*Stat Methods Med Res ; : 962280219850595, 2019 May 30.*

**| MEDLINE**| ID: mdl-31144601

##### RESUMO

As individuals may respond differently to treatment, estimating subgroup effects is important to understand the characteristics of individuals who may benefit. Factors that define subgroups may be correlated, complicating evaluation of subgroup effects, especially in observational studies requiring control of confounding variables. We address this problem when propensity score methods are used for confounding control. A common practice is to evaluate candidate subgroup identifiers one at a time without adjusting for other candidate identifiers. We show that this practice can be misleading if the treatment effect modification attributed to a candidate identifier is in truth due to the effect of other correlated true effect modifiers. Whereas jointly analyzing multiple identifiers provides estimates of the desired subgroup effects adjusted for the effects of the other identifiers, it requires the propensity scores to adequately reflect the underlying treatment selection processes and balance the covariates within each subgroup of interest. Satisfying the requirement in practice is hard since the number of strata may increase quickly, while the per stratum sample size may decrease dramatically. A practically helpful approach is utilizing the whole cohort for the propensity score estimation with modeling of interaction terms to reflect the potentially different treatment selection processes across strata. We empirically examine the performance of the whole cohort approach by itself and with subjecting the interaction terms to variable selection. Our results using both simulations and real data analysis suggest that the whole cohort approach should explore inclusion of high-order interactions in the propensity score model to ensure adequate covariate balance across strata, and that variable selection is of limited utility.

*PLoS One ; 13(6): e0198253, 2018.*

**| MEDLINE**| ID: mdl-29902187

##### RESUMO

Data generated from a system of interest typically consists of measurements on many covariate features and possibly multiple response features across all subjects in a designated ensemble. Such data is naturally represented by one response-matrix against one covariate-matrix. A matrix lattice is an advantageous platform for simultaneously accommodating heterogeneous data types: continuous, discrete and categorical, and exploring hidden dependency among/between features and subjects. After each feature being individually renormalized with respect to its own histogram, the categorical version of mutual conditional entropy is evaluated for all pairs of response and covariate features according to the combinatorial information theory. Then, by applying Data Could Geometry (DCG) algorithmic computations on such a mutual conditional entropy matrix, multiple synergistic feature-groups are partitioned. Distinct synergistic feature-groups embrace distinct structures of dependency. The explicit details of dependency among members of synergistic features are seen through mutliscale compositions of blocks computed by a computing paradigm called Data Mechanics. We then propose a categorical pattern matching approach to establish a directed associative linkage: from the patterned response dependency to serial structured covariate dependency. The graphic display of such a directed associative linkage is termed an information flow and the degrees of association are evaluated via tree-to-tree mutual conditional entropy. This new universal way of discovering system knowledge is illustrated through five data sets. In each case, the emergent visible heterogeneity is an organization of discovered knowledge.

##### Assuntos

Modelos Teóricos , Entropia*J Stat Phys ; 156(5): 823-842, 2014 Sep 01.*

**| MEDLINE**| ID: mdl-25071295

##### RESUMO

We propose a new method inspired from statistical mechanics for extracting geometric information from undirected binary networks and generating random networks that conform to this geometry. In this method an undirected binary network is perceived as a thermodynamic system with a collection of permuted adjacency matrices as its states. The task of extracting information from the network is then reformulated as a discrete combinatorial optimization problem of searching for its ground state. To solve this problem, we apply multiple ensembles of temperature regulated Markov chains to establish an ultrametric geometry on the network. This geometry is equipped with a tree hierarchy that captures the multiscale community structure of the network. We translate this geometry into a Parisi adjacency matrix, which has a relative low energy level and is in the vicinity of the ground state. The Parisi adjacency matrix is then further optimized by making block permutations subject to the ultrametric geometry. The optimal matrix corresponds to the macrostate of the original network. An ensemble of random networks is then generated such that each of these networks conforms to this macrostate; the corresponding algorithm also provides an estimate of the size of this ensemble. By repeating this procedure at different scales of the ultrametric geometry of the network, it is possible to compute its evolution entropy, i.e. to estimate the evolution of its complexity as we move from a coarse to a ne description of its geometric structure. We demonstrate the performance of this method on simulated as well as real data networks.

*Acta Crystallogr Sect E Struct Rep Online ; 65(Pt 10): o2431, 2009 Sep 12.*

**| MEDLINE**| ID: mdl-21577887

##### RESUMO

The title compound, C(20)H(24)O(4), was synthesized from the reaction of 2-oxo-2H-chromene-3-acyl chloride and menthol. The mean plane of the ester group and that of the four essentially planar (maximum deviation 0.0112â Å) C atoms of the chair-form cyclo-hexyl ring form dihedral angles of 43.8â (3) ° and 81.8â (1)°, respectively, with the mean plane of the coumarin ring system. In the crystal structure, weak inter-molecular C-Hâ¯O hydrogen bonds connect the mol-ecules into a two-dimensional network.

*Acta Crystallogr Sect E Struct Rep Online ; 65(Pt 11): o2817, 2009 Oct 23.*

**| MEDLINE**| ID: mdl-21578408

##### RESUMO

In the crystal structure of the title compound, C(20)H(16)O(5), the mol-ecule assumes an E configuration with the benzene ring and chromenecarboxyl group located on opposite ends of the C=C double bond. The chromene ring system and benzene ring are oriented at a dihedral angle of 74.66â (12)°. Weak inter-molecular C-Hâ¯O hydrogen bonding is present in the crystal structure.