bluuebunny/crossref_metadata_2025 huggingface dataset:
Testing Equality of Means in the Presence of Correlation and Missing Data
Authors: Bhoj Dinesh S.
Published: May 2007

A statistic, derived from the combination of two dependent tests, is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one or both variates. The null distribution of the statistic is approximated by a well‐known distribution. The empirical powers of the statistic are computed and compared with some of the known statistics. The comparisons support the use of the proposed test.
Generalized Rank Transformations for Tests of Survival
Authors: Schemper Michael
Published: May 2007

The asymptotic equivalence of nonparametric tests and parametric tests based on rank‐transformed data (CONOVER and IMAN, 1981) can be extended to the case of censoring. This paper presents generalized rank transformations for analyses of censored data, of interval‐censored data and of survival data with uncertain causes of death. A Monte Carlo study and an analysis of leukemia remission times demonstrate excellent agreement of suggested procedures with GEHAN'S (1965) and PRENTICE'S (1978) tests.
Some Adaptive Robust Estimators which Work with Real Data
Authors: Hill N. J. , Padmanabhan A. R.
Published: May 2007

An adaptive R‐estimator θA and an adaptive trimmed mean MAT are proposed. The performance of these and a number of other robust estimators are studied on real data sets, drawn from the astronomical, behavioural, biomedical, chemical, engineering and physical sciences. In the case of sets that can be assumed to have come from symmetric distributions, the best performer is θA. The next best performers are the Hodges‐Lehmann estimator, Bisquare (7.5) and Huber (1.5), in that order. MAT works well with all kinds of sets–symmetric or skewed. Extensions of these results to ANOVA and regression models are mentioned.
Designs Suited for Varietal Trials with Multiple Basals
Authors: Jain R. C. , Das M. N.
Published: May 2007

DAS (1960) gave a method of construction of confounded balanced asymmetrical factorial designs of the type v × 22 by using BIB designs. In the present paper a method has been given for construction of balanced asymmetrical factorial designs of the type (v–t) × 22 by using truncated balanced incomplete block designs obtainable by omitting t treatments. Likewise, partially balanced asymmetrical factorial designs can also be obtained by omitting any particular treatment alongwith its first or second associate treatments from the v treatments of a PBIB design. We can get a large number of new designs not available in literature through this technique. These designs are well suited for varietal trials with multiple basals.
Error Normality Testing in a Two‐way Split‐plot Design
Authors: Wagner Wieslaw , Brzeskwiniewicz Henryk
Published: May 2007

Following the principle of DURBIN (1961) a test statistic is determined from the transformed observable and generated random variables.
A Theoretical Basis for Gompertz'S Curve
Authors: Makany Roger
Published: May 2007

GOMPERTZ'S model (1825) has remained a purely empirical one, despite its frequent usage. A theoretical justification is given which permits its employment in cases of accretionary growth.
Restricted BLUP for Mixed Linear Models
Authors: McGilchrist C. A. , Aisbett C. W.
Published: May 2007

A new estimation procedure for mixed regression models is introduced. It is a development of Henderson's best linear unbiased prediction procedure which uses the joint distribution of the observed dependent random variables and the unknown realisations of the random components of the model. It is proposed to replace the likelihood of the observations given the random components by the asymptotic likelihood of the maximum likelihood estimators and the prior distribution of the random components by a restricted prior distribution which is consistent with the usual restrictions placed on the random components when they are considered conditionally fixed.
A General Theory of Life Table Construction and a Precise Abridged Life Table Method
Authors: Hsieh John J.
Published: May 2007

In this paper we lay the foundation of life table construction by unifying the existing life table methods. We also present a new method of constructing current (period) abridged life tables. The proposed method produces more life talbe functions than other existing methods do. The development includes (1) a careful formulation and computation of age‐specific death rates, (2) derivation of a new set of formulas for computing the survivorship function from the observed age‐specific death rates and populations, (3) estimation of the main life table functions by spline interpolation, integration and differentiation, and (4) use of a quadratic and a Gompertz function to close the life table. The new abridged life table method features (i) improved accuracy, (ii) tolerance to observed age distributions with bulges and dents and (iii), together with the infant life table method of HSIEH (1985), coverage of the whole life span. The method is illustrated with construction of abridged life tables using Canadian data.
Comparing Survival Curves Using Rank Tests
Authors: Albers W.
Published: May 2007

Survival times of patients can be compared using rank tests in various experimental setups, including the two‐sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated.
Approximate Confidence Bounds for Ripley's Statistic for Random Points in a Square
Authors: Koen Chris
Published: May 2007

