Approximation for response adaptive designs using Stein's method

Stein's method introduced by Charles Stein (1972) is a powerful tool in distributional approximation, especially in classes of random variables that are stochastically dependent. In recent years, researchers have concentrated more on adaptive designs. For the response adaptive randomization procedures, the patient's allocation depends on the aggregated information that is acquired from the responses of the previously treated patients. This design uses the information of patients' responses to modify treatment allocation in order to assign more patients to a successful treatment, thus introduce dependent structure in the data. In this thesis we investigate the use of Stein's method in statistical inference for response adaptive design. We have acquired asymptotic normality of the maximum likelihood estimators for treatment effects by deriving an upper bound for these estimators using Stein's method. We examine the performance of three types of response adaptive designs under various success probabilities through simulation studies. Since adaptive designs generate a dependent sequence of random variables that are not exchangeable, we present the advantage of using bootstrap re-sampling in adaptive designs and the efficiency of this method. We compare bootstrap confidence intervals with the asymptotic confidence interval under different success rates of three allocation methods. Also, we discuss the normal approximation based on the Wald's statistic in the numerical studies

{4,4′,5,5′-Tetra­methyl-2,2′-[1,1′-(ethane-1,2-diyldinitrilo)diethyl­idyne]diphenolato}nickel(II)–methanol–chloro­form (1/1/1)

In the title compound, [Ni(C22H26N2O2)]·CH3OH·CHCl3, the NiII ion is in a slightly distorted square-planar geometry involving an N2O2 atom set of the tetra­dentate Schiff base ligand. The asymmetric unit contains one mol­ecule of the complex and one mol­ecule each of chloro­form and methanol. The methanol mol­ecule is hydrogen bonded to the phenolate O atoms. In the crystal structure, short inter­molecular distances between the centroids of six-membered chelate rings [3.7002 (9) Å] indicate the presence of π–π inter­actions, which link the mol­ecules into stacks along the a axis. In addition, there are Ni⋯Ni distances which are shorter than the sum of the van der Waals radii of two Ni atoms. The crystal structure is further stabilized by inter­molecular O—H⋯O and C—H⋯O hydrogen bonds, and weak inter­molecular C—H⋯π inter­actions linking mol­ecules into extended one-dimensional chains along the c axis

Spectrophotometric investigation of DL-tryptophan in the presence of Ni(II) or Co(II) ions

In the present study, synthesis of transition metal complexes of DL-tryptophan with metal precursors such as nickel (II) and cobalt (II) ions in water under refluxing conditions and optimization of the reactions to obtain the composition of complexes in water solutions has been reported. The preparation and structural elucidation of the complexes was undertaken by using physico-chemical, potentiometric titration and spectroscopic methods (UV/Vis, FT-IR and XRD). Comparisons of the spectral measurements of DL-tryptophan with those of the nickel (II) and cobalt (II) complexes are useful in determining the atoms of the ligand that are coordinated to the metal ion. In addition, K (dissociation constant) and ΔG (Gibbs free energy) values were calculated using the Babko and Stanley & Turners methods. Antibacterial and antifungal activities of the complexes were studied screened against bacteria and fungi. The activity data shows that and cobalt complexes of DL-tryptophan are more potent than the DL-tryptophan

{4,4′-Dimeth­oxy-2,2′-[1,1′-(ethane-1,2-diyldinitrilo)diethyl­idyne]diphenolato}nickel(II) hemihydrate

In the title complex, [Ni(C20H22N2O4)]·0.5H2O, the NiII ion is in a slightly distorted square-planar geometry involving an N2O2 atom set of the tetra­dentate Schiff base ligand. The asymmetric unit contains one mol­ecule of the complex and half a water solvent mol­ecule. The solvent water mol­ecule lies on a crystallographic twofold rotation axis. An inter­molecular O—H⋯O hydrogen bond forms an R 2 1(4) ring motif involving a bifurcated hydrogen bond to the phenolate O atoms of the complex. In the crystal structure, mol­ecules are linked by π–π stacking inter­actions, with centroid–centroid distances in the range 3.5310 (11)–3.7905 (12) Å, forming extended chains along the b axis. In addition, there are Ni⋯Ni and Ni⋯N inter­actions [3.4404 (4)–4.1588 (4) and 3.383 (2)–3.756 (2) Å, respectively] which are shorter than the sum of the van der Waals radii of the relevant atoms. Further stabilization of the crystal structure is attained by weak inter­molecular C—H⋯O and C—H⋯π inter­actions

