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 Lipsitch^{61}
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
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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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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).
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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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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-
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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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APPENDIX A
FIGURE A7-6 Prior vs posterior number of symptomatic infections, by age, Approach 1.
Figure A7-6
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uneditable bitmapped image