Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Bioequivalence Evaluation of Single Doses of Two Tramadol Formulations: A Randomized, Open-Label, Two-Period Crossover Study in Healthy Brazilian Volunteers

Background: Tramadol is a well tolerated and effective analgesic used to treat moderate to severe pain. Several generic formulations of tramadol are available in Brazil; however, published information regarding their bioequivalence in the Brazilian population is not available. A study was designed for Brazilian regulatory authorities to allow marketing of a generic formulation. Objective: The purpose of this study was to compare the bioequivalence of 2 commercial tablet preparations containing tramadol 100 mg marketed for use in Brazil. Methods: A randomized, open-label, 2 x 2 crossover study was performed in healthy Brazilian volunteers under fasting conditions with a washout period of 12 days. Two tablet formulations of tramadol 100 mg (test and reference formulations) were administered as a single oral dose, and blood samples were collected over 24 hours. Tramadol plasma concentrations were quantified using a validated HPLC method. A plasma concentration time profile was generated for each volunteer and then mean values were determined, from which C(max), T(max), AUC(0-t), AUC(0-infinity), k(e), and t(1/2) were calculated using a noncompartmental model. Bioequivalence between the products was determined by calculating 90% CIs for the ratios of C(max), AUC(0-t), and AUC(0-infinity) values for the test and reference products using log-transformed data. Tolerability was assessed by monitoring vital signs (temperature, blood pressure, heart rate), laboratory tests (hematology, blood biochemistry, hepatic function, urinalysis), and interviews with the volunteers before medication administration and every 2 hours during the study. Results: Twenty-six healthy volunteers (13 men, 13 women) were enrolled in and completed the study. Mean (SD) age was 30 (6.8) years (range, 21-44 years), mean weight was 64 (8.3) kg (range, 53-79 kg), and mean height was 166 (6.4) cm (range, 155-178 cm). The 90% CIs for the ratios of C(max) (1.01-1.17), AUC(0-t) (1.00-1.13), and AUC(0-infinity) (1.00-1.14) values for the test and reference products fell within the interval of 0.80 to 1.25 proposed by most regulatory agencies, including the Brazilian regulatory body. No clinically important adverse effects were reported; only mild somnolence was reported by 4 volunteers and mild headaches by 5 volunteers, and there was no need to use medication to treat these symptoms. Conclusion: Pharmacokinetic analysis in these healthy Brazilian volunteers suggested that the test and reference formulations of tramadol 100-mg tablets met the regulatory requirements to assume bio-equivalence based on the Brazilian regulatory definition. (Clin Ther 2010;32:758-765) (C) 2010 Excerpta Medica Inc.

Bioequivalence and pharmacokinetics of two zidovudine formulations in healthy Brazilian volunteers: An open-label, randomized, single-dose, two-way crossover study

Background: Zidovudine is a thymidine nucleoside reverse transcriptase inhibitor with activity against HIV type 1. Some (similar to 8) generic formulations of zidovudine are available in Brazil; however, based on a literature search, information concerning their bioavailability and pharmacokinetic properties in the Brazilian population has not been reported. Objective: The aim of this study was to compare the bioavailability and pharmacokinetic properties of 2 capsule formulations of zidovudine 100 mg in healthy Brazilian volunteers. Methods: This open-label, randomized, 2-way crossover study utilized a 1-week washout period between doses. Blood samples were collected for 8 hours after a single dose of zidovudine 100-mg test (Zidovudina, Fundaqdo para o Remedio Popular, Sao Paulo, Brazil) or reference formulation (Retrovir (R), GlaxoSmithKline, Philadelphia, Pennsylvania). Plasma zidovudine concentrations were determined using a validated high-performance liquid chromatography method with ultraviolet detection at 265 nm. C-max, T-max, AUC(0-t), AUC(0-infinity), t(1/2), and the elimination constant (k(e)) were determined using noncompartmental analysis. The formulations were considered bioequivalent if the 90% CIS for C-max, AUC(0-t), and AUC(0-infinity) fell within the interval of 80 % to 125 %, the regulatory definition set by the US Food and Drug Administration (FDA). Results: Twenty-four healthy volunteers (12 males, 12 females; mean age, 27 years; weight, 60 kg; height, 167 cm) were enrolled and completed the study. The 90% CIs of the treatment ratios for the logarithmic-transformed values of C-max, AUC(0-t), and AUC(0-infinity) were 80.0% to 113.6%, 93.9% to 109.7%, and 93.6% to 110.1 %, respectively. The values for the test and reference formulations were within the FDA bioequivalence definition intervals of 80% to 125%. Conclusions: In this small study in healthy subjects, no statistically significant differences in C-max, AUC(0-t), and AUC(0-)infinity were found between the test and reference formulations of zidovudine 100-mg capsules. The 90% CIs for the mean ratio values for the test and reference formulations of AUC(0-t), AUC(0-infinity), and C-max indicated that the reported data were entirely within the bioequivalence acceptance range proposed by the FDA of 80% to 125% (using log-transformed data).

