss of patients in the beginning of a trial. We have demonstrated that the simple ad hoc procedure, that raises the estimated sample size in the absence of loss of patients by the factor 1/po, where po is the retention probability for a randomly selected patient, is adequate when po is large (=0.80). When po is small (i.e., a high refusal rate), however, use of this simple ad hoc procedure tends to underestimate the required sample size. Furthermore, we have found that if the individual retention probability varied substantially among patients, then the magnitude of the above underestimation could even be critical and therefore, the application of the simple direct adjustment procedure in this situation should be avoided.
A Stochastic Model for Surname Evolution
Authors: Islam M.
Published: May 2007

Surnames are inherited in much the same way as biological traits like alleles of one locus. Assuming the heritability of surnames, a simple stochastic model for X, the total number of occurrences of a surname, the Consul distribution defined by the probability mass function:

equation image

for x = 1, 2, 3,… and zero otherwise and where either (i) m is a positive integer when 0 ≤ θ ≤ 1 such that θ ≦ mθ ≦ 1, or (ii) m≤0, θ ≤0 such that mθ 1, can be arrived at by considering the branching process mechanism. Some applications of the model to real data are also considered.
Sensitivity Analysis of Variable‐Size Group Testing and its Related Continuous Models
Authors: Chen C. L. , Swallow W. H.
Published: May 2007

Parallels between the discrete group‐testing model and some closely‐related continuous models are elucidated. It is shown that in both the discrete and continuous cases, the maximum likelihood estimators may suffer from similar lack of robustness. Isotonic regression and maximum likelihood estimation were therefore compared for a modified group testing model.
Optimal Experimental Design and Accuracy of Parameter Estimation for Nonlinear Regression Models Used in Long‐term Selection
Authors: Rudolph P. E. , Herrendörfer G.
Published: May 2007

An experimental design problem is considered for the analysis of long‐term selection experiments with nonlinear regression models. For a 3‐parametric exponential regression function whose parameters have also a reasonable biological interpretation approximate formulas for the determination of the necessary number of observations at each generation are constructed in such a way that the half expected length of an (1 — α)‐confidence interval for a chosen parameter is not greater than a given value. In this sense the accuracy of the parameter estimators can be described.
A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data
Authors: El‐Saidi Mohammed A.
Published: May 2007

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.
The Polynomial Model in the Multivariate Analysis of Variance
Authors: Baumgartner Cornelia
Published: May 2007

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy‐coded or effect‐coded design matrices) the so‐called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.
On the HIV Incubation Distribution Under AZT Treatment
Authors: Tan W. Y.
Published: May 2007

Assuming some general models for the HIV epidemic, in this paper I derive the HIV incubation distributions under AZT treatment. It is shown that under some conditions, these probability distributions are mixtures of some generalized Gamma distributions and products of generalized Gamma distributions.
Removing Cancer when it is Correlated with other Causes of Death
Authors: Carrière Jacques F.
Published: May 2007

This paper presents an identifiability theorem in the theory of dependent competing risks and it applies the result by examining the effect of removing cancer from the United States population when cancer is correlated with the other causes of death. The paper shows how dependence can be modeled with copula functions and it shows that calculating the survival probabilities after cancer is removed is equivalent to solving a system of nonlinear differential equations.
Temporal Analogues to Spatial K Functions
Authors: Cannon Ann , Cressie Noel
Published: May 2007

In this article, the spatial statistic known as the K function is adapted for temporal processes and patterns. The (optimal) K‐function estimator is used in a testing procedure to determine whether behavior patterns of exposed rats versus control rats are different. Specifically, the temporal analogue to the K function is given and an approximately optimal estimator is developed. Next, a testing procedure, to determine whether a group of point patterns is generated from complete temporal randomness, is given. Finally, a testing procedure, to compare pairwise two groups of point patterns to each other, is given. The testing procedures are illustrated with rat‐behavior data from both a control‐control experiment as well as an exposed‐control experiment, where in the latter case a difference in behavior is known to exist.
Linear Rank Tests Derived from a Superpopulation Model
Authors: Bouza Carlos
Published: May 2007

A superpopulation model generates the probabilities of a Bernouilli random variable. The ranks of the involved variables are considered as survey weights. The distribution f each linear rank statistic is derived under the null hypothesis for the two sample problem and for the case k2 when a simple random sampling or stratified sampling is used.