Confidence envelopes for Ripley'sLfunction forNrandom points in the unit square were obtained by simulation. The 90, 95 and 99th percentiles of 1000 simulations are given in tabular form forNin the range 10 to 350. Results for a number of choices of the maximum interpoint distance are reported.
A Simple Testing Procedure “Control versus k Treatments” for One‐sided Ordered Alternatives, with Application in Toxicology
Authors: Hothorn L. , Lehmacher W.
Published: May 2007

A simple testing procedure “control versus k treatments” for one‐sided ordered alternatives for univariate, continuous variables is given. With a simulation study both the first kind risk a and the power behaviour under several distributions, expected value profiles, sample sizes and a levels are shown.
Estimating the Tumour Onset Distribution Using Kernel Estimators
Authors: Schäbe H.
Published: May 2007

Kernel estimators are used to obtain new estimators for the tumour onset distribution and its density. Asymptotical properties of the estimators are studied and confidence tests are constructed.
Sampling Schemes for Studying Growth of Children
Authors: Singh Padam , Yadav R. J.
Published: May 2007

Efficiency of linked cross‐sectional scheme has been compared with pure longitudinal schemes for generalised estimation of norm relaxing the condition of constancy of variances. The relevant theory of estimation has been developed and the expression for the optimum estimators alongwith their variances have been derived. The percentage gain in efficiency has been calculated. It has been observed that for higher values of Q, percentage gain in efficiency of proposed scheme over cross‐sectional is very high.
Linked Cross Sectional Schemes for Estimating Growth of Children
Authors: Singh Padam , Yadav R. J.
Published: May 2007

For estimation of growth, the efficiency of linked cross sectional scheme has been compared with pure longitudinal and cross sectional schemes. The relevant estimation theory has been developed and the expressions for the optimum estimators alongwith their variances have been derived. It has been observed that for estimation of growth, the linked cross‐sectional scheme has been observed to be less efficient as compared to pure longitudinal scheme but more efficient than pure cross‐sectional scheme.
On a Special Feature of the Patel‐Gupta Equivalence Test
Authors: Frick H.
Published: May 2007

For small variances level and power of the Patel‐Gupta test show a somewhat irregular behaviour. This phenomenon is mathematically explained here.
Multivariate Polya and Inverse Polya Distributions of Orderk
Authors: Philippou A. N. , Tripsiannis G. A.
Published: May 2007

Multivariate Polya and inverse Polya distributions of orderkare derived by means of generalized urn models and by compounding the type II multinomial and multivariate negative binomial distributions of orderkof PHILIPPOU, ANTZOULAKOSand TRIPSIANNIS(1990, 1988), respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a multivariate hypergeometric distribution of orderk, a negative one, an inverse one, a negative inverse one and a discrete uniform of the same order. The probability generating functions, means, variances and covariances of the new distributions are obtained and five asymptotic results are established relating them to the above‐mentioned multinomial and multivariate negative binomial distributions of orderk, and to the type II negative binomial and the type I multivariate Poisson distributions of orderkof PHILIPPOU(1983), and PHILIPPOU, ANTZOULAKOSand TRIPSIAN‐NIS(1988), respectively. Potential applications are also indicated. The present paper extends to the multivariate case the work of PHILIPPOU, TRIPSIANNISand ANTZOULAKOS(1989) on Polya and inverse Polya distributions of orderk..
Sparse Sampling and Maximum Likelihood Estimation for Boolean Models
Authors: Ayala G. , Ferrandiz J. R. , Montes F.
Published: May 2007

A condition for practical independence of contact distribution functions in Boolean models is obtained. This result allows the authors to use maximum likelihcod methods, via sparse sampling, for estimating unknown parameters of an isotropic Boolean model. The second part of this paper is devoted to a simulation study of the proposed method.

AMS classification: 60D05
The Reliability of Tests of Hypotheses when Overdispersed Logistic‐Linear Models are Fitted by Maximum Quasi‐Likelihood
Authors: Williams D. A.
Published: May 2007

When overdispersed logistic‐linear models are fitted by maximum quasi‐likelihood hypotheses can be tested by comparing either the Wald statistic, or the quasi‐likelihood score statistic, or the quasi likelihood‐ratio statistic, with the approximating nullX2distribution. This paper reports a simulation study of the reliability of these tests. Some factors affecting their relative reliabilities are identified. An extended quasi‐likelihood ratio test is also considered.
Truncation of a Two Sample Sequential Wilcoxon Test
Authors: Skovlund Eva
Published: May 2007

