Global variation in anastomosis and end colostomy formation following left-sided colorectal resection

Background End colostomy rates following colorectal resection vary across institutions in high-income settings, being influenced by patient, disease, surgeon and system factors. This study aimed to assess global variation in end colostomy rates after left-sided colorectal resection. Methods This study comprised an analysis of GlobalSurg-1 and -2 international, prospective, observational cohort studies (2014, 2016), including consecutive adult patients undergoing elective or emergency left-sided colorectal resection within discrete 2-week windows. Countries were grouped into high-, middle- and low-income tertiles according to the United Nations Human Development Index (HDI). Factors associated with colostomy formation versus primary anastomosis were explored using a multilevel, multivariable logistic regression model. Results In total, 1635 patients from 242 hospitals in 57 countries undergoing left-sided colorectal resection were included: 113 (6·9 per cent) from low-HDI, 254 (15·5 per cent) from middle-HDI and 1268 (77·6 per cent) from high-HDI countries. There was a higher proportion of patients with perforated disease (57·5, 40·9 and 35·4 per cent; P < 0·001) and subsequent use of end colostomy (52·2, 24·8 and 18·9 per cent; P < 0·001) in low- compared with middle- and high-HDI settings. The association with colostomy use in low-HDI settings persisted (odds ratio (OR) 3·20, 95 per cent c.i. 1·35 to 7·57; P = 0·008) after risk adjustment for malignant disease (OR 2·34, 1·65 to 3·32; P < 0·001), emergency surgery (OR 4·08, 2·73 to 6·10; P < 0·001), time to operation at least 48 h (OR 1·99, 1·28 to 3·09; P = 0·002) and disease perforation (OR 4·00, 2·81 to 5·69; P < 0·001). Conclusion Global differences existed in the proportion of patients receiving end stomas after left-sided colorectal resection based on income, which went beyond case mix alone

MATRIX FORMULATION FOR INFINITE-RANK OPERATORS

Every finite-rank operator on a linear space X is the composition of an operator from X to a finite dimensional Euclidean space and of an operator from that Euclidean space to X. We consider operators which are the sum of a finite-rank operator and another infinite-rank operator which satisfies an invariance condition with respect to one of the two 'components' of the finite-rank operator. A canonical procedure is given to reduce operator equations, eigenvalue problems and spectral subspace problems involving such operators to corresponding problems for finite matrices

Uniformly Conditioned Bases of Spectral Subspaces

A condition number of an ordered basis of a finite-dimensional normed space is defined in an intrinsic manner. This concept is extended to a sequence of bases of finite-dimensional normed spaces, and is used to determine uniform conditioning of such a sequence. We address the problem of finding a sequence of uniformly conditioned bases of spectral subspaces of operators of the form T n =S n +U n , where S n is a finite-rank operator on a Banach space and U n is an operator which satisfies an invariance condition with respect to S n . This problem is reduced to constructing a sequence of uniformly conditioned bases of spectral subspaces of operators on C nx1. The applicability of these considerations in practical as well as theoretical aspects of spectral approximation is pointed out

Computation of spectral subspaces for weakly singular integral operators

This paper deals with finding bases for finite-dimensional spectral subspaces of a bounded operator on the linear space of all complex-valued continuous functions defined on a compact Hausdorff space. This goal is achieved by computing an exact basis for a spectral subspace of an approximate operator which is not of finite rank. The theoretical framework allows a wide class of approximations, and a special emphasis is given to Kantorovich's singularity subtraction discretization of weakly singular compact integral operators. An application to Hopf's operator in the context of the transfer equation in stellar atmospheres illustrates the numerical computation of a bidimensional spectral subspace corresponding to a cluster of eigenvalues