The growth of a population of insects and the behavior of patients with imsomnia are studied using these procedures.
Subset Selection for Exponential Populations: Determination of the Selection Constant
Authors: van der Laan Paul
Published: May 2007

Given are k(≧2) exponential populations differing only in their location parameter. One wishes to choose the best one, that is the population with the largest value of the location parameter. A possible method for solving this problem is to select a subset of the k populations of size at least one which includes the best population with a required confidence P*(k−1 ≤ P* ≤1). In this paper the required selection constant is determined for different values of k and P*. Also an approximation for the selection constant is derived. A comparison with the exact results is made.
Testing Quasi‐Independence in Stratified Triangular Contingency Tables
Authors: May Warren L. , Johnson William D.
Published: May 2007

A special class of incomplete contingency tables has structural zeroes in one or more cells. Some of these tables have a triangular appearance in the sense that they are square and their cells are known a priori to contain zeroes above (or below) their main diagonals. We propose methods of analyzing log‐linear models and testing quasi‐independence in these triangular tables. We also offer a method for combining such tables that are stratified by a concomitant categorical variable. This strategy follows the same approach used in a Cochran‐Mantel‐Haenszel test.
Generalized Binomial Regression Model
Authors: Famoye Felix
Published: May 2007

The generalized negative binomial distribution has been found useful in fitting over‐dispersed as well as under‐dispersed count data. We define and study the generalized binomial regression model which is used to predict a count response variable affected by one or more explanatory variables. The methods of maximum likelihood and moments are given for estimating the model parameters. Approximate tests for the adequacy of the model are considered. The generalized binomial regression model has been applied to two observed data sets to which binomial regression model was applied earlier.
Improved Shrinkage Estimation of Relative Potency
Authors: Ahmed S. Ejaz
Published: May 2007

This article considers the asymptotic estimation theory for the log relative potency in a symmetric parallel bioassay when uncertain prior information about the true log relative potency is assumed to be a known quantity. Three classes of point estimation, namely, the unrestricted estimator, the shrinkage restricted estimator and shrinkage preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators is presented. Interestingly, proposed shrinkage preliminary test estimator dominates the unrestricted estimator in a range that is wider than that of the usual preliminary test estimator. Most importantly, the size of the preliminary test is much appropriate than the usual preliminary test estimator.
Parameters Estimation in a Simple Linear Regression Using Rank Set Sampling
Authors: Muttlak Hassen A.
Published: May 2007

Ranked set sampling (RSS) as suggested by MCINTYRE (1952) and TAKAHASI and WAKIMOTO (1968) may be used to estimate the parameters of the simple regression line. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the slope and intercept are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.
Additive and Non‐additive Genetic Correlations. I. Properties of Sampling Distributions
Authors: Hohls Trevor , Clarke G. P. Y.
Published: May 2007

The sampling distributions of additive and non‐additive genetic correlations estimated from a diallel experiment were determined through a computer simulation study. The properties of the sampling distributions were investigated in terms of the effect of varying the magnitude of the relevant variance components and the true correlation coefficient (Q), as well as the size of the diallel experiment. It was found that there was a high incidence of Q falling outside the range −1 ≦Q≦1 when Q was close to 1 or ‐1, and the variance components were small. The degrees of freedom of the correlation components were shown to affect the variability of Q, and it was shown that a diallel experiment, that is to be used for a correlation analysis, should not be smaller than a 12 × 12 half diallel. Use of the Z transformation as a means of testing the significance of Q has been verified in this study and improvements on the degrees of freedom used for the transformation have been discussed.
A Multivariate Goodness‐of‐Fit Test for Stochastically Ordered Distributions
Authors: Alam Khursheed , Williams Calvin L.
Published: May 2007

There are a number of nonparametric procedures known for testing goodness‐of‐fit in the univariate case. Similar procedures can be derived for testing goodness‐of‐fit in the multivariate case through an application of the theory of statistically equivalent blocks (SEB). The SEB transforms the data into coverages which are distributed as spacings from a uniform distribution on [0,1], under the null hypothesis. In this paper, we present a multivariate nonparametric test of goodness‐of‐fit based on the SEB when the multivariate distributions under the null hypothesis and the alternative hypothesis are “weakly” ordered. Empirical results are given on the performance of the proposed test in an application to the problem of assessing the reliability of ap‐component system.
Spatial Mark‐Recapture Method in the Estimation of Crayfish Population Size
Authors: Partanen Päivi , Penttinen Antti
Published: May 2007