To reduce the number of patients needed in a clinical trial, a sequential plan is sometimes used. This paper deals with the truncation of a sequential two sample Wilcoxon test which was originally an open plan (SKOVLUND and WALLØE, 1988). The truncated boundaries have been developed by stochastic simulation. These boundaries form a triangular continuation region. The simulated constants of the boundaries are presented in a table which may be used directly. Boundaries for truncation at 50, 100, 150 and 200 patients are developed. The chosen significance level may be 0.01, 0.025 or 0.05, and the power 0.95. To extend the applicability to other treatment differences than those tabulated, smooth curves are fitted to the simulated points. These make the test applicable to any treatment difference within the simulated range.
Notes on the Mack‐Wolfe and Chen‐Wolfe Tests for Umbrella Alternatives
Authors: Chen Y. I.
Published: May 2007

In this paper we find a class of umbrella alternatives for which the MACK‐WOLFE (1981) peak known test is optimal in the sense of Pitman efficiency. The asymptotic null distribution of the CHEN‐WOLFE (1989) statistic for the peak‐unknown umbrella alternatives problem is obtained. Some percentiles of the asymptotic distribution computed by simulation are presented.
A Possible Approach to Comparison of Survival Functions
Authors: Goot R. E. , Osipova T. T.
Published: May 2007

Special numerical index for comparison of survival functions is proposed. The index is called by directed probabilistic semimetric. The examples of these semimetrics are presented. The procedure of the index estimating on sampled data is considered.
Individual Samples and the Bootstrap
Authors: Lefkovitch L. P.
Published: May 2007

It is argued that bootstrap estimates are more efficient if obtained from the distinct units in each of the repeated samples than are those obtained from all the units.
Asymptotic Relative Efficiency of Some Jackknife Estimators of a Common Odds Ratio
Authors: Pigeot Iris
Published: May 2007

In the situation of several 2 × 2 tables the asymptotic relative efficiencies of certain jackknife estimators of a common odds ratio are investigated in the case that the number of tables is fixed while the sample sizes within each table tend to infinity. The estimators show very good results over a wide range of parameters. Some situations in which the estimators have low asymptotic relative efficiency are pointed out:.
Graphical Methods for Analysing Combination Effects in Dose‐Response Experiments
Authors: Guhr S. , Unkelbach H. D. , Pöch G.
Published: May 2007

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.
On Fisher's Method of Combining p‐Values
Authors: Elston R. C.
Published: May 2007

The problem of combining p‐values from independent experiments is discussed. It is shown that Fisher's solution to the problem can be derived from a “weight‐free” method that has been suggested for the purpose of ranking vector observations (Biometrics 19: 85–97, 1963). The method implies that the value p = 0.37 is a critical one: p‐values below 0.37 suggest that the null hypothesis is more likely to be false, whereas p‐values above 0.37 suggest that it is more likely to be true.
Estimation of the Density ofGGiven Observations ofY=G+E
Authors: El‐Amraoui A. , Goffinet B.
Published: May 2007

We study the problem of estimating the density of a random variableG, given observations of a random variableY = G + E.The random variableEis independent ofGand its probability distribution function is considered as known. We build a family of estimators of the density ofGusing characteristic functions. We then derive a family of estimators of the density ofYbased on the model forY.The estimators are shown to be asymptotically unbiased and consistent. Simulations show that these estimators are better, as measured by integrated squared error, than the standard kernel estimators. Finally, we give an example of the use of this method for the detection of major genes in animal populations.
An Improvement of the Westlake Symmetric Confidence Interval
Authors: Müller‐Cohrs J.
Published: May 2007

A common statistical method for assessing bioequivalence of two formulations of a chemical substance is the symmetric confidence interval of WESTLAKE (1972). As mentioned by WEST‐LAKE (1981) and SCHUIRMAN (1981) a more powerful method consists of two one‐sided t‐tests. An (1‐α)‐confidence interval consistent with the two one‐sided t‐tests procedure is given by [min(α, 0), max (0, b)] where [a, b] is the conventional (1–2α)‐confidence interval of the t‐test. This “central” confidence interval is always a strict subset of the symmetric confidence interval and thus has more power in proving bioequivalence. The central confidence interval has properties comparable with those of the conventional one‐sided confidence intervals.
One‐Way Classification ANOVA Model for the Mixture of Two Multivariate Normal Populations
Authors: Gupta A. K. , Kabe D. G.
Published: May 2007

When a sample of size n is available from a mixture of two normal populations with different mean vectors and a common covariance matrix, SRIVASTAVA and AWAN (1982) develop one‐way ANOVA analysis for testing a certain composite linear hypothesis. They show that the error and hypothesis sum of products matrices have independent noncentral Wishart densities of rank unity each. However, they do not obtain the necessary Wilks' λ for testing the desired hypothesis. The present paper obtains the density of λ. This density is doubly noncentral multivariate beta density. The derivation is based on generalized Sverdrup's lemmas, KABE (1965), (1974).
The Relationship Between Two Statistical Tests for the Comparison of Two Exponential Distributions
Authors: Le Chap T.
Published: May 2007

