The severity of pandemic H1N1 influenza in the United States, from April to July 2009: A Bayesian analysis

Background: Accurate measures of the severity of pandemic (H1N1) 2009 influenza (pH1N1) are needed to assess the likely impact of an anticipated resurgence in the autumn in the Northern Hemisphere. Severity has been difficult to measure because jurisdictions with large numbers of deaths and other severe outcomes have had too many cases to assess the total number with confidence. Also, detection of severe cases may be more likely, resulting in overestimation of the severity of an average case. We sought to estimate the probabilities that symptomatic infection would lead to hospitalization, ICU admission, and death by combining data from multiple sources. Methods and Findings: We used complementary data from two US cities: Milwaukee attempted to identify cases of medically attended infection whether or not they required hospitalization, while New York City focused on the identification of hospitalizations, intensive care admission or mechanical ventilation (hereafter, ICU), and deaths. New York data were used to estimate numerators for ICU and death, and two sources of data - medically attended cases in Milwaukee or self-reported influenza-like illness (ILI) in New York - were used to estimate ratios of symptomatic cases to hospitalizations. Combining these data with estimates of the fraction detected for each level of severity, we estimated the proportion of symptomatic patients who died (symptomatic case-fatality ratio, sCFR), required ICU (sCIR), and required hospitalization (sCHR), overall and by age category. Evidence, prior information, and associated uncertainty were analyzed in a Bayesian evidence synthesis framework. Using medically attended cases and estimates of the proportion of symptomatic cases medically attended, we estimated an sCFR of 0.048% (95% credible interval [CI] 0.026%-0.096%), sCIR of 0.239% (0.134%-0.458%), and sCHR of 1.44% (0.83%-2.64%). Using self-reported ILI, we obtained estimates approximately 7-96lower. sCFR and sCIR appear to be highest in persons aged 18 y and older, and lowest in children aged 5-17 y. sCHR appears to be lowest in persons aged 5-17; our data were too sparse to allow us to determine the group in which it was the highest. Conclusions: These estimates suggest that an autumn-winter pandemic wave of pH1N1 with comparable severity per case could lead to a number of deaths in the range from considerably below that associated with seasonal influenza to slightly higher, but with the greatest impact in children aged 0-4 and adults 18-64. These estimates of impact depend on assumptions about total incidence of infection and would be larger if incidence of symptomatic infection were higher or shifted toward adults, if viral virulence increased, or if suboptimal treatment resulted from stress on the health care system; numbers would decrease if the total proportion of the population symptomatically infected were lower than assumed.published_or_final_versio

The Assortment Packing Problem: Multiperiod Assortment Planning for Short-Lived Products

Motivated by retailers ’ frequent introduction of new items to refresh product lines and maintain their market shares, we present the assortment packing problem in which a firm must decide, in advance, the release date of each product in a given collection over a selling season. Our formulation models the trade-offs among profit margins, preference weights, and limited life cycles. A key aspect of the problem is that each product is short-lived in the sense that, once introduced, its attractiveness lasts only a few periods and vanishes over time. The objective is to determine when to introduce each product to maximize the total profit over the selling season. Even for two periods, the corresponding optimization problem is shown to be NP-complete. As a result, we study a continuous relaxation of the problem that approximates the problem well, when the number of products is large. When margins are identical and product preferences decay exponentially, its solution can be characterized: it is optimal to introduce products with slower decays earlier. The structural properties of the relaxation also help us to develop several heuristics, for which we establish performance guarantees. We test our heuristics with data on sales and release dates of woman handbags from an accessories retailer. The numerical experiments show that the heuristics perform very well and can yield significant improvements in profitability. 1