Estimation and forecasting hospital admissions due to Influenza: Planning for winter pressure. The case of the West Midlands, UK

Winters are a difficult period for the National Health Service (NHS) in the United Kingdom (UK), due to the combination of cold weather and the increased likelihood of respiratory infections, especially influenza. In this article we present a proper statistical time series approach for modelling and analysing weekly hospital admissions in the West Midlands in the UK during the period week 15/1990 to week 14/1999. We consider three variables, namely, hospital admissions, general practitioner consultants, and minimum temperature. The autocorrelations of each series are shown to decay hyperbolically. The correlations of hospital admission and the lag of other series also decay hyperbolically but with different speed and directions. One of the main objectives of this paper is to show that each of the three series can be represented by a Fractional Differenced Autoregressive integrated moving average model, (FDA). Further, the hospital admission winter and summer residuals shows significant interdependency, which may be interpreted as hidden periodicities within the last 10-years time interval. The short-range (8 weeks) forecasting of hospital admission of the FDA model and a fourth-order AutoRegressive AR(4) model are quite similar. However, our results reveal that the long-range forecasting of FDA is more realistic. This implies that, using the FDA approach, the respective authority can plan for winter pressure properly.     

Testing for Additivity at Select Mixture Groups of Interest Based on Statistical Equivalence Testing Methods

Several assumptions, defined and undefined, are used in the toxicity assessment of chemical mixtures. In scientific practice mixture components in the low-dose region, particularly subthreshold doses, are often assumed to behave additively (i.e., zero interaction) based on heuristic arguments. This assumption has important implications in the practice of risk assessment, but has not been experimentally tested. We have developed methodology to test for additivity in the sense of Berenbaum (Advances in Cancer Research, 1981), based on the statistical equivalence testing literature where the null hypothesis of interaction is rejected for the alternative hypothesis of additivity when data support the claim. The implication of this approach is that conclusions of additivity are made with a false positive rate controlled by the experimenter. The claim of additivity is based on prespecified additivity margins, which are chosen using expert biological judgment such that small deviations from additivity, which are not considered to be biologically important, are not statistically significant. This approach is in contrast to the usual hypothesis-testing framework that assumes additivity in the null hypothesis and rejects when there is significant evidence of interaction. In this scenario, failure to reject may be due to lack of statistical power making the claim of additivity problematic. The proposed method is illustrated in a mixture of five organophosphorus pesticides that were experimentally evaluated alone and at relevant mixing ratios. Motor activity was assessed in adult male rats following acute exposure. Four low-dose mixture groups were evaluated. Evidence of additivity is found in three of the four low-dose mixture groups. The proposed method tests for additivity of the whole mixture and does not take into account subset interactions (e.g., synergistic, antagonistic) that may have occurred and cancelled each other out.     

Union rents and market structure revisited

Several recent studies give conflicting evidence on whether market power associated with industry concentration is an important source of union rents. Using a 1977 sample of 327 four-digit manufacturing industries, we re-examine the issue with a regression analysis that allows for differential union effects on price-cost margins across three levels of concentration. Large and small firm as well as industry average price-cost margins are analyzed. The results reaffirm those of Hirsch and Connolly (1987), who conclude that the effect of unions on profits is independent of market structure, and thus market power is not an important source of union rents. We find that unionization: (1) reduces industry profits in all three concentration groups with statistically insignificant differential effects, and (2) has a greater negative effect on the profits of large firms than it does on the profits of small firms, regardless of the concentration category. We benefited from the comments of an anonymous referee. Any remaining errors are our own.     

Bayesian Inference Under Partial Prior Information

Partial prior information on the marginal distribution of an observable random variable is considered. When this information is incorporated into the statistical analysis of an assumed parametric model, the posterior inference is typically non‐robust so that no inferential conclusion is obtained. To overcome this difficulty a method based on the standard default prior associated to the model and an intrinsic procedure is proposed. Posterior robustness of the resulting inferences is analysed and some illustrative examples are provided.