The mark‐recapture method is considered for estimation of population size of slowly moving animals like crayfish. The Petersen type estimator for closed population is generalized for situations where recaptures are spatially dependent between the capture sites, and its variance approximation is derived using point processes as models for the population. The method of quadratic forms is suggested to be used as variance estimator. Finally, a trapping design is proposed where one trap at recapture is replaced by four adjacent traps. A simulation experiment is performed to explain the robusticity of the new trapping design against movements of animals.
Structural Changes in the Relationships of Body Dimensions of Four Species of Pulmonate Slugs (Mollusca : Gastropoda : Pulmonata)
Authors: Bhuyan Keshab Chandra , Nair G. Achuthan
Published: May 2007

Four species of pulmonate slugsviz. Milax rusticus, Milax sowerbyi, Milax gagatesandLimax tenellusare colonised along the north eastern region of Libya. These slugs are homogeneous in character since they belong to the same class and order. However, their body dimensions were significantly different. Significant positive relationships existed on most of the body dimensions of each species and these relationships were found to be heterogeneous among the four species studied.
On the Power of Fisher's Combination Test for Two Stage Sampling in the Presence of Nuisance Parameters
Authors: Banik N. , Köhne K. , Bauer P.
Published: May 2007

Combination tests for p‐values are used in meta‐analysis and in multistage testing with adaptive designs (Bauer & Köhne, 1993). The well known combination test due to Fisher is based on the products of p‐values. The power of this test applied to p‐values found from stochastically independent samples at two stages of an experiment is calculated. The probability models assumed correspond to the classical t‐tests for paired comparisons and parallel groups. The loss of power as compared to the optimal t‐tests in the pooled sample is small even for moderate sample sizes differing over stages, however, with one exception: If in the case of parallel groups the sample sizes are substantially unbalanced over treatments, then the combination of two tests with a nonoptimal sample size allocation exaggerates the loss of power.
Fitting Mixed Poisson Regression Models Using Quasi‐Likelihood Methods
Authors: Chen James J. , Ahn Hongshik
Published: May 2007

This paper is to investigate the use of the quasi‐likelihood, extended quasi‐likelihood, and pseudo‐likelihood approach to estimating and testing the mean parameters with respect to two variance models, M1: φ μθ(1+μphis;) and M2: φ μθ(1+τ). Simulation was conducted to compare the bias and standard deviation, and type I error of the Wald tests, based on the model‐based and robust variance estimates, using the three semi‐parametric approaches under four mixed Poisson models, two variance structures, and two sample sizes. All methods perform reasonably well in terms of bias. Type I error of the Wald test, based on either the model‐based or robust estimate, tends to be larger than the nominal level when over‐dispersion is moderate. The extended quasi‐likelihood method with the variance model M1 performs more consistently in terms of the efficiency and controlling the type I error than with the model M2, and better than the pseudo‐likelihood approach with either the M1 or M2 model. The model‐based estimate seems to perform better than the robust estimate when the sample size is small.
A Note on Response to Selection in Non‐Random Mating Populations
Authors: Nomura T.
Published: May 2007

The selection theory proposed by Muralidharan and Jain (1992a, b; Biom. J. 34, 147–152, 633–637) was re‐examined. Although they concluded that the theory is appropriate for any system of mating, the author showed that it is not applicable to inbreeding populations, which is the most important type of non‐random mating.
Incorporating Surrogate Endpoints into Group Sequential Trials
Authors: Cook Richard J. , Farewell Vern T.
Published: May 2007

Recent developments proposed by Lin (1991) which allow for the sequential analysis of multivariate failure time data, are discussed in the context of clinical trials with marker process data. In particular, a marker based response observed as a univariate failure time variable is considered in a univariate manner and in combination with the primary failure time variable through global measures of treatment effect. A weighting scheme is introduced that is designed to make greater use of the marker process responses when they are consistent with the responses for the primary endpoint.

Univariate analyses and analyses based on global test statistics are evaluated with respect to duration of study and type I and type II error rates for a variety of relative risk parameter configurations. The simulation study is designed to extend the work of Machado, Gail and Ellenberg (1990) to sequential trials and to assess the performance of the global test statistics in this context. The global measures are found to be preferable over the univariate primary endpoint analyses when the treatment affects all transition intensities in a consistent manner. Further, there are advantages over the univariate marker based analysis when the treatment effects on some transition intensities are in opposite directions. Such a scenario remains problematic however with the relative error rates determined to a large extent by the baseline weighting scheme.
A Model for the Censoring Process in Incomplete Repeated Measurement Experiments
Authors: Ducharme Gilles R. , Lepage Yves
Published: May 2007

