An evaluation of a Bayesian method of dose escalation based on bivariate binary responses

Recently, various approaches have been suggested for dose escalation studies based on observations of both undesirable events and evidence of therapeutic benefit. This article concerns a Bayesian approach to dose escalation that requires the user to make numerous design decisions relating to the number of doses to make available, the choice of the prior distribution, the imposition of safety constraints and stopping rules, and the criteria by which the design is to be optimized. Results are presented of a substantial simulation study conducted to investigate the influence of some of these factors on the safety and the accuracy of the procedure with a view toward providing general guidance for investigators conducting such studies. The Bayesian procedures evaluated use logistic regression to model the two responses, which are both assumed to be binary. The simulation study is based on features of a recently completed study of a compound with potential benefit to patients suffering from inflammatory diseases of the lung.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

A score test for binary data with patient non-compliance

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is all-or-nothing, in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds. Copyright © 2003 John Wiley & Sons, Ltd.

Active-control trials with binary data: a comparison of methods for testing superiority or non-inferiority using the odds ratio

This paper considers methods for testing for superiority or non-inferiority in active-control trials with binary data, when the relative treatment effect is expressed as an odds ratio. Three asymptotic tests for the log-odds ratio based on the unconditional binary likelihood are presented, namely the likelihood ratio, Wald and score tests. All three tests can be implemented straightforwardly in standard statistical software packages, as can the corresponding confidence intervals. Simulations indicate that the three alternatives are similar in terms of the Type I error, with values close to the nominal level. However, when the non-inferiority margin becomes large, the score test slightly exceeds the nominal level. In general, the highest power is obtained from the score test, although all three tests are similar and the observed differences in power are not of practical importance. Copyright (C) 2007 John Wiley & Sons, Ltd.

Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

Bayesian decision procedures for binary and continuous bivariate dose-escalation studies

In this paper, Bayesian decision procedures are developed for dose-escalation studies based on binary measures of undesirable events and continuous measures of therapeutic benefit. The methods generalize earlier approaches where undesirable events and therapeutic benefit are both binary. A logistic regression model is used to model the binary responses, while a linear regression model is used to model the continuous responses. Prior distributions for the unknown model parameters are suggested. A gain function is discussed and an optional safety constraint is included. Copyright (C) 2006 John Wiley & Sons, Ltd.

A practical approach to a multi-level analysis with a sparse binary outcome within a large surgical trial

Objectives: To assess the potential source of variation that surgeon may add to patient outcome in a clinical trial of surgical procedures. Methods: Two large (n = 1380) parallel multicentre randomized surgical trials were undertaken to compare laparoscopically assisted hysterectomy with conventional methods of abdominal and vaginal hysterectomy; involving 43 surgeons. The primary end point of the trial was the occurrence of at least one major complication. Patients were nested within surgeons giving the data set a hierarchical structure. A total of 10% of patients had at least one major complication, that is, a sparse binary outcome variable. A linear mixed logistic regression model (with logit link function) was used to model the probability of a major complication, with surgeon fitted as a random effect. Models were fitted using the method of maximum likelihood in SAS((R)). Results: There were many convergence problems. These were resolved using a variety of approaches including; treating all effects as fixed for the initial model building; modelling the variance of a parameter on a logarithmic scale and centring of continuous covariates. The initial model building process indicated no significant 'type of operation' across surgeon interaction effect in either trial, the 'type of operation' term was highly significant in the abdominal trial, and the 'surgeon' term was not significant in either trial. Conclusions: The analysis did not find a surgeon effect but it is difficult to conclude that there was not a difference between surgeons. The statistical test may have lacked sufficient power, the variance estimates were small with large standard errors, indicating that the precision of the variance estimates may be questionable.

Separation of Ba-137m from Cs-137 using new ion exchanger Na-2(H2O)(4)(H3O)[Al(OH)(6)Mo6O18]

A new polyoxometalate of chemical formula, Na-2(H2O)(4)(H3O)[Al(OH)(6)Mo6O18] (1) containing Anderson type large anion has been synthesized and characterized by single-crystal X-ray structure determination and IR spectroscopic studies. The crystal of 1 is triclinic, spacegroup P-1 with cell dimensions, a = 6.365(9) angstrom, b = 10.37(1) angstrom, c = 10.44(1) angstrom and alpha = 65.41(1), beta = 77.18(1), gamma = 86.58(1) and Z = 1. The compound 1 behaves as an ion exchanger and is stable in thermal, radiation and chemical environments. Radiochemical separation of the short-lived daughter Ba-137m (t(1/2) = 2.50 min) from its long-lived parent Cs-137 using this newly designed and synthesized ion exchanger has been developed.

