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A7
THE SEVERITY OF PANDEMIC H1N1 INFLUENZA IN THE UNITED STATES, FROM APRIL TO JULY 2009: A BAYESIAN ANALYSIS50

Anne M. Presanis,51 Daniela De Angelis,52 The New York City Swine Flu Investigation Team,53,54 Angela Hagy,55 Carrie Reed,56 Steven Riley,57 Ben S. Cooper,58 Lyn Finelli,59 Paul Biedrzycki,60 Marc Lipsitch61

Abstract

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.

50

Reprinted with permission from Presanis et al. 2009. The severity of pandemic H1N1 influenza in the United States, from April to July 2009: a Bayesian analysis. PLoS 6(12), http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2762775/ (accessed December 15, 2009).

51

Medical Research Council Biostatistics Unit, Cambridge, United Kingdom.

52

Medical Research Council Biostatistics Unit, Cambridge, United Kingdom. Statistics, Modelling and Bioinformatics Department, Health Protection Agency Centre for Infections, London, United Kingdom.

53

Department of Health and Mental Hygiene, City of New York, New York, New York, United States of America.

54

Membership of The New York City Swine Flu Investigation Team is provided in the Acknowledgments.

55

Department of Health, City of Milwaukee, Milwaukee, Wisconsin, United States of America.

56

Influenza Division, Centers for Disease Control and Prevention, Atlanta, Georgia, United States of America.

57

Department of Community Medicine and School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong SAR, China.

58

Statistics, Modelling and Bioinformatics Department, Health Protection Agency Centre for Infections, London, United Kingdom.

59

Influenza Division, Centers for Disease Control and Prevention, Atlanta, Georgia, United States

60

Department of Health, City of Milwaukee, Milwaukee, Wisconsin, United States of America.

61

Center for Communicable Disease Dynamics, Departments of Epidemiology and Immunology & Infectious Diseases, Harvard School of Public Health, Boston, Massachusetts, United States of America E-mail: mlipsitc@hsph.harvard.edu.



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208 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC A7 THE SEVERITY OF PANDEMIC H1N1 INFLUENZA IN THE UNITED STATES, FROM APRIL TO JULY 2009: A BAYESIAN ANALYSIS50 Anne M. Presanis,51 Daniela De Angelis,52 The New York City Swine Flu Investigation Team,53,54 Angela Hagy,55 Carrie Reed,56 Steven Riley,57 Ben S. Cooper,58 Lyn Finelli,59 Paul Biedrzycki,60 Marc Lipsitch61 Abstract 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, detec- tion of severe cases may be more likely, resulting in overestimation of the sever- ity 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. 50 Reprinted with permission from Presanis et al. 2009. The severity of pandemic H1N1 influenza in the United States, from April to July 2009: a Bayesian analysis. PLoS 6(12), http://www.ncbi.nlm. nih.gov/pmc/articles/PMC2762775/ (accessed December 15, 2009). 51 Medical Research Council Biostatistics Unit, Cambridge, United Kingdom. 52 Medical Research Council Biostatistics Unit, Cambridge, United Kingdom. Statistics, Modelling and Bioinformatics Department, Health Protection Agency Centre for Infections, London, United Kingdom. 53 Department of Health and Mental Hygiene, City of New York, New York, New York, United States of America. 54 Membership of The New York City Swine Flu Investigation Team is provided in the Acknowledgments. 55 Department of Health, City of Milwaukee, Milwaukee, Wisconsin, United States of America. 56 Influenza Division, Centers for Disease Control and Prevention, Atlanta, Georgia, United States of America. 57 Department of Community Medicine and School of Public Health, Li Ka Shing Faculty of Medi- cine, The University of Hong Kong, Hong Kong SAR, China. 58 Statistics, Modelling and Bioinformatics Department, Health Protection Agency Centre for Infec- tions, London, United Kingdom. 59 Influenza Division, Centers for Disease Control and Prevention, Atlanta, Georgia, United States of America. 60 Department of Health, City of Milwaukee, Milwaukee, Wisconsin, United States of America. 61 Center for Communicable Disease Dynamics, Departments of Epidemiology and Immunology & Infectious Diseases, Harvard School of Public Health, Boston, Massachusetts, United States of America E-mail: mlipsitc@hsph.harvard.edu.

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209 APPENDIX A 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 hospitaliza- tions, 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 symp- tomatic cases to hospitalizations. Combining these data with estimates of the fraction detected for each level of severity, we estimated the proportion of symp- tomatic patients who died (symptomatic case-fatality ratio, sCFR), required ICU (sCIR), and required hospitalization (sCHR), overall and by age category. Evi- dence, 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 7–9 × lower. 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 propor- tion of the population symptomatically infected were lower than assumed. Please see later in the article for the Editors’ Summary. Introduction The H1N1 2009 influenza (pH1N1) pandemic has resulted in over 209,000 laboratory-confirmed cases and over 3,205 deaths worldwide as of 11 September 2009 (http://www.who.int/csr/don/2009_09_11/en/index.html, accessed 14 Sep-