To compare two exponential distributions with or without censoring, two different statistics are often used; one is the F test proposed by COX (1953) and the other is based on the efficient score procedure. In this paper, the relationship between these tests is investigated and it is shown that the efficient score test is a large‐sample approximation of the F test.
Simple Nonparametric Inference for Monotonic Processes
Authors: Schemper M.
Published: May 2007

A scoring system for possibly censored monotonic processes is presented which allows to analyze such processes by means of standard parametric or nonparametric tests. In either case the analyses are invariant to monotonic transformations of time. Such analyses are of relevance whenever changes in degree of function are observed rather than the single and 100% loss of function of survival analysis. An example of gradually increasing function after particular reconstructive surgery is supplied.
Crossover Designs with Random Periods
Authors: Roebruck P.
Published: May 2007

Crossover experiments usually are modelled with fixed treatment, carryover, and period effects while the effects of subjects are assumed to be random. In actual realisations of crossover experiments however periods are quite arbitrary intervals of time, depending on administrative affairs for instance and possibly they are even varying from subject to subject. Modelling these arbitrary periods as random effects either globally for all subjects or individually for each one seems to be more adequate than the assumption of fixed period effects. This paper is concerned with the two treatments, two periods crossover design. It is described that—in spite of the somewhat involved covariance structure—the estimators and tests developed for models with fixed period effects remain valid for models with random effects for periods provided that no treatment X period interaction exists.
Experiments with Three‐Treatment Three‐Period Crossover Design: Analysis Through the General Linear Model
Authors: Botter Denise A. , Singer Julio M.
Published: May 2007

In this paper we consider balanced three‐treatment three‐period crossover designs. Using a strategy similar to that applied in the analysis of split‐plot experiments we describe both the within and the between sample units models, as well as the corresponding Analysis of Variance. We illustrate these procedures with a numerical example and discuss their implementation through computer programs designed for the analysis of the general linear model.
Rate Constants and the Variation of Random Concentration Curves in a 2‐Compartment System
Authors: Helfenstein U.
Published: May 2007

In biology and medicine many substances and drugs enter the system not at regular time intervals but rather according to a random process. In the present article a situation is investigated where input enters a 2‐compartment system according to a Poisson process. The arising two random concentration curves y(t), one for the central and one for the peripheral compartment are discussed (shot noise).

The equations for E[y(t)] and Var [y(t)] are derived. The dependence of E[y(t)] and Var [y(t)] and of the index of dispersion ID[y(t)] on the rate parameters is analysed and discussed in both compartments. The arising calculations were considerably simplified by means of “Mathematica”, a computer program which allows to perform symbolic calculations.
Concomitant Information in Competing Risk Analysis
Authors: Spivey L. B. , Gross A. J.
Published: May 2007

A competing risk model, accommodating both Type I censoring and random withdrawals, is expanded to incorporate concomitant information by allowing the parameters of the underlying distributions to be a linear function of two covariates. The model is developed for two competing risks, one following a Weibull distribution and the other a Rayleigh distribution, and random withdrawals following a Weibull distribution. A method is developed for testing the equality of the coefficients for a given covariate for each of the competing risks using MLE'.
Rank Covariance Methods for the Analysis of Survival Data
Authors: Amini S. B. , Woolson R. F.
Published: May 2007

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSONand LACHENBRUCH(1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right‐censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, QR2, is recommended for general use for the rank analysis of covariance of right‐censored survivorship data.
Parametric and Parametrically Smoothed Distribution‐Free Proportional Hazard Models with Discrete Data
Authors: Sturm Roland
Published: May 2007

This paper discusses discrete time proportional hazard models and suggests a new class of flexible hazard functions. Explicitly modeling the discreteness of data is important since standard continuous models are biased; allowing for flexibility in the hazard estimation is desirable since strong parametric restrictions are likely to be similarly misleading. Simulation compare continuous and discrete models when data are generated by grouping and demonstrate that simple approximations recover underlying hazards well and outperform nonparametric maximum likelihood estimates in term of mean squared error.
Random Censorship, Competing Risks and a Simple Proportional Hazards Model
Authors: Rao B. Raja , Talwalker Sheela
Published: May 2007

The present paper discusses a health situation in which the individuals in a biomedical or an epidemiological cohort study are exposed simultaneously to several risks of death, such as cancer, heart disease, stroke, renal failure, emphysema, etc. and in which the life times of these individuals are independently censored on the right by some censoring mechanism. ARMITAGE' (1958) simple proportional hazards model is examined with respect to several probability models for the life time and censoring distributions.
A Multiraters Agreement Index for Ordinal Classification
Authors: Jolayemi E. Teju
Published: May 2007