6,6 '-bis-(5,6-diethyl-[1,2,4]triazin-3-yl)-2,2 '-bipyridyl the first example of a new class of quadridentate hetercyclic extraction reagents for the separation of americium(III) and europium(III)

The synthesis of the first example of a new class of tetradentate reagents for the efficient separation of americium(Ill) and europium(111) is reported together with the structure of the complex formed with europium(III), (C) 2004 Elsevier B.V. All rights reserved.

Separation of lanthanides and actinides(III) using tridentate benzimidazole, benzoxazole and benzothiazole ligands

The ability of new hydrophobic tridentate ligands based on 2,6-bis(benziinidazol-2-yl)pyridine, 2,6-bis(benzoxazol-2-yl)pyridine and 2,6-bis(benzothiazol-2-yl)pyridine to selectively extract americium(III) from europium(III) was measured. The most promising ligand-2,6-bis(benzoxazol-2-yl)-4-(2-decyl-1-tetradecyloxy)pyridine L-9 was found to give separation factors (SFAm/Eu) of up to 70 when used to extract cations from 0.02-0.10 M HNO3 into TPH in synergy with 2-bromodecanoic acid. Six structures of lanthanide complexes with 2,6-bis(benzoxazol-2-yl)pyridine L-6 were then determined to evaluate the types of species that are likely to be involved in the separation process. Three structural types were observed, namely [LnL(6)(NO3)(3)(H2O)2], 11-coordinate only for La, [LnL(6) (NO3)(3) (CH3CN)], 10-coordinate for Pr, Nd and Eu and [LnL(6) (NO3)(3)(H2O)], L 10-coordinate for Eu and Gd. Quantum Mechanics calculations were carried out on the tridentate ligands to elucidate the conformational preferences of the ligands in the free state and protonated and diprotonated forms and to assess the electronic properties of the ligands for comparison with other terdentate ligands used in lanthanide/actinide separation processes.

6,6 '-bis (5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-benzo[1,2,4]triazin-3-yl) [2,2 ']bipyridine, an effective extracting agent for the separation of americium(III) and curium(III) from the lanthanides

The extraction of americium(III), curium(III), and the lanthanides(III) from nitric acid by 6,6'- bis (5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-benzo[1,2,4]triazin-3-yl)-[2,2'] bipyridine (CyMe4-BTBP) has been studied. Since the extraction kinetics were slow, N,N'-dimethyl-N,N'-dioctyl-2-(2-hexyloxy-ethyl)malonamide (DMDOHEMA) was added as a phase transfer reagent. With a mixture of 0.01 M CyMe4-BTBP + 0.25 M DMDOHEMA in n -octanol, extraction equilibrium was reached within 5 min of mixing. At a nitric acid concentration of 1 M, an americium(III) distribution ratio of approx. 10 was achieved. Americium(III)/lanthanide(III) separation factors between 50 (dysprosium) and 1500 (lanthanum) were obtained. Whereas americium(III) and curium(III) were extracted as disolvates, the stoichiometries of the lanthanide(III) complexes were not identified unambiguously, owing to the presence of DMDOHEMA. In the absence of DMDOHEMA, both americium(III) and europium(III) were extracted as disolvates. Back-extraction with 0.1 M nitric acid was thermodynamically possible but rather slow. Using a buffered glycolate solution of pH=4, an americium(III) distribution ratio of 0.01 was obtained within 5 min of mixing. There was no evidence of degradation of the extractant, for example, the extraction performance of CyMe4-BTBP during hydrolylsis with 1 M nitric acid did not change over a two month contact.