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210 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC tember 2009), but national and international authorities have acknowledged that these counts are substantial underestimates, reflecting an inability to identify, test, confirm, and report many cases, especially mild cases. Severity of infection may be measured in many ways, the simplest of which is the case-fatality ratio (CFR), the probability that an infection causes death. Other measures of severity, which are most relevant to the burden a pandemic exerts on a health care system, are the case-hospitalization and case-intensive care ratios (CHR and CIR, respectively), the probabilities that an infection leads to hospitalization or intensive care unit (ICU) admission. In the absence of a widely available and validated serologic test for infection, it is impossible to estimate these quantities directly, and in this report we instead focus on the probabilities of fatality, hospitalization, and ICU admission per symptomatic case; we denote these ratios sCFR, sCHR, and sCIR respectively. Although it is difficult to assess these quantities, estimates of their values and associated uncertainty are important for decision making, planning, and response during the progression of this pandemic. Initially, some national and international pandemic response plans were tied partly to estimates of the CFR, but such plans had to be modified in the early weeks of this pandemic, as it became clear that the CFR could not at that time be reliably estimated (Lipsitch et al., 2009a). Costly measures to mitigate the pandemic, such as the purchase of medical countermeasures and the use of disruptive social distancing strate- gies may be acceptable to combat a more severe pandemic but not to slow a milder one. While past experience (Jordan et al., 1958) and mathematical models (Ferguson et al., 2006; Halloran et al., 2008; Mills et al., 2004) suggest that between 40% and 60% of the population will be infected in a pandemic with a reproduction number similar to those seen in previous pandemics, the number of deaths and the burden on the health care system also depend on the age-specific severity of infection, which varies by orders of magnitude between pandemics (Miller et al., 2008) and even between different waves in the same pandemic (Andreasen et al., 2008). Reports from the Southern Hemisphere suggest that a relatively small fraction of the population experienced symptomatic pH1N1 infection (7.5% in New Zealand, for example; Baker et al., 2009), although these numbers are considered highly uncertain (Baker et al., 2009). On the other hand, primary care utilization for influenza-like illness (ILI) has been considerably higher than in recent years (Baker et al., 2009), and anecdotal reports in the Southern Hemisphere have indicated that some intensive care units (ICUs) have been overwhelmed and surgery postponed due to a heavy burden of pH1N1 cases (Bita, 2009; Newton, 2009). The problem of estimating severity of pH1N1 infection includes the problem of estimating how many of the infected individuals in a given population and time period subsequently develop symptoms, are medically attended, hospitalized, admitted to ICU, and die due to infection with the virus. No large jurisdiction in the world has been able to maintain an accurate count of total pH1N1 cases once

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211 APPENDIX A the epidemic grew beyond hundreds of cases, because the effort required to con- firm and count such cases is proportionate to the size of the exponentially grow- ing epidemic (Lipsitch et al., 2009b), making it impossible to reliably estimate the frequency of an event (e.g., death) that occurs on the order of 1 in 1,000 patients or fewer. As a result, simple comparisons of the number of deaths to the number of cases suffer from underascertainment of cases (making the estimated ratio too large), and underascertainment of deaths due to inability to identify deaths caused by the illness and due to delays from symptom onset to death (making the estimated ratio too small; Lipsitch et al., 2009a). Imperfect ascertainment of both numerator and denominator will lead to biased estimates of the CFR. Estimating the number of persons at these varying levels of severity therefore depends on estimating the proportion of true cases that are recognized and reported by exist- ing surveillance systems. Similar problems affect estimates of key parameters for other diseases, such as HIV. In HIV, a solution to this problem—which now forms the basis for the UK’s annual HIV prevalence estimates published by the Health Protection Agency (Health Protection Agency Centre for Infections, 2009a, b)— has been to synthesize evidence from a variety of sources that together provide a clearer picture of incidence, prevalence, and diagnosis probabilities. This synthe- sis is performed within a Bayesian framework that allows each piece of evidence, with associated uncertainties, to be combined into an estimate of the numbers of greatest interest (Goubar et al., 2008; Presanis et al., 2008). Here we use a similar framework to synthesize evidence from two cities in the United States—New York and Milwaukee—together with estimates of important detection probabilities from epidemiologic investigations carried out by the US Centers for Disease Control and Prevention (CDC) and other data from CDC. We estimate the severity of pH1N1 infection from data from spring– summer 2009 wave of infections in the United States. The New York City and Milwaukee health departments pursued differing surveillance strategies that pro - vided high-quality data on complementary aspects of pH1N1 infection severity, with Milwaukee documenting medically attended cases and hospitalizations, and New York documenting hospitalizations, ICU/ventilation use, and fatalities. These are the numerators of the ratios of interest. The denominator for these ratios is the number of symptomatic pH1N1 cases in a population, which cannot be assessed directly. We use two different approaches to estimate this quantity. In the first (Approach 1), we use self- reported rates of patients seeking medical attention for ILI from several CDC investigations to estimate the number of symptomatic cases from the number of medically attended cases, which are estimated from data from Milwaukee. In the second (Approach 2), we use self-reported incidence of ILI in New York City, and making the assumption that these ILI cases represent the true denominator of symptomatic cases, we directly estimate the ratio between hospitalizations, ICU admissions/mechanical ventilation, and deaths (adjusting for ascertainment) in New York City. Each of these two methods provides estimates for the general

