The evaluation of bioequivalence using nonparametric procedures

Applications of nonparametric methods to the evaluation of bioequiv-alence for two treatments are presented for independent samples and for a crossover design. Included are procedures for testing for equivalence in location, in dispersion, and in general. Also presented are procedures for the calculation of confidence limits. A general strategy for the evaluation of bioequivalence is developed which involves both hypothesis testing and the calculation of confidencelimits for parameters which characterize departures from equivalene.     

Nonparametric tests for cause specific hazard rates with censored data for competing risks among several groups

For the competing risk setting where the lifetime data are due to one of several distinct and exclusive causes, comparison of cause-specific hazard rates is of interest to researchers. In this paper we survey existing methods for related tests and provide a new test for a common overall rate for all causes and groups. Tests given in the literature for checking for a common rate for causes and a common rate for the groups are shown to be in the same framework as the proposed test for common overall rate. Asymptotics are shown to follow a common theme for each test. An extensive numerical and graphical investigation and an example are presented to substantiate the proposed methods.     

Comparing several experimental groups with a control in the multivariate case

This paper presents a multivariate extension of Dunnett's test for comparing simultaneously k treatment group means with a single control group mean. A test based on Hotelling T²statistics is presented and approximate critical values are evaluated for the case of equal numbers of observations in each group, for the .05 and .01 levels of significance, for 1 to 5 variates, for 1 to 10 treatment groups, and for varying degrees of freedom. The accuracy of the procedure for generating approximate critical values is assessed via simulation studies conducted for selected cases and an example is presented using real data.     

Tests for symmetry of two-piece normal distribution

In this paper, classical optimum tests for symmetry of two-piece normal distribution is derived. Uniformly most powerful one-sided test for the skewness parameter is obtained when the location and scale parameters are known and is compared with sequential probability ratio test. An ad-hoc test for symmetry and likelihood ratio test for symmetry for large samples, can be found in literature for this distribution. But in this paper, we derive exact likelihood ratio test for symmetry, when location parameter is known. The exact power of the test is evaluated for different sample sizes.     

Correlation type gogdness-of-fit statistics with censored sampling

Some comments are made concerning the possible forms of a correlation coefficient type goodness-of-fit statistic, and their relationship with other goodness-of-fit statistics, Critical values for a correlation goodness-of-fit statistic and for the Cramer-von Mises statistic are provided for testing a completely-specified null hypothesis for both complete and censored sampling, Critical values for a correlation test statistic are provided for complete and censored sampling for testing the hypothesis of normality, two parameter exponentiality, Weibull (or, extreme value) and an exponential-power distribution, respectively. Critical values are also provided for a test of one-parameter exponentiality based on the Cramer-von Mises statistic     

Estimation in linear mixed models for longitudinal data under linear restricted conditions

In the paper, we consider a linear mixed model (LMM) for longitudinal data under linear restriction and find the estimators for the parameters of interest. The strong consistency and asymptotic normality of the estimators are obtained under some regularity conditions. Besides, we derive the strong consistent estimator of the fourth moment for the error which is useful for statistical inference for random effects and error variance. Simulations and an example are reported for illustration.     

Partitioning with Respect to a Control: Unequal Sample Sizes Case

This article describes a method for partitioning with respect to a control for the situation in which the treatment sample sizes are unequal and also for the situation where the treatment sample sizes are equal except for a few missing values. Calculation of the critical values required for finding confidence limits is discussed and tables are presented for the “almost equal” sample size case. An application of this method to length of stay data for congestive heart failure patients is also provided.     

Statistical methods of risk assessment for continuous variables

Adverse health effects for continuous responses are not as easily defined as adverse health effects for binary responses. Kodell and West (1993) developed methods for defining adverse effects for continuous responses and the associated risk. Procedures were developed for finding point estimates and upper confidence limits for additional risk under the assumption of a normal distribution and quadratic mean response curve with equal variances at each dose level. In this paper, methods are developed for point estimates and upper confidence limits for additional risk at experimental doses when the equal variance assumption is relaxed. An interpolation procedure is discussed for obtaining information at doses other than the experimental doses. A small simulation study is presented to test the performance of the methods discussed.     

Uniform validity of saddlepoint expansion on compact sets

This paper shows that Daniels's (1954) saddlepoint expansion for the density of a sample mean is, for all practical purposes, always uniformly valid on compact subsets in the interior of the domain of the mean. This uniform validity is the key for establishing the relation between the saddlepoint expansion for the density function and Lugannani and Rice's expansion for the tail probability, and for establishing the validity of a high-order asymptotic expansion for the density of a standardized mean.     

Repeated confidence intervals and prediction intervals using stochastic curtailment

Jennlson and Turnbull (1984,1989) proposed procedures for repeated confidence intervals for parameters of interest In a clinical trial monitored with group sequential methods. These methods are extended for use with stochastic curtailment procedures for two samples in the estimation of differences of means, differences of proportions, odds ratios, and hazard ratios. Methods are described for constructing 1) confidence intervals for these estimates at repeated times In the course of a trial, and 2) prediction intervals for predicted estimates at the end of a trial. Specific examples from several clinical trials are presented.     