Bioequivalence study of two oral formulations of cefadroxil in healthy volunteers

Two different cefadroxil (CAS 50370-12-2) formulations were evaluated for their relative bioavailability in 24 healthy volunteers who received a single 500 mg oral dose of each preparation. An open, randomized clinical trial designed as a two-period crossover study with a 7-day washout period between doses was employed. Plasma samples for assessments of their cefadroxil concentration by HPLC-UV were obtained over 8 h after administration. Values of 48.94 +/- 10.18 mu g . h/ml for test, and 48.51 +/- 9.02 mu g . h/ml for the reference preparation AUC(0-t) demonstrate a nearly identical extend of drug absorption. Maximum plasma concentration C-max of 16.04 +/- 4.94 mu g/ml and 16.01 +/- 4.02 mu g/ml achieved for the test and reference preparations did not differ significantly. The parametric 90% confidence intervals (CI) of the mean of the difference (test-reference) between log-transformed values of the two formulations were 96.80% to 104.51% and 92.01% to 107.00% for AUC(0-t) and C-max, respectively. Since for both AUC(0-t) or C-max the 90% CI values are within the interval proposed by the Food and Drug Administration, the test product is bioequivalent to the reference product for both the rate and extent of absorption after single dose administration.

A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.

The Scientific Basis for High-Intensity Interval Training: Optimising Training Programmes and Maximising Performance in Highly Trained Endurance Athletes

While the physiological adaptations that occur following endurance training in previously sedentary and recreationally active individuals are relatively well understood, the adaptations to training in already highly trained endurance athletes remain unclear. While significant improvements in endurance performance and corresponding physiological markers are evident following submaximal endurance training in sedentary and recreationally active groups, an additional increase in submaximal training (i.e. volume) in highly trained individuals does not appear to further enhance either endurance performance or associated physiological variables [e.g. peak oxygen uptake (V-dot O2peak), oxidative enzyme activity]. It seems that, for athletes who are already trained, improvements in endurance performance can be achieved only through high-intensity interval training (HIT). The limited research which has examined changes in muscle enzyme activity in highly trained athletes, following HIT, has revealed no change in oxidative or glycolytic enzyme activity, despite significant improvements in endurance performance (p < 0.05). Instead, an increase in skeletal muscle buffering capacity may be one mechanism responsible for an improvement in endurance performance. Changes in plasma volume, stroke volume, as well as muscle cation pumps, myoglobin, capillary density and fibre type characteristics have yet to be investigated in response to HIT with the highly trained athlete. Information relating to HIT programme optimisation in endurance athletes is also very sparse. Preliminary work using the velocity at which V-dot O2max is achieved (Vmax) as the interval intensity, and fractions (50 to 75%) of the time to exhaustion at Vmax (Tmax) as the interval duration has been successful in eliciting improvements in performance in long-distance runners. However, Vmax and Tmax have not been used with cyclists. Instead, HIT programme optimisation research in cyclists has revealed that repeated supramaximal sprinting may be equally effective as more traditional HIT programmes for eliciting improvements in endurance performance. Further examination of the biochemical and physiological adaptations which accompany different HIT programmes, as well as investigation into the optimal HIT programme for eliciting performance enhancements in highly trained athletes is required.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

What is the Problem of Ad Hoc Hypotheses?

The received view of an ad hoc hypothesis is that it accounts for only the observation(s) it was designed to account for, and so non-adhocness is generally held to be necessary or important for an introduced hypothesis or modification to a theory. Attempts by Popper and several others to convincingly explicate this view, however, prove to be unsuccessful or of doubtful value, and familiar and firmer criteria for evaluating the hypotheses or modified theories so classified are characteristically available. These points are obscured largely because the received view fails to adequately separate psychology from methodology or to recognise ambiguities in the use of 'ad hoc'.

Watkins and the Pragmatic Problem of Induction

Watkins proposes a neo-Popperian solution to the pragmatic problem of induction. He asserts that evidence can be used non-inductively to prefer the principle that corroboration is more successful over all human history than that, say, counter-corroboration is more successful either over this same period or in the future. Watkins's argument for rejecting the first counter-corroborationist alternative is beside the point. However, as whatever is the best strategy over all human history is irrelevant to the pragmatic problem of induction since we are not required to act in the past, and his argument for rejecting the second presupposes induction.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

(FAB11_2_003) Authentic Japanese architecture after Bruno Taut: the problem of eclecticism

This paper will examine attitudes to eclectic stylistic borrowing in Japan in the twentieth century in light of the concept of authenticity. I am particularly interested in how an earlier claim correlating European modernist and traditional Japanese architecture continues to colour conceptions about what is an 'authentic' response for Japanese architects to make to contemporary conditions. Non-Western and vernacular architectures generally have been the repository for touristic desires for regional authenticity and difference. Yet Japan's unique role in the development of modernist architecture has given a peculiar intensity to the demand for its architecture to resist a perceived postmodern decadence.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.