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212 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC population, and also for broad age categories 0–4, 5–17, 18–64, and 65+ years. The result of each approach is a tiered severity estimate of the pandemic. Methods Methods Overview The overall goal of this study was to estimate, for each symptomatic pH1N1 case, the probability of hospitalization, ICU admission or mechanical ventilation, or death, overall and by age group. The challenge is that in any population large enough to have a significant number of patients with these severe outcomes, there is no reliable measure of the number of symptomatic pH1N1 cases. This problem was approached in two ways. Approach 1 was to view the severity of infection as a “pyramid” (Garske et al., 2009), with each successive level representing greater severity; to estimate the ratio of the top level to the base (symptomatic cases), we estimated the ratios of each successive level to the one below it (Figure A7-1, left side). Thus we broke down (for example) the sCFR (Figure A7-1, black), i.e., the probability of death per symptomatic case, into components for which data were available – the probability of a case coming to medical attention given symp- tomatic infection (CDC survey data); the probability of being hospitalized given medical attention (Milwaukee data); and the probability of dying given hospital- ization (New York data, including a correction for those who died of pH1N1 but were not hospitalized). Approach 2 was to use the self-reported incidence of ILI from a telephone survey in New York City as the estimate of total symptomatic pH1N1 disease, and the total number of confirmed deaths in New York City as the estimate of the deaths (after accounting for imperfect ascertainment, in this case due to possibly imperfect viral testing sensitivity). In each case, prior dis- tributions were used to quantify information on the probability that cases at each level of severity were detected; these prior distributions reflected the limited data available on detection probabilities and associated uncertainty. All of these estimates were combined within a Bayesian evidence synthesis framework. This framework permits the estimation of probabilities for the quanti- ties of interest (the sCFR, sCIR, and sCHR) and associated uncertainty (expressed as credible intervals [CIs]). These credible intervals appropriately reflect the com- bined uncertainties associated with each of the inputs to the estimate—mainly, the true numbers of cases at each level of severity, after accounting for imperfect detection—as well as the uncertainties due to sampling error (chance). Study Populations Data were obtained from enhanced pandemic surveillance efforts by the City of Milwaukee Health Department and the New York City Department of Health and Mental Hygiene (DOHMH). Details of testing policies, data acquisition, and

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213 APPENDIX A FIGURE A7-1 Diagram of two approaches to estimating the sCFR. Approach 1 used three datasets to estimate successive steps of the severity pyramid. Approach 2 used self- reported IU for the denominator, and confirmed deaths for the numerator, both from New York City. Both approaches used prior distributions, in some cases informed by additional data, to inform the probability of detecting (confirming and reporting) cases at each level Figure A7-1 of severity (not shown in the diagram; see text S1). The Bayesian evidence synthesis R01627 framework was used as a formal way to combine information and uncertainty about each level of severity into a single estimate and associated uncertainty that reflected all of the uneditable bitmapped image uncertainty in the inputs. analysis are given in Text S1. All data were analyzed first in aggregate and then by age category. Milwaukee Data Between April 6 and July 16, 2009, Milwaukee recorded 3,278 confirmed cases and four deaths due to pH1N1, reflecting sustained efforts to test patients reporting ILI and their household contacts from the start of the epidemic in April until mid- July. On April 27, Milwaukee initiated protocols including recommendations for testing persons with influenza symptoms and travel history to areas reporting novel H1N1 cases, using a reverse transcriptase polymerase chain reaction (RT-PCR) test specific for pH1N1. By May 7, Milwaukee issued testing guidance updated to recommend testing persons with moderate to severe symptoms, except that test-

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214 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC ing continued to be recommended for health care workers with mild, moderate or severe symptoms. We used a line list dated July 21, and in a preliminary analysis examined the frequency of hospitalization among cases by “episode date” (the ear- liest date in their case report). The proportion of confirmed cases hospitalized was stable around 3% up to May 20, after which it increased markedly to 6%–8% in the following weeks. We judged that this change reflected reduced testing of mild cases and limited our analysis (used to inform the ratio of hospitalizations to medically attended cases) to the 763 cases with an episode date up to or including May 20. While Milwaukee data were not the main source of estimates of ICU admission or death probabilities, we did employ hospitalized cases up to an episode date of June 14 to contribute to estimates of the ratio of deaths or ICU admissions to hos- pitalizations, since these should not be affected by failure to test mild cases. New York Case Data New York City maintained a policy from April 26 to July 7, 2009 of testing hospitalized patients with ILI according to various criteria. These criteria evolved up to May 12, from which point they remained as follows: all hospitalized ILI patients received a rapid influenza antigen test. Those patients who tested posi- tive on rapid test (which is known to have low sensitivity for seasonal influenza (Uyeki et al., 2009) and for pH1N1 (CDC, 2009)), and any patient in the ICU or on a ventilator, regardless of rapid test result, received RT-PCR tests for pH1N1. We obtained a line list of confirmed or probable hospitalized cases dated July 7, and found in a preliminary analysis that all patients in this line list had a date (onset or admission) in their record no later than June 30, 7 d prior to the date of the line list. Given that >90% of hospitalizations were reported in New York within 7 d, we used this entire line list without accounting for delays in reporting of hospitalizations. Also, given that 98% of admissions occurred after May 12, we did not attempt to account for changes in testing practices before May 12. This line list included a field indicating whether the patient had been admitted to the ICU or ventilated; patients were not followed up after admission to determine if this status changed. However, a chart review of 99 hospitalized cases indicated that none had been admitted to the ICU after admission, so no effort was made to account for this limitation. Separately, we obtained a list of 53 patients whose deaths were attributed to pH1N1, of whom 44 (83%) had been hospitalized before dying. All patients with known influenza or unexplained febrile respiratory illness at the time of death had postmortem samples and/or samples taken before they died sent for PCR testing. New York Telephone Survey Data To estimate levels of ILI in New York City, DOHMH conducted 1,006 surveys between May 20 and May 27, 2009, and 1,010 between June 15 and

