A Bayesian adaptive marker‐stratified design for molecularly targeted agents with customized hierarchical modeling

It is well known that the treatment effect of a molecularly targeted agent (MTA) may vary dramatically, depending on each patient's biomarker profile. Therefore, for a clinical trial evaluating MTA, it is more reasonable to evaluate its treatment effect within different marker subgroups rather than evaluating the average treatment effect for the overall population. The marker‐stratified design (MSD) provides a useful tool to evaluate the subgroup treatment effects of MTAs. Under the Bayesian framework, the beta‐binomial model is conventionally used under the MSD to estimate the response rate and test the hypothesis. However, this conventional model ignores the fact that the biomarker used in the MSD is, in general, predictive only for the MTA. The response rates for the standard treatment can be approximately consistent across different subgroups stratified by the biomarker. In this paper, we proposed a Bayesian hierarchical model incorporating this biomarker information into consideration. The proposed model uses a hierarchical prior to borrow strength across different subgroups of patients receiving the standard treatment and, therefore, improve the efficiency of the design. Prior informativeness is determined by solving a “customized” equation reflecting the physician's professional opinion. We developed a Bayesian adaptive design based on the proposed hierarchical model to guide the treatment allocation and test the subgroup treatment effect as well as the predictive marker effect. Simulation studies and a real trial application demonstrate that the proposed design yields desirable operating characteristics and outperforms the existing designs

Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop☆☆The work was supported in part by Australia Research Counsil under the Discovery Projects scheme (grant ID: DP0559111).

AbstractThis paper deals with Liénard equations of the form x˙=y, y˙=P(x)+yQ(x,y), with P and Q polynomials of degree 5 and 4 respectively. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree six, exhibiting a double figure eight loop. The number of limit cycles and their distributions are given by using the methods of bifurcation theory and qualitative analysis

Diaqua­(5-carb­oxy­benzene-1,3-dicarboxyl­ato-κ2 O 1,O 1′)(6,6′-dimethyl-2,2′-bipyridine-κ2 N,N′)nickel(II) hepta­hydrate

In the title compound, [Ni(C9H4O6)(C12H12N2)(H2O)2]·7H2O, the NiII atom is six-coordinated by two O atoms from a chelating carboxyl­ate group of a 5-carb­oxy­benzene-1,3-dicarboxyl­ate ligand, two O atoms of two water mol­ecules and two N atoms from a 6,6′-dimethyl-2,2′-bipyridine ligand in a distorted octa­hedral geometry. The compound exhibits a three-dimensional supra­molecular structure composed of the complex mol­ecules and lattice water mol­ecules, which are linked together by inter­molecular O—H⋯O hydrogen bonds and partly overlapping π–π inter­actions between the pyridine and benzene rings [centroid–centroid distances = 3.922 (2) and 3.921 (2) Å]. One of the lattice water mol­ecules is disordered over two positions in an occupancy ratio of 0.521 (6):0.479 (6)

3-(Pyridin-4-ylmeth­oxy)phenol

In the title compound, C12H11NO2, the phenolic ring is inclined at an angle of 32.70 (1)° with respect to the pyridine ring. In the crystal, inter­molecular O—H⋯N hydrogen bonds link the mol­ecules into C(11) chains along [001]

Poly[[hexa­aqua­bis­(μ3-benzene-1,3,5-tricarboxyl­ato-κ3 O 1:O 3:O 5)bis­(5,5′-dimethyl-2,2′-bipyridine-κ2 N,N′)trizinc] hexa­hydrate]

In the title compound, {[Zn3(C9H3O6)2(C12H12N2)2(H2O)6]·6H2O}n, one ZnII atom, lying on an inversion center, is six-coordinated by two O atoms from two benzene-1,3,5-tricarboxyl­ate (btc) ligands and four water mol­ecules in a distorted octa­hedral geometry. The other ZnII atom is five-coordinated by two N atoms from a 5,5′-dimethyl-2,2′-bipyridine (dmbpy) ligand, two O atoms from two btc ligands and one water mol­ecule in a distorted trigonal–bipyramidal geometry. The compound features a one-dimensional ladder structure, with windows of ca 10.245 (1) × 15.446 (2) Å. The ladders are linked together by inter­molecular O—H⋯O hydrogen bonds and π–π inter­actions between the benzene rings and between the pyridine rings [centroid-to-centroid distances 3.858 (2) and 3.911 (3) Å, respectively] to form a three-dimensional supra­molecular structure. One of the lattice water molecules is disordered over two positions in a 0.592:0.408 ratio

catena-Poly[[[aqua­(pyridine-4-carboxyl­ato-κN)silver(I)]-μ-hexa­methyl­ene­tetra­amine-κ2 N:N′] dihydrate]

In the title compound, {[Ag(C6H4NO2)(C6H12N4)(H2O)]·2H2O}n, the AgI atom shows a distorted triangular pyramidal geometry,, formed by two N atoms from two hexa­methyl­ene­tetra­amine (hmt) ligands and one N atom from a pyridine-4-carboxyl­ate (4-pdc) ligand and one water mol­ecule. The hmt ligands bridge the Ag atoms, forming a chain along [001]. The carboxyl­ate group of the 4-pdc ligand is uncoordinated. O—H⋯O hydrogen bonds between the water mol­ecules and carboxyl­ate groups stabilize the structure