Premature terminations or dropouts occur often in repeated measurement experiments. A number of methods have been proposed to analyze such data but most of them assume that the censoring mechanism is, within each group, unaffected by the mechanism generating the response variables. In this paper, we propose a model for the censoring mechanism that generates dropouts. We then show how this model can be used to check whether the censoring mechanism is affected by the response variables and other covariates. Finally, the methods of the paper are applied to the “Halothane” data set.
Weighting Class Importance in Agricultural Crop Classification from Remotely Sensed Data with an Artificial Neural Network
Authors: Foody G. M.
Published: May 2007

In some classifications the importance of classes varies and it is desirable to weight allocation to selected classes. This is common in classifications of remotely sensed imagery, especially as class occurrence can vary markedly. If, for instance, there is prior knowledge on the distribution of class occurrence this weighting can be achieved with widely used statistical classifiers by setting appropriate a priori probabilities of class membership. With an arificial neural network the incorporation of prior knowledge is more problematic. An approach to weight class allocation in an artificial neural network classifcation by replicating selected training patterns is discussed. In comparison against a discriminant analysis for the classification of synthetic aperture radar imagery the results showed that training pattern replication could be used to weight class allocation with an effect similar to that of incorporating a priori probabilities of class membership into the discriminant analysis and resulted in a significant increase in classification accuracy.
Notes on Confidence Limits for the Odds Ratio in Case‐Control Studies under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

When the disease of interest is rare or chronic, we often apply the case control study design and the odds ratio to determine the possibly risk factors. In this paper, three simple closed‐form interval calculation procedures for the odds ratio under inverse sampling are proposed. Results on the basis of a Monte Carlo simulation to evaluate and compare the performance of these three procedures are presented. A discussion on the limitation of the proposed procedures when the probability of exposure is extremely common in both the case and the control groups and a suggestion to overcome this limitation are included as well.
Confidence Limits for the Intraclass Correlation in Compound‐Poisson Sampling
Authors: Lui Kung‐Jong , Kuo Lynn
Published: May 2007

When the underlying responses are discrete, the interval estimation of the intraclass correlation derived from the normality assumption is not strictly valid for use. This paper focuses the interval estimation on the intraclass correlation under the negative binomial distribution, that has been commonly applied in epidemiological or consumer purchasing behaviour studies. This paper develops two simple asymptotic interval estimation procedures in closed forms for the intraclass correlation. To evaluate the performance of these procedures, a Monte Carlo simulation is carried out for a variety of situations. An example about consumer purchasing behaviors is also included to illustrate the use of the two proposed interval estimation procedures.
Hypothesis Testing Procedures for a Series of Independent Fourfold Tables under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

This paper considers four summary test statistics, including the one recently proposed by Bennett (1986, Biometrical Journal 28, 859–862), for hypothesis testing of association in a series of independent fourfold tables under inverse sampling. This paper provides a systematic and quantitative evaluation of the small‐sample performance for these summary test statistics on the basis of a Monte Carlo simulation. This paper notes that the test statistic developed by Bennett (1986) can be conservative and thereby possibly lose the power when the underlying disease is not rare. This paper also finds that for given a fixed total number of cases in each table, the conditional test statistic is the best in controlling type I error among all test statistics considered here.
Linear Rank Statistics for the Simple Tree Alternatives
Authors: Desu M. M. , Park S. , Chakraborti S.
Published: May 2007

The problem of comparing several treatments with a control is considered. It is formulated as a test of homogeneity with one‐sided alternatives that at least one treatment is better than the control, while no treatment is worse than the control. A class of linear rank tests for the simple tree alternatives is proposed, assuming a location model. The most efficient test of the proposed class for detecting a specified pattern is derived. Two optimal tests for use in the case of vaguely specified tree alternatives are derived. In a simulation study the power of these two tests are compared with the power of Kruskal‐Wallis test. Recommendations about the use of the proposed tests are made.
On the Power Behaviour of Läuter's Exact Multivariate One‐sided Tests
Authors: Frick H.
Published: May 2007

Recently Läuter [1996] developed a new class of parametric tests for the one‐sided multivariate hypothesis with unknown covariances. Unlike most procedures for this problem, Läuter's tests are exact, i.e. they strictly maintain the nominal level. In this paper two scale invariant Läuter tests are considered, the standardized sum and the principal component test. Here conditions are investigated under which the powers of these tests are insufficient for arbitrarily large alternatives and, for the second test, also for unbounded sample sizes. It turns out that power insufficiencies can happen only at the boundary of the set of alternatives so that for alternatives usually occurring in biometrical practice both tests prove to be efficient.
A Multivariate Procedure for Comparing Mean Vectors for Populations with Unequal Regression Coefficient and Residual Covariance Matrices
Authors: Misra R. K.
Published: May 2007