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215 APPENDIX A June 19. Interviews lasted 5 min and were conducted with households in both English and Spanish. The survey used a random-digit dialing (RDD) telephone sampling methodology to obtain data from a random sample of residential house- holds in New York City. A nonrandom individual from each selected household was interviewed and provided information about all household members. Sam- pled numbers were dialed between five and 15 times to contact and interview a household, or until the sampled number was determined to be nonworking. To account for this design, the data were weighted to the 2007 Ameri- can Community Survey (ACS); respondents were weighted to householders by borough, age, gender, and race/ethnicity, and the population was weighted by age to the borough of residence. The survey’s RDD sampling methodology gave a useful overview of ILI in the community, but it has limitations. The design does not include individuals living in households only reachable by cellular telephone but not by a landline telephone number, and it omitted those living in group or institutional housing. Although households were randomly selected, for the sake of efficiency the interviewed adult was not. Instead, an available adult in the household provided information about all household members and themselves, which may have introduced bias. The results of the survey are being compiled for publication elsewhere. Here, we use summaries of these results by age group (see Text S1) as one means to provide denominators of symptomatic cases. Data on Detection Probabilities from CDC Investigations Sources of data include two community surveys on ILI and health-seeking behavior, and two field investigations conducted during early outbreaks of pH1N1 in the US. These sources are described in further detail elsewhere (Reed et al., 2009), but are summarized here briefly. In 2007, the Behavioral Risk Factor Sur- veillance Survey (BRFSS), an RDD telephone survey, included a module on ILI in nine states. This module included questions to assess the incidence of ILI, health- seeking behavior, physician diagnosis of influenza, and treatment of influenza with antiviral medications during the annual 2006–2007 influenza season. In May 2009, following the emergence of pH1N1, an RDD telephone survey sampled similar to the BRFSS was conducted in the same nine states using only the ILI module from the 2007 BRFSS and limited demographic questions. In addition, some data were available from field investigations conducted during large outbreaks of pH1N1 in one community in Chicago and a university campus in Delaware. Investigations of these outbreaks consisted of household interviews in a Chicago neighborhood and an online survey of students and faculty in Delaware. These data were used to inform detection probabilities. In addition, these data were used to inform a prior distribution on the ratio between symptomatic and medically attended cases, cM|S: these surveys estimated that between 42% and 58% of symptomatic ILI patients sought medical attention (Reed et al., 2009).

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216 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC Analysis Estimation of the probabilities of primary interest, cH|S, cI|S, and cD|S, respec- tively the sCHR, sCIR, and sCFR, was undertaken using a Bayesian evidence synthesis framework (Goubar et al., 2008). Details are given in Text S1, and a schematic illustration of the model is given in Figure A7-2. Briefly, in this frame- work, prior information about the quantities of interest (including the uncertainty associated with this prior information) is combined with the information coming from the observed cases at each severity level to derive a posterior distribu- tion on these quantities. This posterior distribution fully reflects all information about the quantities of interest thatFigure A7-2 the prior distribution and the is contained in R01627 observed data. Specifically, it was assumed that detected cases O at each level of uneditable bitmapped image severity—medically attended (M), hospitalized (H), ICU-admitted (I), and fatal (D)—represented binomiallylandscape above, portraitnumber of cases N scaled for distributed samples from the true below at the corresponding level of severity, in the given location (New York, abbrevi- ated N or Milwaukee, abbreviated W), with probability equal to the probability of detection at each level (d). The probability d for each level was informed by evidence on the probability of testing at each level of severity (which may have depended on the sensitivity of the rapid test if this was required for PCR testing) and the sensitivity of the PCR test (Table A7-1). Thus, for example, we defined FIGURE A7-2 Schematic illustration of the relationship between the observed data (rect- angles) and the conditional probabilities (blue circles). The key quantities of interest, sCHR, sCIR, and sCFR, are products of the relevant conditional probabilities. (A) Approach 1, synthesizing data from New York City and Milwaukee. Note that cM/S (double circle) is informed by prior information (Reed et al., 2009) rather than observed data. (B) Approach 2, using data from New York City only, including the telephone survey. Variables: cD/M: the ratio of non-hospitalized deaths to medically-attended cases; cD/H: the ratio of deaths to hospitalized cases; cI/H: the ratio of cases admitted to intensive care or using mechanical ventilation to hospitalized cases; cH/M: the ratio of hospitalized cases to medically attended cases; cM/S: the ratio of medically attended cases to symptomatic cases; cD/S: the ratio of deaths to symptomatic cases; cH/S: the ratio of hospitalized cases to symptomatic cases.