Some new strategies for the chemical separation of actinides and lanthanides

A future goal in nuclear fuel reprocessing is the conversion or transmutation of the long-lived radioisotopes of minor actinides, such as americium, into short-lived isotopes by irradiation with neutrons. In order to achieve this transmutation, it is necessary to separate the minor actinides(III), [An(Ill)], from the lanthanides(III), [Ln(Ill)], by solvent extraction (partitioning), because the lanthanides absorb neutrons too effectively and hence limit neutron capture by the transmutable actinides. Partitioning using ligands containing only carbon, hydrogen, nitrogen and oxygen atoms is desirable because they are completely incinerable and thus the final volume of waste is minimised [1]. Nitric acid media will be used in the extraction experiments because it is envisaged that the An(III)/Ln(III) separation process could take place after the PUREX process. There is no doubt that the correct design of a molecule that is capable of acting as a ligand or extraction reagent is required for the effective separation of metal ions such as actinides(III) from lanthanides. Recent attention has been directed towards heterocyclic ligands with for the preferential separation of the minor actinides. Although such molecules have a rich chemistry, this is only now becoming sufficiently well understood in relation to the partitioning process [2]. The molecules shown in Figures I and 2 will be the principal focus of this study. Although the examples chosen here are used rather specific, the guidelines can be extended to other areas such as the separation of precious metals [3].

Coordination and separation studies of the uranyl ion with iso-butyramide based ligands: Synthesis and structures of [UO2(NO3)(2)((C3H7CON)-C-i{(C4H9)-C-i}(2))(2)] and [UO2(C6H5COCHCOC6H5)(2)((C3H7CON)-C-i{(C3H7)-C-i}(2))]

The coordination chemistry of iso-butyramide based ligands such as: (C3H7CON)-C-i((C3H7)-C-i)(2), (C3H7CON)-C-i(C4H9)(2) and (C3H7CON)-C-i((C4H9)-C-i)(2) with [UO2(NO3)(2) center dot 6H(2)O], [UO2(OO)(2) center dot 2H(2)O] {where OO = C4H3SCOCHCCCF3 (TTA), C6H5COCHCOCF3 (BTA) and C6H5COCHCOC6H5 (DBM)), [Th(NO3)(4) center dot 6H(2)O] and [La(NO3)(3) center dot 6H(2)O] has been evaluated. Structures for the compounds [UO2(NO3)(2)CC3H7CON{(C4H9)-C-i}(2))(2)] and [UO2(C6H5COCHCOC6H5)(2)((C3H7CON)-C-i{(C3H7)-C-i)(2))] have been determined by single crystal X-ray diffraction methods. Preliminary separation studies from nitric acid medium using the amide (C3H7CON)-C-i((C4H9)-C-i)(2) with U(VI), Th(IV) and La(Ill) ions showed the selective precipitation of uranyl ion from the mixture. Thermal study of the compound [UO2(NO3)(2)((C3H7CON)-C-i((C4H9)-C-i)(2))(2)] in air revealed that the ligands can be destroyed completely on incineration. (C) 2008 Elsevier Ltd. All rights reserved.

Phase mixing and phase separation accompanying the catalytic oxidation of CO on Ir{100}

The co-adsorption of CO and O on the unreconstructed (1 x 1) phase of Ir {100} was examined by low energy electron diffraction (LEED) and temperature programmed desorption (TPD). When CO is adsorbed at 188 K onto the Ir{100} surface precovered with 0.5 ML O, a mixed c(4 x 2)-(2O + CO) overlayer is formed. All CO is oxidised upon heating and desorbs as CO2 in three distinct stages at 230 K, 330 K and 430 K in a 2:1:2 ratio. The excess oxygen left on the surface after all CO has reacted forms an overlayer with a LEED pattern with p(2 x 10) periodicity. This overlayer consists of stripes with a local p(2 x 1)-O arrangement of oxygen atoms separated by stripes of uncovered It. When CO is adsorbed at 300 K onto the surface precovered with 0.5 ML O an apparent (2 x 2) LEED pattern is observed. LEED IV analysis reveals that this pattern is a superposition of diffraction patterns from islands of c(2 x 2)-CO and p(2 x 1)-O structures on the surface. Heating this co-adsorbed overlayer leads to the desorption of CO, in two stages at 330 K and 430 K; the excess CO (0.1 ML) desorbs at 590 K. LEED IV structural analysis of the mixed c(4 x 2) O and CO overlayer shows that both the CO molecules and the O atoms occupy bridge sites. The O atoms show significant lateral displacements of 0.14 angstrom away from the CO molecules; the C-O bond is slightly expanded with respect to the gas phase (1.19 angstrom); the modifications of the Ir substrate with respect to the bulk-terminated surface are very small. (c) 2006 Elsevier B.V. All rights reserved.