Keh-Wei Chen

A Note on Sample Size Determination for Bioequivalence Studies with Higher-Order Crossover Designs

Similar to Liu and Chow, approximate formulas for sample size determination are derived based on Schuirmanns two one-sided tests procedure for bioequiealence studies for the additive and the multiplicative models under various higher order crossover designs for comparing two formulations of a drug product. The higher order crossover designs under study include Balaams design, the two-sequence dual design, and two four-period designs (with two and four sequences), which are commonly used for assessment of bioequivalence between formulations. The derived formulas are simple enough to be carried out with a pocket calculator. The number of subjects required for each of the four higher order designs are tabulated for selected powers and various parameter values.

A nonparametric method for estimating the joint probability density of BOD and DO

Abstract A nonparametric probability estimator, having a uniform biochemical-oxygen demand kernel, is utilized to obtain the joint probability density function of (BOD) and dissolved oxygen (DO) along the stretch of a stream when the pollutant is discharged over an interval and the velocity is distance-dependent. Furthermore, probabilistic confidence bounds for BOD and DO are derived. An example and computations are presented to illustrate the usefulness of the model.

Comparison of the linear least squares and nonlinear least squares spheres

Two important, to scientists and engineers, sphere fitting procedures, namely the linear least squares (LLS) and the non-linear least squares (NLLS) methods and their general random-error analysis are described. The first-order random errors of the center coordinates and the radius of the fitted sphere using the above mentioned procedures are derived in detail under the assumption that the variance-covariance matrix exists for the random error vector. With the additional trivariate normal error distribution assumption, the Maximum Likelihood (ML) estimators and their standard deviations are also derived. The effectiveness of these procedures are studied through computer stimulation.

ON BAYES ESTIMATION FOR MIXTURES OF TWO WEIBULL DISTRIBUTIONS UNDER TYPE I CENSORING

Abstract A failure population need not be homogeneous. It can be a mixture of two or more distinct subpopulations. In this paper a population which can be divided into two subpopulations each representing a different cause of failure, is considered. The subpopulations each follow a Weibull distribution. Maximum likelihood estimators, Bayes estimators with respect to proper priors, and with respect to improper priors for the population parameters and the reliability function are derived. All analysis is based on samples censored at a predetermined test termination time. A comparison of the Bayes estimation and the maximum likelihood estimation is made through Monte Carlo simulation.

Shortest bayes credibility intervals for the lognormal failure model

Abstract The lognormal distribution with density function f(x|λ,δ 2 )= (2π) 1 2 δx −1 exp − ( In x−λ) 2 2δ 2 , for x>0,δ>0,−∞ is considered as a failure model from the Bayesian point of view. The shortest Bayesian confidence intervals for the parameters and reliability function are obtained for two cases. First, it is assumed that σ2 is known and that γ has a normal prior distribution. Then, the case that γ is known and σ2 has an inverted gamma prior distribution is considered. Some computer simulations are given to demonstrate the advantage of the shortest Bayesian confidence intervals over the ordinary Bayesian confidence intervals in terms of their length ratios.

Estimation for the distribution of BOD and DO

Abstract A nonparametric probability estimator, having a uniform kernel, is utilized to obtain the joint probability density function of BOD and DO along the stretch of a stream when the velocity is distance dependent. The stochastic model is used to obtain probabilistic confidence bounds for BOD and DO. An example and computations are presented which illustrate the usefulness of the model.

On the test of liu and chow's procedure for assessing equivalence in variability of bioavailability

Similar to Schuirmanns two one-sided tests procedure for assessment of bioequivalence in average bioavailability (Schuirmann,), Liu and Chow proposed a two one-sided tests procedure for assessment of equivalence of variability of bioavailability. Their procedure is derived based on the correlation between crossover differences and subject totals. In this paper, we examined the performance of their test procedure in terms of its test size and power for various situations where the intersubject variability and the intrasubject variability of the test drug product are relatively larger, similar, and smaller than that of the intrasubject variability of the reference drug product.