Unit roots and structural breaks: The case of India 1900-1988

SUMMARY This paper tests the hypothesis of difference stationarity of macro-economic time series against the alternative of trend stationarity, with and without allowing for possible structural breaks. The methodologies used are that of Dickey and Fuller familiarized by Nelson and Plosser, and that of dummy variables familiarized by Perron, including the Zivot and Andrews extension of Perron's tests. We have chosen 12 macro-economic variables in the Indian economy during the period 1900-1988 for this study. A study of this nature has not previously been undertaken for the Indian economy. The conventional Dickey-Fuller methodology without allowing for structural breaks cannot reject the unit root hypothesis (URH) for any series. Allowing for exogenous breaks in level and rate of growth in the years 1914, 1939 and 1951, Perron's tests reject the URH for three series after 1951, i.e. the year of introduction of economic planning in India. The Zivot and Andrews tests for endogenous breaks confirm the Perron tests and lead to the rejection of the URH for three more series.     

Methods for national population forecasts: a review

"Three widely used classes of methods for forecasting national populations are reviewed: demographic accounting/cohort-component methods for long-range projections, statistical time series methods for short-range forecasts, and structural modeling methods for the simulation and forecasting of the effects of policy changes. In each case, the major characteristics, strengths, and weaknesses of the methods are described. Factors that place intrinsic limits on the accuracy of population forecasts are articulated. Promising lines of additional research by statisticians and demographers are identified for each class of methods and for population forecasting generally."     

Complete censuses and samples

"Complete decennial censuses are needed for small areas and other domains. Sample surveys yield diverse and timely data. Censuses can also be combined with samples, and sometimes with data from registers, for diverse estimates that are detailed over both space and time, and hence are timely for small domains. Methods of 'postcensal estimates' for small domains are described. We note uses of censuses for improving samples and of samples for improving censuses, and propose a method for cumulating data from 'rolling' (or rotating) periodic (weekly, monthly or quarterly) samples specifically designed to cover the population in detail over designed spans (annual and quinquennial)."     

A selection criterion for choosing between functional forms of income distribution

The value of Elderton's k - criterion can be bounded for a given pdf. This paper presents these bounds for the most widely used distribution functions for income and computes the value of K for household incomes as reported in the Consumer Population Survey. The variance for theK are also estimated using the bootstrap, jackknife and delta methods. We find that the K can be used to narrow the field of potential pdfs for income and that all three methods for estimating the variance coincide in flagging low precision in the estimated K.     

Sums of powers of binomial coefficients

An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration.     

On Non Overlapping Segmentation of the Response Surfaces for Solving Constrained Programming Problems Through Super Convergent Line Series

The solutions of Constrained Programming Problems (linear, quadratic, and cubic) by segmentation of the response surfaces through Super Convergent Line Series were obtained. The line search exchange algorithm was exploited. The response surfaces were explored and segmented up to four segments for linear, six for quadratic, and eight for cubic programming problems, respectively. It was verified and established that the number of segments, S, for which optimal solutions are obtained are two for linear, four for quadratic, and eight for cubic programming problems, respectively.     

Numerical computation of rectangular bivariate and trivariate normal and t probabilities

Algorithms for the computation of bivariate and trivariate normal and t probabilities for rectangles are reviewed. The algorithms use numerical integration to approximate transformed probability distribution integrals. A generalization of Plackett's formula is derived for bivariate and trivariate t probabilities. New methods are described for the numerical computation of bivariate and trivariate t probabilities. Test results are provided, along with recommendations for the most efficient algorithms for single and double precision computations.     

Censored Exponential Data: Large Deviations for MLEs and Posterior Distributions

In this article, we consider several statistical models for censored exponential data. We prove a large deviation result for the maximum likelihood estimators (MLEs) of each model, and a unique result for the posterior distributions which works well for all the cases. Finally, comparing the large deviation rate functions for MLEs and posterior distributions, we show that a typical feature fails for one model; moreover, we illustrate the relation between this fact and a well-known result for curved exponential models.     

Semiparametric estimation of regression quantiles with application to standardizing weight for height and age in US children

The appropriate interpretation of measurements often requires standardization for concomitant factors. For example, standardization of weight for both height and age is important in obesity research and in failure-to-thrive research in children. Regression quantiles from a reference population afford one intuitive and popular approach to standardization. Current methods for the estimation of regression quantiles can be classified as nonparametric with respect to distributional assumptions or as fully parametric. We propose a semiparametric method where we model the mean and variance as flexible regression spline functions and allow the unspecified distribution to vary smoothly as a function of covariates. Similarly to Cole and Green, our approach provides separate estimates and summaries for location, scale and distribution. However, similarly to Koenker and Bassett, we do not assume any parametric form for the distribution. Estimation for either cross-sectional or longitudinal samples is obtained by using estimating equations for the location and scale functions and through local kernel smoothing of the empirical distribution function for standardized residuals. Using this technique with data on weight, height and age for females under 3 years of age, we find that there is a close relationship between quantiles of weight for height and age and quantiles of body mass index (BMI=weight/height²) for age in this cohort.     

Horwitz's rule, transforming both sides and the design of experiments for mechanistic models

Summary. The paper develops methods for the design of experiments for mechanistic models when the response must be transformed to achieve symmetry and constant variance. The power transformation that is used is partially justified by a rule in analytical chemistry. Because of the nature of the relationship between the response and the mechanistic model, it is necessary to transform both sides of the model. Expressions are given for the parameter sensitivities in the transformed model and examples are given of optimum designs, not only for single-response models, but also for experiments in which multivariate responses are measured and for experiments in which the model is defined by a set of differential equations which cannot be solved analytically. The extension to designs for checking models is discussed.