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217 APPENDIX A TABLE A7-1 Detection Probabilities and Their Prior Distributions Detection Probability Components Distributions Rationale dM Medically dM1 probability of Uniform (0.2,0.35) Data from CDC attended illness testing, follow-up, epi-aids in Delaware and reporting among and Chicago (Reed et medically attended al., 2009) patients dM2 PCR test Uniform (0.95,1) Assumption (Reed et dM = dM1dM2 sensitivity al., 2009) dHW Hospitalization dHW1 probability of Uniform (0.2,0.4) Assumption (Reed et (Milwaukee) testing, follow-up, al., 2009) and reporting among hospitalized patients dHW = dHW1dHW2 dHW2 PCR test Uniform (0.95,1) Assumption (Reed et sensitivity al., 2009) dIW ICU admission dIW1 probability of Uniform (0.2,0.4) Assumption (Reed et (Milwaukee) testing, follow-up, al., 2009) and reporting among hospitalized patients dIW = dIW1 dIW2 dIW2 PCR test Uniform (0.95,1) Assumption (Reed et sensitivity al., 2009) dDW Deaths PCR test sensitivity Beta (45,5) Assumption (Reed et (Milwaukee) and other detection al., 2009) (mean 0.9, standard deviation 0.05) dHW Hospitalization dHN1 probability of 0.27+0.73 27% of test cases (New York City) oerforming PCR (Uniform (0.2,0.71)) were ICU-admitted (rapid A positive or so received PCR test; ICU/ventilated) remainder were tested if rapid A positive, which has a sensitivity of 0.2 (Uyeki et al., 2009) to 0.71 (sensitivity among ICU patients in NYC) dHN = dHN1dHN2 dHN2 PCR test Uniform (0.95,1) Assumption (Reed et sensitivity al., 2009) dIN ICU/ventilation PCR test sensitivity Uniform (0.95,1) Assumption (Reed et (New York City) al., 2009) dDN Deaths PCR test sensitivity Beta (45,5) Assumption (Reed et (New York City) and other detection al., 2009)

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218 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC the probability of detecting a hospitalized case in New York as dHN = dHN1dHN2, where dHN1 was the probability of performing an RT-PCR–based test and dHN2 was the sensitivity of that test. Hence, the observed number of hospitalized patients in New York, OHN, was assumed to be distributed as Binomial(NHN,dHN). We noted that the ratios cH|S, cI|S, and cD|S can be built up multiplicatively from simpler components: for instance, the ratio of deaths to symptomatic infec- tions may be expressed as cD|S = cD|HcH|McM|S, the product of the ratios of deaths: hospitalizations, of hospitalizations:medically attended cases, and of medically attended cases:symptomatic cases. These ratios of increasing severity are similar to conditional probabilities but are not strictly so in all cases, since for example some deaths in New York City occurred in persons who were not hospitalized. For this reason we model deaths separately among hospitalized and nonhospitalized patients, i.e., cD|S = cD|HcH|McM|S + cD|McM|S. For each observed level of severity (medically attended, hospitalized, ICU, death), the true number of cases was modeled as a binomial sample from the true number of cases at an appropriate lower level, hence NMk ~ Binomial (NSk,cM|S); NHk ~ Binomial (NMk,cH|M); NIk ~ Binomial (NHk,cI|H); NDk ~ Binomial (NHk,cD|H) + Binomial (NMk,cD|M), where the first subscript indicates severity and the second indicates the population (New York, Milwaukee to May 20, Milwaukee to June 14). In Approach 1 (New York and Milwaukee data combined), for the unobserved level of severity (symptomatic cases) we used a prior distribution of cM|S ~ Beta (51.5,48.5) to represent uncertainty between 42% and 58% (Reed et al., 2009); this distribution has 90% of its mass in this range, with a mean of 0.515. The main analysis of this first approach was performed using prior information to inform the detection probabilities. An additional “naïve” analysis was performed, in which the detection probabilities d were set equal to 1 at all levels of severity. Our prior distributions for the number of symptomatic cases in New York (overall and by age) were taken as ranging uniformly between zero and the proportion reporting ILI in the telephone survey (with the upper bound of that distribution itself having a prior distribution reflecting the confidence bounds of the survey results; details in Text S1). For Milwaukee, the prior distribution on symptomatic cases was taken as uniform between 0 and 25% of the population. In Approach 2 (New York case data and telephone survey data), we made the assumption that self-reported ILI cases represented symptomatic pH1N1 infec- tion, and used the mean and 95% confidence intervals from that survey to define a prior distribution on the number of symptomatic cases overall and by age group. We then used observed hospitalizations, ICU/ventilator use, and fatalities along with prior distributions on detection probabilities as above to inform estimates

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237 APPENDIX A FIGURE A7-3 Assumed severity hierarchy. for ICU admissions and ND for deaths. Each of these true numbers also varies by Figure A7-3 age group i and location k (Milwaukee, k = W or NYC, k = N). We assume that R01627 in each age group, for each level of severity, the true number of persons at that level of severity is binomially distributed based on theimage uneditable bitmapped corresponding conditional probability and the true number at the preceding level of severity: ) ( N iMk ~ Binomial N iSk , ciM S ~ Binomial ( N , c ) N iHk iMk iH M ~ Binomial ( N , c ) (1a) N iIk iHk iI H ~ Binomial ( N , c ) N iD∩ Hk iHk iD H ) ~ Binomial ( N , c N iD∩ Hk iMk iD ∩ H M NiSk is given a prior reflecting our uncertainty about the number of symptomatic cases (see details in section on symptomatic vs. medically attended infection).