An agreement index among more than two raters who employ ordinal classification is proposed here as an extension of the agreement index set up to consider such agreement between two raters as outlined by (JOLAYEMI, Biom. J. 32 (1990), 87–93). The method of application is outlined using a clinical diagnosis involving seven pathologists.
A Computer Programme Package for the Statistical Analysis of Spatial Point Processes in a Square
Authors: Koen C.
Published: May 2007

A computer programme for the statistical analysis of point data in a square is described. Several tests for randomness of the distribution of points are possible. The most comprehensive of these are comparisons of the empirical distributions of the inter‐point and closest neighbour distances with their respective expected distributions under complete randomness, and tests based on Ripley' L function; using these, significant aggregation or regularity can be identified. It is also possible to calculate statistics of properties (“attributes”) associated with each spatial point, as well as to compare statistics for sub‐areas of the experimental square. Several measures of spatial autocorrelation are available, amongst them correlograms and variograms. The programme can also find the tesselation of the study area and correlate tile properties with the point attributes. The procedures are illustrated by references to the spatial distribution and mound heights of Trinevitermes trinervoides on a study area in South Africa. Although the programme was developed specifically for application in entomology, it could be used to analyse data from many other disciplines.
The Consideration of Latency Periods in Cumulative Damage Models
Authors: Rittgen W. , Becker N.
Published: May 2007

The cumulative damage model as outlined in previous papers is unable to reproduce latency periods, particularly after short‐term exposures. A refinement being straightforward within the present frame of point process theory is proposed using displacement processes applied to the single damages. For the displacement distribution, the lognormal distribution has been suggested. As in the previous model, exact formula for the behaviour of the survival function after the onset and the cessation of an additional exposure can be derived. Qualitative examinations demonstrate that the thus extended model shows the relevant features known from reports on shortterm exposures. Fitting the model to data of follow‐up studies should provide a measure for the impact of an environmental exposure and the parameters for the distribution of the related latency period.
Choice of Smoothing Parameters for Direct Kernels in Discrimination
Authors: Tutz Gerhard
Published: May 2007

Direct kernels, due to LAUDER (1983), as an alternative to the indirect kernel method in discriminant analysis are considered. It is shown that direct kernels may be based on any kernel function known in discrete density estimation. The choice of smoothing parameters is based on general loss functions and a family of loss functions which are specific for the discrimination problem is introduced. Examples with distance dependent and distance independent smoothing parameters are given to illustrate the applicability.
Estimation of Population Mean Under Successive Sampling Scheme when Various Weights and Regression Coefficients are Unknown
Authors: Tikkiwal G. C. , Gupta A. K.
Published: May 2007

In this paper properties of an estimator of the population mean on current occasion under successive sampling scheme, when various weights (φh'S) and regression coefficients (βh,h‐1) are estimated forh≥ 2, have been studied. Some empirical results on the estimation of the variance of an unbiased estimator of population mean forh= 2 are also given.
Prediction Intervals in Nonlinear Regression
Authors: 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 θ, we construct two‐sided nominally‐q‐prediction intervals by applying the usual linear model theory. The derivation of the truncated series expansion of the expected coverage of the prediction intervals at a feasible value of the parameter vector is described. The quadratic approximation of the expected coverage is then obtained for a two‐parameter nonlinear model. Finally we show how we may construct the prediction intervals when a certain type of nonlinear transformation of the parameter vector has been applied.
A Multiplicative Model Imposed More Restrictions on the Quasi‐Symmetry Model for the Analysis of Square Contingency Tables
Authors: Tomizawa Sadao
Published: May 2007

For the analysis of square contingency tables, this note proposes a multiplicative model imposed more restrictions on CAUSSINUS' (1965) quasi‐symmetry (QS) model. The model is not so strict as in the quasi‐double symmetry model considered by TOMIZAWA (1985b). The proposed model has the structure of the QS about the main diagonal plus an extended QS about the reverse diagonal of the square contingency table. The model is applied to the data on unaided vision of students in a university in Japan.
Confidence Intervals for the Relative Relapse Rate of Placebo VS 6‐Mercaptopurine Group of Acute Leukemia Patients Under a Random Censorship Model
Authors: Rao B. Raja , Talwalker Sheela , Kundu Debasis
Published: May 2007

The present paper considers a random censorhip model in which the remission times of acute leukemia patients in a study are randomly censored according to a given probability distribution and constructs confidence intervals for the Relative Relapse Rate [RRR] of the placebo versus 6‐Mercaptopurine group of acute leukemia patients. Two important models are discussed for the probability distributions of the remission times‐the exponential and the Weibull distributions. The censoring distributions are also regarded as following exponential and Weibull distributions. Several methods are used to construct the confidence intervals including its maximum likelihood estimator and its approximate sampling distribution. Sprott'S and Cox'S methods as well as the Box‐Cox transformations are also utilized.