In fisheries research there is a need to compare vectors of means of continuous random response variables adjusted for concomitant variations of covariables for populations that have unequal regression coefficient and residual covariance matrices. A multivariate procedure that provides an extended comparison of vectors of adjusted means is presented. An example is presented using a real data set. The procedure is quite general and applicable to many other fields of research.
Estimation of a Generalized Linear Mixed‐Effects Model with a Finite‐Support Random‐Effects Distribution via Gibbs Sampling
Authors: Leung Moon K. , Elashoff Robert M.
Published: May 2007

We discuss a Bayesian hierarchical generalized linear mixed‐effects model with a finite‐support random‐effects distribution and show how Gibbs sampling can be used for estimating the posterior distribution of the parameters and for clustering on the basis of longitudinal data. When directly sampling from the conditional distributions is laborious, the adaptive rejection sampling (ARS, Gilks and Wild, 1992; Gilks, 1992) algorithm or adaptive rejection Metropolis sampling (ARMS, Gilks et al., 1995) algorithm is used. Log‐concavity, a prerequisite of ARS, of the conditional distributions is examined. We also discuss a Bayesian solution to the uncertainty of the support size of the random‐effects distribution in statistical inference. The methodology is illustrated with an analysis of data from a study of regulation of serum parathyroid hormone secretion.
Dynamic Trends in Distributions
Authors: Voit Eberhard O.
Published: May 2007

Transformations of distributions belong to the standard repertoire of theoretical statistics, if they are given as explicit, algebraic functions. In practical applications, transformations are often not given explicitly, however, but as processes that are best described as solutions of ordinary differential equations. The paper describes how trends in distributions can be computed under such conditions. It begins with a description of the method, illustrates it with didactic examples, and applies the method to the accumulation of mercury in king mackerel (Scomberomorus cavalla). A brief discussion alludes to limitations and to other potential application areas.
A Class of Multivariate Survival Functions Characterized by Minimum and Marginal Distribution
Authors: Ma Chunsheng
Published: May 2007

This paper characterizes a class of multivariate survival functions in terms of the minimum and marginal distributions.
Detection of Cyclic Trends in Incidence Data Using the Efficiency Score Method
Authors: Nam Jun‐Mo
Published: May 2007

In studies involving a cyclic regularity, researchers usually have a good working knowledge regarding the peak time in the cycle. Capitalizing on this information, we derive the asymptotically uniformly most powerful unbiased test for detecting a cyclic trend using the likelihood score, and present the asymptotic power function of the test and the approximate formula for sample size. Numerical studies demonstrate great advantages of the proposed test over the standard test in terms of power and sample size. Asymptotic power of the score test is satisfactorily close to actual power. We also generalize this method so that it is applicable for incidence data from unequally spaced intervals or risk populations of unequal size.
Predictors for Seasonal and Nonseasonal Fractionally Integrated ARIMA Models
Authors: Peiris M. Shelton , Singh N.
Published: May 2007

This paper derives easy‐to‐calculate preditors for seasonal and nonseasonal fractionally integrated autoregressive‐moving average (ARIMA (p, d, q) × (P, D, Q)s) models with both differencing parametersdandDassuming values on the real line. It is shown that these predictors are optimum. Special attention is given to the one‐step‐ahead predictors as they are constantly in demand in almost every practical situation.
Estimating the Weighting Components of a Health Quality Index
Authors: Jeong Jinook , Mauldin Patrick D.
Published: May 2007

This paper introduces a maximum likelihood estimation model that uses patients' pretherapy characteristics to determine the weighting components of multipe outcomes of quality health. The resulting health quality index' can then be included in cost‐effectiveness analyses to compare alternative treatment plans. A Monte Carlo simulation is performed to test the model's robustness and power.
Testimation in Regression Parameter Estimation
Authors: Rahman Mezbahur , Gokhale D. V.
Published: May 2007

Testimation is considered in the problem of estimation of regression parameters. The first stage sample is used to test a (null) hypothesis that specifies initial (preassumed) values for some of the regression parameters. Linear combination of the preassumed values and the ordinary least square (OLS) estimates is considered as the estimate if the data agree with the hypothesis. Otherwise, a second sample is taken and parameters are estimated only by using OLS, based on the combined sample. The procedure protects against type II error and against taking larger samples when inference can be made from a smaller sample.
Predictive Performance of the Methods of Restricted and Mixed Regression Estimators
Authors: Toutenburg H. , Shalabh
Published: May 2007