2-[(E)-(5-Amino-2,3-diphenyl­quinoxalin-6-yl)imino­meth­yl]-4-chloro­phenol

The title Schiff base compound, C27H19ClN4O, features two intra­molecular O—H⋯N and N—H⋯N hydrogen bonds involving the hydr­oxy and amino groups to generate S(6) and S(5) ring motifs, respectively. In the crystal structure, weak inter­molecular N—H⋯O and C—H⋯N inter­actions, together with π–π contacts [centroid–centroid distances = 3.6294 (11)–3.6881 (11) Å], link neighboring mol­ecules

{5,5′-Dihydr­oxy-2,2′-[o-phenyl­enebis­(nitrilo­methyl­idyne)]diphenolato}nickel(II) dihydrate

In the title complex, [Ni(C20H14N2O4)]·2H2O, the NiII ion is in an essentially square-planar geometry involving an N2O2 atom set of the tetra­dentate Schiff base ligand. The Ni atom lies on a crystallographic twofold rotation axis. The asymmetric unit contains one half-mol­ecule of the complex and a water mol­ecule. An inter­molecular O—H⋯O hydrogen bond forms a four-membered ring, producing an R 1 2(4) ring motif involving a bifurcated hydrogen bond to the phenolate O atoms of the complex mol­ecule. In the crystal structure, mol­ecules are linked by π–π stacking inter­actions, with centroid–centroid distances in the range 3.5750 (11)–3.7750 (11) Å. As a result of the twofold symmetry, the central benzene ring makes the same dihedral angle of 15.75 (9)° with the two outer benzene rings. The dihedral angle between the two hydroxy­phenyl rings is 13.16 (5)°. In the crystal structure, mol­ecules are linked into infinite one-dimensional chains by directed four-membered O—H⋯O—H inter­actions along the c axis and are further connected by C—H⋯O and π–π stacking into a three-dimensional network. An inter­esting feature of the crystal structure is the short Ni⋯O, O⋯O and N⋯N inter­actions which are shorter than the sum of the van der Waals radii of the relevant atoms. The crystal structure is stabilized by inter­molecular O—H⋯O and C—H⋯O hydrogen bonds and by π–π stacking inter­actions

2-[(E)-(5-Amino-2,3-diphenyl­quinoxalin-6-yl)imino­meth­yl]-4-bromo­phenol

The title compound, C27H19BrN4O, is a mono-anil Schiff base ligand. Three intra­molecular O—H⋯N and N—H⋯N hydrogen bonds involving the hydr­oxy and amino groups generate S(6) and S(5) ring motifs, respectively. In the crystal structure, weak inter­molecular N—H⋯O and C—H⋯O hydrogen bonds together with π–π inter­actions [centroid–centroid distances = 3.628 (3)–3.729 (3) Å] link neighboring mol­ecules

{6,6′-Dieth­oxy-2,2′-[2,2-dimethyl­propane-1,3-diylbis(nitrilo­methyl­idyne)]diphenolato}nickel(II) monohydrate

In the title complex, [Ni(C23H28N2O4)]·H2O, the NiII ion is coordinated by the N2O2 unit of the tetra­dentate Schiff base ligand in a slightly distorted planar geometry. The asymmetric unit of the title compound comprises one complex mol­ecule and a water mol­ecule of crystallization. The H atoms of the water mol­ecule make bifurcated inter­molecular hydrogen bonds with the O atoms of the phenolate and eth­oxy groups with R 1 2(5) and R 1 2(6) ring motifs, which may, in part, influence the mol­ecular configuration. The dihedral angle between the two benzene rings is 31.43 (5)°. The crystal structure is further stabilized by inter­molecular C—H⋯O and C—H⋯π inter­actions, which link neighbouring mol­ecules into one-dimensional extended chains along the a axis. An inter­esting feature of the crystal structure is the short inter­molecular C⋯C [3.3044 (14) Å] contact which is shorter than the sum of the van der Waals radii