These methods are used to illustrate the construction of the confidence intervals with the FREIREICHet al. data (1964) involving a placebo and a 6‐MP group of acute leukemia patients. The results of the present paper provide valuable alternatives to the usual parametric and nonparametric tests for the treatment effect, that are discussed in the literature, such as Gehan'S test, Logrank test, and the Mantel‐Haenszel test.
Estimation of Population Regression Coefficient in Successive Sampling
Authors: Singh P. , Talwar H. K.
Published: May 2007

An attempt has been made to derive the theory of successive sampling for estimation of regression coefficient. The situations considered are estimation of regression coefficient for current occasion, estimation of change of regression coefficients over two occasions and estimation of average of regression coefficients over two occasions. The expressions of optimum estimators along with their variances have been worked out. On comparing their efficiencies empirically, it has been observed that similar to the estimation of mean, successive sampling can also be used with advantage for estimation of regression coefficient.
On the Dependence of the Quadratic Risk of the Classical Predictor and the Prediction‐Horizon
Authors: Kozák J.
Published: May 2007

When constructing predictors on the basis of the linear model of time series of various indicators often the question arises on the dependence of forecasting accuracy and the changing prediction horizon. The dependency of the quadratic risk of the classical predictor and the time horizon is considered.
Analysis of a Series of Yield Trials with Common Checks
Authors: Singh M.
Published: May 2007

Sometimes a large number of new selected lines, although evaluated with replications, are not repeated over trials. However, there are a number of checks common across trials. The new selected lines from different trials are compared with the help of the common checks. Some limitations of an existing analysis has been described, and ways to overcome them are presented. An assessment of genotype X environment interaction has been made by check X trial interaction. A general case of incomplete block design at each trial and the connected nature of checkvstrial classification considered to obtain the adjustment for comparing selected lines from different trials. A set of cereal trials has been considered for illustration.
On Edge‐Corrected Probability Density Function Estimators for Point Processes
Authors: Doguwa S. I. , Choji D. N.
Published: May 2007

FIKSEL(1988) provides an asymptotically unbiased kernel estimator for the densityhs(r) of the spherical contact distribution function of stationary and isotropic point processes. This paper proposes alternative estimators ofhs(r) for use with regular grid of locations. The existing estimator ofhs(r) and the alternatives proposed in this paper are then tested out in a simulation study.
A Friedman‐type Test for Circular Data and Arbitrary Cell Frequencies
Authors: Ackermann H.
Published: May 2007

To analyse directional data resulting from unifactorial block designs a Friedman‐type test is described and the exact and asymptotical properties of the defined test statistic are considered.
Evaluating Chessboard MANOVA Designs Using Predictive and Matching Configural Frequency Analysis
Authors: Bergman L. R. , Lienert G. A.
Published: May 2007

This paper concerns the nonparametric evaluation of chessboard MANOVA designs. For this purpose, a matching procedure based on rook methodology is suggested as a complement to predictive coafigural frequency analysis. Using this procedure, a multivariate hypothesis can be tested in a single test. It is also possible to design a significance test to fit a specific composite hypothesis. The procedure is illustrated by results from a multivariate psychopharmacological experiment in which the effects of alcohol and caffeine were studied on test performance and volatility.
Testing Equality of Correlated Means in the Presence of Unequal Variances and Missing Values
Authors: Bhoj D. S.
Published: May 2007

Several statistics are proposed for testing the hypothesis of equality of the means of bivariate normal distribution with unknown variances and correlation coefficient when observations are missing on both variatea. The null distributions of the statistics are approximated by well‐known distributions. The empirical sizes and powers of the statistics are computed and compared with paired t test and some of the known statistics based on available data. The comparisons support the use of two of the statistics proposed in this paper.
Estimation of Odds Ratios from Matched Case‐Control Studies with Incomplete Data
Authors: Haber M. , Chen C. C.‐H.
Published: May 2007

Matched case‐control studies often include pairs with incomplete exposure information. This work presents and compares two estimators for the odds ratio that can be used when the exposures of some of the cases and controls are missing. A simulation study shows that the estimator that uses the marginal exposure frequencies is usually more efficient than the estimator based on discordant pairs.
Using Generalized Distances in Classification of Groups
Authors: Dagnelie P. , Merckx A.
Published: May 2007

The Mahalanobis generalized distance can advantageously be used to achieve the hierarchical clustering of groups of individuals. With a set of nearly 12,000 biometrical data, comprising populations of 14 different species of clover, we tried four methods to cluster those populations, in order to compare their results and to see whether the numerical classification obtained agrees with the botanical taxonomy. One of those methods is a conventional hierarchical clustering technique, based upon the Euclidean distances between the means of the populations, while the three other methods make use, with an increasing degree of complexity, of the generalized distances. These methods gave obviously better results.
On the Estimation of Mean Infecundable Period Following Childbirth (Using Information on Lactation Period)—A Competing Risk Theory Approach
Authors: Biswas S. , Abid M. A.
Published: May 2007