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238 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC Approach 2 For the NYC only analysis, we do not consider the medically attended level, such that cD S = cD H cH S cD ∩ H S , cI S = cI H c H S cH|S is given by ) ( N iH ~ Binomial N iS , ciH S ) N ~ Binomial ( N , ciI H (1b), iI iH ) ( N iD∩ H ~ Binomial N iH , ciD H ) ~ Binomial ( N , ciD∩ H S N iD∩ H iS and NiS ~ Binomial (NiP ,ciS|P) where NiP is the NYC population size (considered constant), and ciS|P are given priors, to reflect estimates from the NYC telephone survey, see section on symptomatic vs. medically attended infection. 2b. Observation Model For a variety of reasons, detection at each level of severity will be imperfect, and thus the true values N are not observed. However, we do observe detected medically attended cases OiMW and detected hospitalizations OiHW in Milwaukee, and we observe detected hospitalizations OiHN, detected ICU stays OiIN, and detected deaths OiDN in New York City. We assume that these observations O are related to the true numbers N as follows: OiMk ~ Binomial (NiMk,dM) OiHk ~ Binomial (NiHk,dH) (2) OiIk ~ Binomial (NiIk,dI) OiDk ~ Binomial (NiDk,dD) where for each level of severity j, dj is the detection probability, i.e. the prob- ability that a case enters our database. 2c. Combining the models—a Bayesian approach Given (1a) or (1b) and (2), we wish to estimate the values of the age-specific cij, which can then be multiplied appropriately to estimate the age-specific (symp- tomatic) case-hospitalization, case-ICU and case-fatality ratios. Figure A7-4 is a schematic representation of the relationship between the quantities we wish to estimate and the quantities we observe. The figure shows only a small part of the whole model in approach 1, for one generic age group and

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239 APPENDIX A FIGURE A7-4  Simplified  directed  acyclic  graph  displaying  the  dependencies  in  part  of  the model. Figure A7-4 location,  and  for  the  first  three  levels  of  severity  (symptomatic  to  hospitalized).  R01627 Circles  denote  parameters,  double  circles  denote  parameters  for  which  we  have  uneditable bitmapped  imagenes  denote  distribu- prior  information,  and  squares  denote  observations. Solid  li tional relationships and dashed lines denote functional relationships. The arrows  represent the process by which the parameters, if known, would generate the data.  In  our  case,  the  problem  is  reversed,  i.e.  to  infer  the  values  of  the  parameters  given the available information. The figure provides an illustration of the flow of  information from the observations and prior distributions to the unknown param- eters.  So  for  example,  the  information  on  OH  (the  observed  number  of  hospital- izations) together with the prior on dH gives information on NH, the true number  of  hospitalizations.  Note  that  estimation  of  the  parameters  of  primary  interest  (e.g.  sCHR,  the  symptomatic  case-hospitalization  ratio)  is  informed  indirectly 

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240 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC by the combination of prior and sample information on intermediate but related parameters (OH and OM, together with dM, dH, NS and cM|S, via the true numbers N and the conditional probabilities c). More generally, the complete set of unknown parameters is θ = (cij, djk, Nijk, sCHR, sCIR, sCFR), and we have observations O = (Oijk). Inference is then carried out in a Bayesian setting using the prior information, P(θ ), and the likelihood of the observations given the parameters, L(O| θ ) to obtain, via Bayes’ Theorem, the posterior distribution P (θ O ) ∝ P (θ ) L (O θ ) of the parameters. 3. Data 3a. Milwaukee On April 27th, Milwaukee sent out messaging to local healthcare providers recommending testing anyone presenting with signs and symptoms characteristic of influenza (fever >100 degrees, cough or sore throat, myalgia) and travel to an area with documented H1N1. By May 7th more than 100 confirmed cases had been identified, and testing guidance was updated to recommend testing persons with moderate to severe symptoms (temperature of > 101.5 and significant respi- ratory symptoms and significant constitutional symptoms). Testing of persons with mild symptoms was limited to health care workers. On June 15th providers were told to begin testing on a fee-for-service basis. Throughout the outbreak, healthcare providers have been asked to report any suspect, probable or confirmed case of H1N1. Providers were advised about concerns regarding the accuracy of rapid flu tests and urged to use PCR as the preferred method for analysis. All confirmed and probable cases were entered into a line list on a rolling basis, and we used a line list dated July 21. Because our primary focus for Milwaukee was on hospitalization probabili- ties, in a preliminary analysis we plotted the frequency of hospitalization by week of “episode date,” the earliest date (of illness onset, report or hospitalization) in an individual record. The hospitalization frequency was around 3% overall with no temporal trend up to an episode date of May 20, after which there was a dramatic upward trend in the proportion hospitalized, with 8.2%, 6.0%, and 7.0% hospital- ized in the weeks that followed. We interpreted this increased hospitalization rate as evidence of declining ascertainment of mild cases, and we therefore restricted our attention to cases with illness onset date up to and including May 20. This also obviated the need to deal with censoring, as the date of the line list was two months later, far longer than the delay in reporting for nearly all cases. This cre- ated a data set of 763 cases, of whom 25 (3%) were hospitalized. While the main source of data on the probability of ICU admission or death was New York City, such data were available, albeit in small numbers, for

