The ecological fallacy of the role of age in chronic disease and hospital demand

Objective: To examine the relationship between age and all-cause hospital utilization in the years preceding and following a diagnosis in hospital of heart failure, type 2 diabetes, or chronic obstructive pulmonary disease (COPD). Research Design: A cohort study of all patients in Western Australia who have had a principal diagnosis of heart failure, type 2 diabetes, or COPD, upon admission to hospital. All-cause hospital utilization 6 years preceding and 4 years following cardinal events, that is, a disease-specific diagnosis upon hospital admission, where such an event has not occurred in the previous 2 years, are examined in specific age groups. Results: Six years preceding a cardinal event, all-cause emergency department (ED) presentations are similar in all age groups, from under 55 to over 85 years of age, except in COPD where ED presentation rates are higher in younger groups. All-cause hospital inpatient days are transiently higher in the years preceding and following a cardinal event in older age groups, yet return to similar levels across all age cohorts after 4 years. ED presentations are significantly higher in the 4 years following cardinal events in younger compared with older groups. Conclusions: Longitudinal analysis of utilization around cardinal events overcomes the confounding effect of differences in chronic disease rates between age groups, avoiding a source of ecologic bias that erroneously attributes increasing utilization in individuals with chronic disease to age. Programs designed to reduce hospital demand in patients with chronic disease should possibly focus on younger, rather than older, individuals

A General Framework for Constrained Smoothing

There are a wide array of smoothing methods available for finding structure in data. A general framework is developed which shows that many of these can be viewed as a projection of the data, with respect to appropriate norms. The underlying vector space is an unusually large product space, which allows inclusion of a wide range of smoothers in our setup (including many methods not typically considered to be projections). We give several applications of this simple geometric interpretation of smoothing. A major payoff is the natural and computationally frugal incorporation of constraints. Our point of view also motivates new estimates and it helps to understand the finite sample and asymptotic behaviour of these estimates

Discretization Methods for Average Derivative Estimation

Nonparametric smoothing methods are increasingly used since computing power is easier available. One of the ways to analyze samples by these methods is to check graphically what happens if the smoothing parameter is varied. This may lead to an enormous amount of calculations which make an interactive analysis impossible. In this paper we demonstrate how the computational burden can be reduced by discretization methods. We first focus on density estimation and density derivatives estimation since most nonparametric smoothing methods involve the estimation of such quantities. The ideas derived in this context are then employed for Average Derivative Estimation. A Monte--Carlo study demonstrates that this methods are very efficient for practical use. Keywords: Density--estimation, Estimation of density derivatives, Multi--variate density estimation, Estimation of partial derivatives of multi--variate densities, Average Derivative Estimation, Discretizing methods, Binning. y This paper wa..