LETTERS Estimating Deaths Due to Influenza and Respiratory Syncytial Virus To the Editor: Dr Thompson and colleagues 1 developed a sta- tistical model to estimate deaths attributable to influenza and respiratory syncytial virus (RSV). We are concerned that their model was inappropriate. When designing a model to at- tribute causality to deaths, a reasonable initial approach would be to assume that the number of deaths due to a specific virus in any given week was proportional to the number of labora- tory reports of that virus in that week. The total number of deaths would be the sum of the contributions from each virus, plus the seasonal background of deaths due to other causes. Simi- lar models have been used successfully to estimate the propor- tion of gastrointestinal disease attributable to rotavirus 2 and the proportion of bronchiolitis and pneumonia attributable to RSV and other pathogens. 3 Additional terms and factors could be included to account, for example, for improving sensitivity of surveillance over time, but the core of the model would re- main linear and additive. An appropriate analysis could use linear regression, a gen- eralized linear model (GLM) with a Poisson error distribution and an identity link, or maximum likelihood for a non-GLM. Instead, Thompson et al used a Poisson model in which the number of deaths increased exponentially with the number of laboratory reports and the effects of each virus (and the sea- sonal background) on the number of deaths were multiplica- tive rather than additive. We do not believe that there is plau- sible justification for fitting such a model to these data. Nigel J. Gay, MSc Nick J. Andrews, MSc Caroline L. Trotter, MSc W. John Edmunds, PhD Statistics, Modelling and Economics Division Communicable Disease Surveillance Centre London, England 1. Thompson WW, Shay DK, Weintraub E, et al. Mortality associated with influ- enza and respiratory syncytial virus in the United States. JAMA. 2003;289:179- 186. 2. Ryan MJ, Ramsay M, Brown D, et al. Hospital admissions attributable to rota- virus infection in England and Wales. J Infect Dis. 1996;174(suppl 1):S12-S18. 3. Muller-Pebody B, Edmunds WJ, Zambon MC, et al. Contribution of RSV to bron- chiolitis and pneumonia-associated hospitalizations in English children, April 1995- March 1998. Epidemiol Infect. 2002;129:99-106. To the Editor: Dr Thompson and colleagues 1 presented a model that uses influenza and RSV surveillance data to estimate virus- associated mortality. The authors propose that this model re- place Serfling-type models, which have been used for 40 years to estimate deaths attributed to influenza by subtracting a model- generated baseline from observed winter deaths. 2,3 The model of Thompson et al averages 34 470 (range, 7608- 68 328) total seasonal influenza-related deaths for 1976-1999. This average, much higher than previous reports (approxi- mately 20 000; range, 0-40 000 for 1972-1992), 3 suggests that the Serfling models underestimate the mortality burden and that the new model corrects this problem. In fact this is not the case. A Serfling-type model 4 estimated an average of 37 500 (range 0-74 500) all-cause excess deaths for 1976-1999. Both models report an increase in influenza-related deaths in the 1990s, which for Serfling models is fully explained by a rap- idly increasing population of very elderly Americans (for whom influenza-related mortality risk increases exponentially), 5 to- gether with increased circulation of the virulent subtype in- fluenza A(H3N2). 4 Although Thompson et al offer their model as superior, they do not provide graphical or statistical evidence of acceptable fit or model validation. Nor do they compare their influenza mortality estimates with those based on Serfling models. In fact, their individual season estimates of pneumonia and influenza deaths correlate poorly with Serfling estimates (R 2 0.5), and this comparison reveals an unexplained time dependency (FIGURE). The doubling in their surrogate measure of virus ac- tivity (from 8% to 16% influenza-positive specimens, Table 1 1 ) over the study period leads to large underestimates (1970s) and overestimates (1990s) of influenza mortality relative to Serfling estimates. For perspective, the 1980-1981 season was considered very severe, yet the authors’ model estimated only 4068 influenza-related pneumonia and influenza deaths com- pared with 9700 by a Serfling model. 1,4 The Thompson model produces essentially constant esti- mates of RSV-related mortality for the 1990s, 80% of which are stated to be deaths in elderly individuals. If this is so, then the authors should be able to demonstrate a 40% increase in RSV deaths among those aged 85 years or older during the 1990s when this population increased by approximately 40%. Such straight- forward validation would provide evidence that this model does indeed measure RSV deaths in the elderly population. A model that requires the additional complexity of viral sur- veillance data for mortality estimates sharply limits historical comparison within the United States and eliminates compari- son with most other countries. We propose that rigorous dem- GUIDELINES FOR LETTERS. Letters discussing a recent JAMA article should be received within 4 weeks of the article’s publication and should not exceed 400 words of text and 5 references. Letters reporting original research should not ex- ceed 500 words and 6 references. All letters should include a word count. Letters must not duplicate other material published or submitted for publication. Letters will be published at the discretion of the editors as space permits and are subject to editing and abridgment. A signed statement for authorship criteria and respon- sibility, financial disclosure, copyright transfer, and acknowledgment is required for publication. Letters not meeting these specifications are generally not consid- ered. 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