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241 APPENDIX A Milwaukee. To inform the ratio of ICU+ventilation:hospitalization and death: - hospitalization, we used a larger subset of the data, on the assumption that the change in ascertainment after May 20 was due to reduced ascertainment of mild cases, not changes in ascertainment of hospitalized or more severe cases. There- fore, we considered the 147 hospitalizations with episode date up to and including June 14. Again, this was more than 30 days prior to the close of the line list, so we did not correct for censoring. Of these 147 hospitalizations, 25/147 (17%) were admitted to the ICU and/or ventilated, and 4 (3%) died. 3b. New York City From April 26 to July 7, 2009, New York City maintained a policy of test- ing hospitalized patients with influenza-like illness (ILI) under various criteria. Criteria for testing varied up to May 12, after which point all hospitalized patients with influenza-like illness (ILI) were tested with a rapid influenza antigen test. Those patients who tested positive, and also any patient on a ventilator or in an intensive care unit (ICU) regardless of rapid test result, were tested for H1N1pdm by PCR. We obtained a line list of confirmed cases dated August 24, 2009, includ- ing 996 hospitalizations, of whom 882 had a known date of onset. Preliminary analysis indicated that >99% of hospitalizations were reported within 21 days of symptom onset. Since the last date of admission in the data set was July 6, 49 days prior to the date of the line list (August 24), we did not restrict this data set. Also, >97% of admissions in the data set were after May 12, so we did not attempt to account for differences in testing prior to May 12. Separately, we obtained a list of 53 deaths attributed to H1N1pdm, of whom 44 (83%) had been hospitalized before dying. The dates of death ranged from 17 May to 19 July, but the dates of case report to New York City ranged from 13 May to 4 July; hence, these cases were all included within the time frame in which hospitalizations were being investigated. Based on the time-to-death dis- tribution and the timing of hospitalizations, we estimated that >99.9% of deaths which would be reported from the hospitalized cases had already been reported. We therefore made no effort to account for censoring of deaths. The data are shown in Table A7-1 of the main text. 4. Detection Probabilties We require information on the detection probabilities, dM, dH, dI, dD. In general, these are assumed location-specific, and may consist of multiple com- ponents. We present below the evidence or prior assumptions available to inform estimates of these detection probabilities.

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242 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC 4a. Detection of medically attended illness The detection probability for medically attended (M) illness (in Milwaukee), dMW, may be expressed as dMW = Pr{specimen collected & tested | true M case already M} Pr{test positive | specimen collected & tested for a true M case} = dMW1dMW2 where dMW2 is the sensitivity of the PCR-based tests recommended for use in Milwaukee. We assume dMW1 ~ Uniform(.2,.35), dMW2 ~ Uniform(.95,1), and that the probability of censoring is 0, for the reasons described in Section 3. These assumptions are based on estimates from Reed et al. (2009), using data from seasonal influenza and from Epi-Aids in Delaware and Chicago and are not Milwaukee-specific. Unlike Reed et al., we do not assume a separate probability for specimens being sent for confirmatory testing, since Milwaukee recommended against use of rapid antigen testing for screening (which would have led to false negatives and reduced detection) and since Milwaukee recommended testing of all persons with moderate to severe symptoms. 4b. Detection of hospitalizations (Milwaukee) We define dHW, the detection probability for hospitalization (in Milwaukee) as dHW = Pr{report hosp case | test pos} Pr{test pos | true hosp case already hosp and tested}Pr{tested | true hosp case already hosp} = dHW1dHW2 By using the July 21 line list but restricting analysis to cases with an episode date prior to or on May 20 (or June 14) we believe it reasonable to assume the prob- ability of censoring is 0. We have no Milwaukee-specific data on the probability that some true hospitalizations go unreported, either because testing was not performed, or because a positive case was not reported. Hence we again follow Reed et al. in assuming dHW1 = Pr{report hosp case | test pos} Pr{tested | true hosp case already hosp} ~ Uniform(.2,.4) and dHW2 ~ Uniform(.95,1) to account for imperfect PCR test sensitivity. We assume the same priors for the detection probabilities in ICU admissions.

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243 APPENDIX A 4c. Detection of deaths (Milwaukee) dDW is the detection probability for deaths in Milwaukee. As with hospitaliza- tions, we assume no censoring, since the date of the line list is a month after the last episode date in the data set we are considering (episode dates up to 14th June), so that dDW = Pr{report death | true H1n1pdm-attributable death (already died)}. We have no data to assess the probability of a death being tested for H1N1pdm, hence we assume a prior reflecting failure to detect of dDW ~ Beta(45,5) giving a prior mean of 0.9 and standard deviation 0.05 (a range of 0.8 – 1, as in New York, see below), covering both test sensitivity and failure to detect. 4d. Detection of hospitalizations (New York) dHN is the detection probability for hospitalization (in New York). In New York, rapid antigen testing was used as a screen for most patients. From May 12, PCR testing for H1N1pdm was performed only on hospitalized patients who (a) tested positive on a rapid influenza A test, or (b) were in the ICU or on ventilator, regardless of their rapid influenza A status. Thus one component of dHN is dHN1, the probability of PCR testing. 27% (242/909) of hospitalized H1N1pdm patients in New York were in the ICU, so for these we assume that the probability of PCR testing was 1. For the other 73% we assume the probability of PCR testing was equal to the sensitivity of the rapid test, which we model as Uniform(.2,.71). Thus we model dHN1~.27+.73(Uniform(.2,.71)). Finally we account for imperfect sensitivity of the PCR, dHN2 ~ Uniform(.95,1). Because of active surveillance for hospitalized cases, we assume that testing was performed as advised and was reported in all cases; hence we do not assume a separate fac- tor for failure to test or report. As noted above, we made no effort to account for censoring of hospitalized cases. 4e. Detection of ICU admissions, New York Here we assume that detection is equal to the sensitivity of the PCR test, dIN ~ Uniform(.95,1), since rapid testing was not required for PCR testing. As with hospitalizations, we assume the probability of censoring is 0. A limitation is that we only detect ICU admissions that are known by the time the hospitalized case is reported to the NYC Department of Health. Later admissions from the ward are not reported. Thus we will underestimate the pro- portion of ICU admissions among hospitalized cases. However, a chart review of 99 hospitalizations found that 24 (24%) were admitted to the ICU during their entire stay, a proportion indistinguishable from that in our overall dataset. Hence we conclude that this underestimation is not severe.