This article considers the problem of simultaneous prediction of actual and average values of the study variable in a linear regression model when a set of linear restrictions binding the regression coefficients is available, and analyzes the performance properties of predictors arising from the methods of restricted regression and mixed regression besides least squares.
The Residual Likelihood Ratio Test for the Variance Ratio in a Linear Model with Two Variance Components
Authors: Li Yulan , Birkes David , Thomas David R.
Published: May 2007

Residual maximum likelihood has proved to be a successful approach to the estimation of variance components. In this paper, its counterpart in testing, the residual likelihood ratio test, is applied to testing the ratio of two variance components. The test is compared with the Wald test and the locally most powerful invariant test.
Biased Estimation of Adjusted Odds Ratios from Incomplete Covariate Data Due to Violation of the Missing at Random Assumption
Authors: Vach Werner , Illi Sabina
Published: May 2007

We investigate the possible bias due to an erroneous missing at random assumption if adjusted odds ratios are estimated from incomplete covariate data using the maximum likelihood principle. A relation between complete case estimates and maximum likelihood estimates allows us to identify situations where the bias vanishes. Numerical computations demonstrate that the bias is most serious if the degree of the violation of the missing at random assumption depends on the value of the outcome variable or of the observed covariate. Implications for the analysis of prospective and retrospective studies are given.
Bayesian Testing of Relative Mortality, with Application to Occupational Cohort Studies
Authors: Giudici Paolo , Crosignani Paolo
Published: May 2007

An important issue in epidemiology, often exploratory, is to compare the mortality of a certain cohort, exposed to some dangerous conditions, to that of a reference population. The main statistical tool to study relative mortality has long been the subject‐years method.

We propose a Bayesian version of the subject‐years method, particularly suited to analyse the mortality of small cohorts. In particular, we employ the Bayes factor in order to test whether the mortality of a cohort exceeds that of a reference population. The methodology is applied to an occupational epidemiology study. The results are compared to those obtained from the classical one‐sided tests on the same data.
A General Framework for Longitudinal Data through Marked Point Processes
Authors: Scheike Thomas H.
Published: May 2007

This paper reviews a general framework for the modelling of longitudinal data with random measurement times based on marked point processes and presents a worked example. We construct a quite general regression models for longitudinal data, which may in particular include censoring that only depend on the past and outside random variation, and dependencies between measurement times and measurements. The modelling also generalises statistical counting process models. We review a non‐parametric Nadarya‐Watson kernel estimator of the regression function, and a parametric analysis that is based on a conditional least squares (CLS) criterion. The parametric analysis presented, is a conditional version of the generalised estimation equations of LIANG and ZEGER (1986). We conclude that the usual nonparametric and parametric regression modelling can be applied to this general set‐up, with some modifications. The presented framework provides an easily implemented and powerful tool for model building for repeated measurements.
Measurement of Diversity and Dissimilarity for Stochastic Populations
Authors: Adke S. R. , Ratnaparkhi M. V.
Published: May 2007

The existing measures of diversity within a population and of dissimilarity between two populations postulate a static population with unchanging probabilistic structure. We assume that the measurements associated with an individual change with time according to a stochastic process. General measures of diversity and of dissimilarity when the underlying process is a finite Markov chain are developed. An aportionment of these measures based on a partition of the state‐space is provided. Their asymptotic behaviour is investigated. The spectral analysis of measures of diversity is carried out. Some specific measures of diversity and dissimilarity are obtained when the underlying stochastic process is a general vector‐valued process. An indication of directions for future work is provided.
On the Efficiency of Nearest Neighbour Balanced Block Designs with Correlated Error Structure
Authors: Santharam C. , Ponnuswamy K. N.
Published: May 2007

Nearest Neighbour Balanced Block Designs (NNBD) are widely used in biological and industrial experiments. In this article we examine the optimality and efficiencies of NNBD under various correlated error structure models. A numerical comparison of NNBD with regular block design (RBD) is also presented.
A Note on the Bias of O'Brien's OLS Test
Authors: Frick Hans
Published: May 2007

O'Brien's Ordinary Least Squares (OLS) test is a well known procedure for testing the multivariate one‐sided hypothesis when the covariance matrix is unknown. Simulation results have been reported where the actual test level exceeds the nominal one. Here it is shown analytically that the actual level is always larger than the nominal one if the covariance matrix is nonnegative.
Conditional Maximum Likelihood Estimate and Exact Test of the Common Relative Difference in Combination of 2 × 2 Tables under Inverse Sampling
Authors: Lui Kung‐Jong
Published: May 2007