The methodological paper envisages to provide two measures of infecundable period following childbirth; one based on the lactation period when expiry period of amenorrhoea (P.P.A.) follows the same immediately. The other one is based on P.P.A. when expiry of P.P.A. precedes the lactation period. The weighted average of the two measures (duly weighted by the probabilities of both the events) has been given as the estimate of the mean infecundable period. A competing risk oriented approach is adopted to evolve the methodology.
Improvement of Ratio‐Type Estimators‐II
Authors: Dharmadhikari S. , Tankou V.
Published: May 2007

This paper generalizes the results of AGARWAL (1980) and AGARWAL and KUMAR (1985) by constructing a multivariate ratiotype estimator which, to a first order of approximation, is as efficient as the regression estimator.
Statistical Evaluation of the Effect of Gemfibrosil, a Cholesterol Reducing Drug, on Some Biochemical Coronary Heart Disease Risk Variables
Authors: Bartkowiak A. , Łsukasik S. , Chwistecki K.
Published: May 2007

The evaluation is based on the clinic trial with gemfibrosil (“Gevilon”, Parke‐Davis) carried out in a group of 48 patients, to whom the drug was administered in the single dose of 900 mg daily during the period of 3 months. In this paper we show the results of the treatment on five biochemical Coronary Heart Disease (CHD) risk variables: Cholesterol (CHOL), High Density Lipoprotein (HDL), Triglyccrides (TGL), Uric Acid (UA) and Glucose (GL).

We are concerned with a statistical model allowing to predict which and how large changes in the considered variable can be expected in a patient taking the drug. This is done considering the “regression to the mean” effect.
A Model with Three Compartments and Nonnegative Transfers
Authors: Berg L.
Published: May 2007

We consider a periodic model with three compartments, which can be considered as a simplified model for the dynamics of follicles. We give necessary and sufficient conditions for the solvability in nonnegative inputs, transfers and outputs, and we determine the minimal solution. If the problem is not solvable according to measurement errors of the given data, we recover suitable values by the method of least‐squares, solving a quadratic optimization problem.
Linearized Growth Curve, Proper Age and Age at Menarche
Authors: Masuyama M.
Published: May 2007

A mathematical model of the linearized growth curve and its physiological interpretation by the introduction of proper age, which is proportional to the chronological age, are presented here. In the second phase, but not in the first phase, this constant of proportionality is highly correlated with the age at menarche.
Some Frequentist Properties of a Bayesian Method in Clinical Trials
Authors: Ho C. H.
Published: May 2007

Interim analysis in clinical trials involving two treatments are commonplace nowadays. Concerns from different points of view are widely seen in the literature. With a Bayesian approach there is no consideration of type I error and no power calculation. In contrast, there is no difficulty or arbitrariness in picking a prior distribution with a classical approach. In this paper, however, a stopping rule based on the Bayesian approach is discussed from a classical point of view. In specific, we consider application to normal sampling analyzed in stages and demonstrate the role of the prior distributions. In the first part of the paper, we define the stopping rules based on the posterior probabilities. We then develop the stopping boundaries in explicit forms, which can be easily computed with a hand calculator and a standard normal probability distribution table. We also summarize the frequency characteristics of this stopping rule into several results. The major question that is addressed in the second part of the paper is: how will a prior affect the results of a clinical trial study based on the posterior probabilities? The criteria for assessment will be strictly of a Neyman‐Pearson kind. We use N(v, τ2) as the prior distribution for the difference between treatments, δ. We show that the test is unbiased if v = 0 or τ = ∞. In addition, some rather obvious facts are again summarized into a couple of results. We also discuss, with a table and a figure, the power functions of non‐trivial cases with extreme v and τ using a numerical example.
Ascertainment: An Overwiew of the Classical Segregation Analysis Model for Independent Sibships
Authors: George V. T. , Elston R. C.
Published: May 2007

Several different methodologies for parameter estimation under various ascertainment sampling schemes have been proposed in the past. In this article, some of the methodologies that have been proposed for independent sibships under the classical segregation analysis model are synthesized, and the general likelihoods derived for single, multiple and complete ascertainment. The issue of incorporating the sibship size distribution into the analysis is addressed, and the effect of conditioning the likelihood on the observed sibship sizes is discussed. It is shown that when the number of probands in a sibship is not specified, the corresponding likelihood can be used for a broader class of ascertainment schemes than is subsumed by the classical model.
Stratified or Multicentre Analysis with Extended Mantel–Haenszel Statistics
Authors: Schindel F. , Kwasny H.
Published: May 2007

Since its introduction in 1959 the ability of the classical Mantel‐Haenszel (M–H) procedure for combining the odds ratios of a set of I 2 × 2 tables has led to its use also in stratified or multicentre type clinical trials. A familiar application is the M–H logrank test in survival analysis.

