The Quality of Health Care Providers

Obtaining better information on the quality of health care providers is one of the most pressing issues in health policy today. In this paper we (1) develop a new method for measuring quality of care that overcomes the key limitations of available quality measures, and (2) apply this method to estimating the quality of hospital care for elderly patients with heart disease. Our approach optimally combines information from all available current and past quality indicators in order to more accurately estimate and forecast each provider's quality level. For patients with heart disease, the method is able to predict and forecast differences in patient outcomes across hospitals remarkably well - far better than existing methods. Our approach also provides an empirical basis for choosing among potential quality indicators. In particular, we find that differences across hospitals in short-term mortality rates following a heart attack, adjusted for patient demographics, are excellent indicators of quality of care: They vary dramatically across hospitals, are persistent over time, are highly correlated with alternative quality indicators, and are highly correlated with mortality rates that adjust more extensively for patient severity. Thus, comparing quality of care across providers may be far more feasible than many now believe.

Vector Reachability Problem in SL(2,Z)\mathrm{SL}(2,\mathbb{Z})

The decision problems on matrices were intensively studied for many decades as matrix products play an essential role in the representation of various computational processes. However, many computational problems for matrix semigroups are inherently difficult to solve even for problems in low dimensions and most matrix semigroup problems become undecidable in general starting from dimension three or four. This paper solves two open problems about the decidability of the vector reachability problem over a finitely generated semigroup of matrices from $\mathrm{SL}(2,\mathbb{Z})$ and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are from $\mathrm{SL}(2,\mathbb{Z})$. The approach to solving reachability problems is based on the characterization of reachability paths between points which is followed by the translation of numerical problems on matrices into computational and combinatorial problems on words and formal languages. We also give a geometric interpretation of reachability paths and extend the decidability results to matrix products represented by arbitrary labelled directed graphs. Finally, we will use this technique to prove that a special case of the scalar reachability problem is decidable

Robust regularized singular value decomposition with application to mortality data

We develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leave-one-row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS649 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Endogenous Fishing Mortalities: a State-Space Bioeconomic Model

A methodology that endogenously determines catchability functions that link fi shing mortality with contemporaneous stock abundance is presented. We consider a stochastic age-structured model for a fishery composed by a number of fi shing units (fleets, vessels or métiers) that optimally select the level of fishing effort to be applied considering total mortalities as given. The introduction of a balance constrain which guarantees that total mortality is equal to the sum of individual fi shing mortalities optimally selected, enables total fishing mortality to be determined as a combination of contemporaneous abundance and stochastic processes affecting the fishery. In this way, future abundance can be projected as a dynamic system that depends on contemporaneous abundance. The model is generic and can be applied to several issues of fisheries management. In particular, we illustrate how to apply the methodology to assess the floating band target management regime for controlling fishing mortalities which is inspired in the new multi-annual plans. Our results support this management regime for the Mediterranean demersal fishery in Northern Spain.This work was funded by the European Commission as part of the MINOUW project (H2020-SFS-2014-2, number 634495) and the Spanish Ministry of Economy, Industry and Competitiveness (ECO2016-78819-R, AEI/FEDER, UE