On the basis of the conditional distribution, given the marginal totals of non‐cases fixed for each of independent 2 × 2 tables under inverse sampling, this paper develops the conditional maximum likelihood (CMLE) estimator of the underlying common relative difference (RD) and its asymptotic conditional variance. This paper further provides for the RD an exact interval calculation procedure, of which the coverage probability is always larger than or equal to the desired confidence level and for investigating whether the underlying common RD equals any specified value an exact test procedure, of which Type I error is always less than or equal to the nominal α‐level. These exact interval estimation and exact hypothesis testing procedures are especially useful for the situation in which the number of index subjects in a study is small and the asymptotically approximate methods may not be appropriate for use. This paper also notes the condition under which the CMLE of RD uniquely exists and includes a simple example to illustrate use of these techniques.
A Clinically Orientated Approach for Combining Discordant and Concordant Sib Pairs
Authors: Ziegler Andreas , Hebebrand Johannes , Schäfer Helmut
Published: May 2007

The use of extreme discordant sib pairs (EDSP) or extreme concordant sib pairs (ECSP) has recently been proposed to increase power for mapping quantitative traits in humans (RISCH and ZHANG, 1995, 1996). In this paper we propose a test statistic to jointly analyze EDSP and ECSP based on a clinical sampling procedure. This test statistic does not fulfill any optimality criteria. However, this approach is useful for quantitative traits of clinical significance for which EDSP are rare and/or expensive to ascertain. We show how sample size calculations can be adjusted for recombination using single markers, multipoint analysis, incompletely polymorphic markers and varying proportions of ECSP. If the true genetic model is unknown, the combined approach appears to be more robust than sampling based on only EDSP or only ECSP. We discuss how to find the optimal proportion of EDSP and ECSP to be included in an analysis under power considerations.
Estimation of Variance Components Based on a Diallel Model Involving Maternal and Maternal Interaction Effects
Authors: Venkateswarlu K.
Published: May 2007

For a diallel model (TOPHAM, 1966) estimators of variance components are obtained by adopting the general approach outlined by SEELY (1969, 1970, 1971), SEELY and ZYSKIND (1971) and YUAN (1977) in the case of unbalanced data.
Significance Levels of Randomization Trend Tests in the Event of Rare Occurrences
Authors: Chen James J. , Kodell Ralph L. , Pearce Bruce A.
Published: May 2007

In the statistical evaluation of data from a dose‐response experiment, it is frequently of interest to test for dose‐related trend: an increasing trend in response with increasing dose. The randomization trend test, a generalization of Fisher's exact test, has been recommended for animal tumorigenicity testing when the numbers of tumor occurrences are small. This paper examines the type I error of the randomization trend test, and the Cochran‐Armitage and Mantel‐Haenszel tests. Simulation results show that when the tumor incidence rates are less than 10%, the randomization test is conservative; the test becomes very conservative when the incidence rate is less than 5%. The Cochran‐Armitage and Mantel‐Haenszel tests are slightly anti‐conservative (liberal) when the incidence rates are larger than 3%. Further, we propose a less conservatived method of calculating the p‐value of the randomization trend test by excluding some permutations whose probabilities of occurrence are greater than the probability of the the observed outcome.
Crockett's Test of Fit for the Bivariate Poisson
Authors: Best D. J. , Rayner J. C. W.
Published: May 2007

An improved version of the test of CROCKETT (1979) for testing for the bivariate Poisson distribution is given and evaluated.
Extended Poisson Process Modelling and Analysis of Count Data
Authors: Faddy M. J.
Published: May 2007

It is shown that any discrete distribution with non‐negative support has a representation in terms of an extended Poisson process (or pure birth process). A particular extension of the simple Poisson process is proposed: one that admits a variety of distributions; the equations for such processes may be readily solved numerically. An analytical approximation for the solution is given, leading to approximate mean‐variance relationships. The resulting distributions are then applied to analyses of some biological data‐sets.
Sample Size Determination for Designing a Strata‐Matched Case‐Control Study to Detect Multiple Risk Factors
Authors: Nam Jun‐Mo
Published: May 2007