An extension of the M–H procedure covering the case of 2 × K contingency tables (MANTEL, 1963) with ordered levels retains the essential property of pooling the results of I homogeneous tables (i.e. in absence of qualitative interactions). The assignment of some score for the K columns of a table is essential for the use of the method (in comparing 2 treatments).

Some possibilities of score assignment are discussed: for clinical outcome variables such as the degree of severity of a disease, pain and so on, the score is at hand in a natural way. A less well‐known type of scoring consists in ranking the observations of a continuous variable, leading to cell sizes of 1 or 0. In this case, however, if equidistant ranking was used, the E–M–H procedure appears as an extension of Wilcoxon's rank sum test and represents a powerful non‐parametric approach in stratified or multicentre type designs with non normally distributed outcome variables.

The results of some Monte‐Carlo simulations for 2 possible equidistant ranking procedures are presented, which indicate only a moderate gain in power as compared to Wilcoxon's rank sum test under the common situation of centre effects not exceeding treatment effects. Use of the E–M–H proćedure is also recommended as a simple method to overcome the potential bias due to unequally distributed prognostic factors among treatment groups.
Non‐Iterative Least Squares Estimation of Missing Values in Graeco‐Latin Square Designs
Authors: Subramant J.
Published: May 2007

The present paper deals with the estimation of several missing values in Graeco‐Latin Square‐designs. When the observations are missing in a particular pattern, explicit computable expressions are presented for the estimators of the missing values. This procedure is illustrated with the help of a numerical example.
A Note on Testing Equality of Means when Sample Sizes are Random with Application
Authors: Razzaghi Mehdi
Published: May 2007

The problem of testing the equality of means of two normal populations is considered when independent random samples of random sizes are given with the total number of observations from both populations being a fixed number. An application in forestry is discussed.
Models of Chance when Measuring Interrater Agreement with Kappa
Authors: von Eye Alexander , Sörensen Silvia
Published: May 2007

Two measures of reliability for nominal scales are compared: Coefficient Kappa and kn, a modification suggested for agreement matrices with free marginals. It is illustrated that the evaluation of two rater's agreement may come to a contradictory conclusion, depending on whether k or kn is used. On the basis of the underlying chance models it is concluded that k and kn cannot be interpreted in the same manner. Specifically when raters disagree, the two measures can be widely discrepant.
Generalized Wilcoxon Rank Tests and Sensitivity Curves
Authors: Öhman M. L.
Published: May 2007

In this paper we use the sensitivity curves of TUKEY (1977) and the change of decision point (cdp) (a modified version of the breakdown point of YLVISAKER, 1977), supplemented by simulation studies to acquire knowledge about sensitivity in generalized Wilcoxon rank test statistics. Sensitivity depends on balanced or unbalanced sample size cases, censoring, combinations of failure distributions and sources of errors in the data. It is important to consider the quality of the data, and the results show that cdp and some properties of the sensitivity curves may serve as a hint when selecting a test statistic and when making a decision for a given test statistic.
Fitting Regression Models to Ordinal Data
Authors: Jansen J.
Published: May 2007

This paper deals with the analysis of ordinal data by means of a threshold model. Maximum likelihood estimation is discussed and two examples are used to illustrate the methods.
Stopping Rules for Clinical Trials Implicitly Incorporating Safety Information
Authors: Ho C.‐H.
Published: May 2007

Clinical trials research is mainly conducted for the purpose of evaluating the relative efficacy of two or more treatments. However, a positive response due to treatment is not sufficient to put forward a new product because one must also demonstrate safety. In such cases, clinical trials which show a positive effect would need to accrue enough patients to also demonstrate that the new treatment is safe. It is our purpose to show how the efficacy and safety problems can be combined to yield a more practical clinical trial design. In this paper we propose an asymmetric stopping rule which allows the experimenter to terminate a clinical trial early for a sufficiently negative result and to continue to a specified number of patients otherwise. As it turns out, a few interim tests will have negligible effects on the overall significance level.
Graphical Method to Detect Departure from Normality with Special Application to Tukey's g and h Distributions
Authors: Khan B. A. , Katti S. K.
Published: May 2007

Given a sample, the problem of choosing one of a variety of theoretical distributions for data analysis has been a major concern to both theoretical and applied statisticians. On the basis of a graph drawn using a normal characterization, a method is given to detect departure from normality. Special mathematical study is presented for the proposed graphs. Tukey's g and h family of distributions are used as an alternate to normality.