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244 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC 4f. Detection of deaths, New York New York had a policy of PCR testing all unexplained respiratory deaths involving fever. We have no data to assess the completeness of such testing. Given issues of PCR sensitivity and possible failure to test, we assume a prior distribution for ascertainment of deaths of, dDN ~ Beta(45,5) giving prior mean 0.9 and standard deviation 0.05), reflecting possible failure to detect H1N1pdm- attributable deaths. 5. Symptomatic vs. Medically Attended Infection We have no direct data on the number of symptomatic but not medically attended H1N1pdm infections. However, multiple epidemiological investigations have estimated the proportion of influenza-like illness that is medically attended; these estimates range from 42% to 58% (Reed et al., 2009) and include data both from prior influenza seasons and from the spring 2009 H1N1pdm influenza period. Thus we model the conditional probability of being medically attended given symptomatic infection, cM|S ~ Beta(51.5,48.5) giving a mean of 0.515 and standard deviation 0.05, with 90% of the probability mass between 0.42 and 0.58. For approach 1, we also require prior distributions for the true number of symptomatic infections, NS. For Milwaukee, we assume NiSW ~ Uniform(HiMW, 0.25 × popniW), i.e. a lower limit of the observed number of medically attended cases, with an upper limit of 25% of the population size. This implies a maximum clinical attack rate of 25%. For New York, we assume NiSN ~ Uniform(0,upperiN × popniN): we have not observed medically attended cases in New York, so cannot use the observation as a lower limit. We used an upper bound of symptomatic infection in New York City based on the number of persons reporting ILI in a telephone survey conducted by the New York City Department of Health and Mental Hygiene covering a 30-day period in May-June at the height of the spring epidemic (NYC DOHMH, unpublished data): upper0-4,N ~ Beta(18.2,72) upper5-17,N ~ Beta (50.4,178) upper18-64,N ~ Beta(38.7,338) upper65+,N ~ Beta(27.6,446) upperall,N ~ Beta(91.4,654) In approach 2, the telephone survey data is used directly to inform priors for the proportion of the NYC population with symptomatic infection, rather than an upper bound:

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245 APPENDIX A c0-4,S|P ~ Beta(18.2,72) c5-17,S|P ~ Beta(50.4,178) c18-64,S|P ~ Beta(38.7, 338) c65+,S|P ~ Beta(27.6,446) cAll,S|P ~ Beta(91.4,654) 6. Implementation The Bayesian model described in Section 2 used the data and priors as pre- sented in Sections 3 to 5, and was implemented in the OpenBUGS software. This uses Markov chain Monte Carlo to obtain samples from the posterior distributions of the parameters of interest. Three chains of 1,000,000 iterations each were run, starting from different initial values. Summary statistics were based on the last 200,000 iterations of each chain, after discarding the first 800,000 as a burn-in period. Convergence for the quantities of primary interest which were reported in the main text, the conditional probabilities cij, was assessed both visually and using Gelman-Rubin-Brooks plots and we are satisfied the chains converged for these in most age groups. In approach 1, the probability of hospitalization given medi- cal attendance did not reach quite the same level of convergence as the other cij, particularly for the 65+ age group. This is due to the paucity of data available for this ratio: only data from Milwaukee is available, up till May 20th, the period for which ascertainment of mild cases was assumed constant over time. The observed numbers of hospitalizations in particular are very small, with 0 hospitalizations observed in the 65+ age group. This has a knock-on effect on the true numbers of medical attendances and symptomatic infections (NiSk and NiMk), so that their Markov chains also did not quite reach the same level of convergence as the chains for the true numbers of hospitalizations, ICU admissions and deaths. The posterior estimates for the symptomatic case-fatality, case-ICU admis- sion and case-hospitalization ratios are reliant on the estimates of NiSk, the true number of symptomatic cases, and are hence sensitive to the choice of prior. Convergence for NiSk improves as the upper limit for its prior is reduced, i.e. as the maximum clinical attack rate becomes smaller. However, it would not be reasonable to assume a maximum clinical attack rate of less than the telephone survey estimates for New York or less than 25% for Milwaukee, given our lack of prior knowledge on these. For this reason we do not report estimates of the total number symptomatic. Despite the uncertainty, there is some information available in the likelihood to update the estimates of the number symptomatic: the posteriors do not simply reflect the prior distributions (Figures A7-5 and A7-6). In approach 2, we are satisfied that the chains converged for the conditional probabilities cij in all age groups.

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246 IMPACTS OF THE 2009-H1N1 INFLUENZA A PANDEMIC FIGURE A7-5 Prior versus posterior number of symptomatic infections, Approach 1. Reference Figure A7-5 Reed C, Angulo F, Swerdlow D, Lipsitch M, Meltzer M, et al. (2009) Estimating the burden of pan- R01627 demic influenza A/H1N1—United States, April-July 2009. Emerg Infect Dis. In press. DOI: 10.3201/eid1512.091413uneditable bitmapped image

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247 APPENDIX A FIGURE A7-6 Prior vs posterior number of symptomatic infections, by age, Approach 1. Figure A7-6 R01627 uneditable bitmapped image