Investigations of sample size for planning case‐control studies have usually been limited to detecting a single factor. In this paper, we investigate sample size for multiple risk factors in strata‐matched case‐control studies. We construct an omnibus statistic for testing M different risk factors based on the jointly sufficient statistics of parameters associated with the risk factors. The statistic is non‐iterative, and it reduces to the Cochran statistic when M = 1. The asymptotic power function of the test is a non‐central chi‐square with M degrees of freedom and the sample size required for a specific power can be obtained by the inverse relationship. We find that the equal sample allocation is optimum. A Monte Carlo experiment demonstrates that an approximate formula for calculating sample size is satisfactory in typical epidemiologic studies. An approximate sample size obtained using Bonferroni's method for multiple comparisons is much larger than that obtained using the omnibus test. Approximate sample size formulas investigated in this paper using the omnibus test, as well as the individual tests, can be useful in designing case‐control studies for detecting multiple risk factors.
Estimation of Residual Valve Gradient from Incomplete Data with Outliers
Authors: Chen Chao L. , Fernandez Javier , McGrath Lynn B.
Published: May 2007

An important indicator for the long‐term recovery after valve replacement surgery is postoperative valve gradient. This information is available only for patients received catheterization or echocardiogram postoperatively. It is plausible that sicker patients are more inclined to undergo these postoperative procedures and their valve gradients tend to be higher. Under this situation, ignoring the missing values and using sample mean based on the available information as an estimate of the whole study population leads to overestimation. Regression estimator is a reasonable choice to eliminate this bias if independent (explanatory) variables closely associated with both residual valve gradient and non‐response mechanism can be identified. Using a series of patients receiving St. Jude Medical prosthetic valves, we found that valve area index can be used as an independent variable in the regression estimator. Two digressions from the standard assumptions used in linear regression, heteroscedastic trend of the error term and outliers were found in the data set. Iteratively reweighted least square (IRLS) was adopted to handle heteroscedasticity. Influence function approach was used to evaluate the sensitivity of outliers in regression estimator. Under an equal response rate mechanism, IRLS not only solves the problem of heteroscedasticity, but is also less sensitive to outliers.
Simple Correspondence Analysis of Ordinal Cross‐Classifications Using Orthogonal Polynomials
Authors: Beh Eric J.
Published: May 2007

A method is developed that caters for the application of correspondence analysis to two‐way contingency tables with one and two ordered sets of categories. The method involves calculating orthogonal polynomials of the type described by EMERSON (1968), and partitioning the chi‐square statistic using the method described in LANCASTER (1953). The method has all the features of simple correspondence analysis, although allows for additional information about the structure and association of the data to be made by isolating location, dispersion and higher order components of the rows and columns.
Stereological Implications of the Geometry of Cones
Authors: Gual‐Arnau X.
Published: May 2007

Given a cone around a curve β in IR3it is shown that there is no relation between the curvature of β and the volume of the cone but, in contrast to the volume, the surface area of the cone depends, albeit rather weakly, on the curvature of β. The geometric meaning of the stereological formulae when applied to cones is considered and it is noted that stereological methods to estimate the surface area of a cone need to be extremely precise to provide information concerning curvature or tortuosity.
A Coefficient of Agreement Adjusted for Bias in Paired Ordered Categorical Data
Authors: Svensson Elisabeth , Svensson Elisabeth
Published: May 2007

The quality of ordered categorical recordings is determined from repeated measurements on the same subject in order to assess the level of agreement between raters, scales or occasions. The presented rating‐invariant method for ordered categorical data provides means of analysing the quality of single‐item rating scales, irrespective of the number of possible response values and the marginal distributions. Marginal heterogeneity implies systematic disagreement, so‐called bias. An augmented ranking approach is the basis for the separation of inter‐rater disagreement into systematic and random components. Correlation between pairs of augmented rank values provides a measure of agreement to the best common ordering of paired classifications, given inter‐rater bias. The essential differences in interpretation and applicability of the proposed coefficient of agreement and the Spearman rank‐order correlation for ordered categorical data are discussed.
On a Birth‐and‐Death Process Induced Distribution
Authors: Zheng Qi
Published: May 2007

A type of distribution induced by the linear birth‐and‐death processes is useful in modeling certain biological phenomena. In addition to extending some existing results, new findings are presented concerning the mathematical properties of the distribution.
Adjustment of Prediction Intervals in Nonlinear Regression
Authors: Goh K. L. , Pooi A. H.
Published: May 2007

By treating the nonlinear model as if it were linear in the parameterization θ in the neighbourhood of the least squares estimate θC, two‐sided nominally‐q‐prediction intervals can be constructed by applying the usual linear model theory. The quadratic approximation of the expected coverage of the prediction intervals is derived for ap‐parameter nonlinear model. An adjustment of the nominally‐q‐prediction intervals is proposed. It is shown that, to the extent that quadratic approximation is adequate, the actual expected coverage of the adjusted prediction intervals isq.