American Journal of Epidemiology
Copyright ª 2005 by the Johns Hopkins Bloomberg School of Public HealthAll rights reserved; printed in U.S.A.

Vol. 163, No. 2
DOI: 10.1093/aje/kwj024
Advance Access publication November 30, 2005

Practice of Epidemiology
Mortality due to Inﬂuenza in the United States—An Annualized Regression
Approach Using Multiple-Cause Mortality Data

Jonathan Dushoff1,2, Joshua B. Plotkin3, Cecile Viboud2, David J. D. Earn4, and Lone Simonsen5
1

Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ.
Fogarty International Center, National Institutes of Health, Bethesda, MD.
3
Harvard University, Cambridge, MA.
4
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada.
5
National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD.
2

Received for publication March 2, 2005; accepted for publication September 14, 2005.

Inﬂuenza is an important cause of mortality in temperate countries, but there is substantial controversy as to thetotal direct and indirect mortality burden imposed by inﬂuenza viruses. The authors have extracted multiple-cause
death data from public-use data ﬁles for the United States from 1979 to 2001. The current research reevaluates
attribution of deaths to inﬂuenza, by use of an annualized regression approach: comparing measures of excess
deaths with measures of inﬂuenza virus prevalence by subtype over entire inﬂuenza seasons and attributing
deaths to inﬂuenza by a regression model. This approach is more conservative in its assumptions than is earlier
work, which used weekly regression models, or models based on ﬁtting baselines, but it produces results consistent with these other methods, supporting the conclusion that inﬂuenza is an important cause of seasonal excess
deaths. The regression model attributes an annual average of 41,400 (95% conﬁdence interval: 27,100, 55,700)
deaths to inﬂuenza over the period 1979–2001. The study also uses regional death data to investigate the effects ofcold weather on annualized excess deaths.
cause of death; inﬂuenza; linear regression; mortality; seasons; temperature; time series; United States

Abbreviations: NAD, normalized annual death series; Tthresh, threshold temperature.

In temperate countries, more people die in the winter thanin the summer (1). The contribution of influenza to theseseasonal excess deaths remains a subject of controversy,
with some authors arguing that influenza epidemics trigger
the majority of excess deaths (1, 2) and others arguing thatthey trigger only a small minority (3). Retrospective cohort
studies have shown a surprisingly large protective effect ofinfluenza vaccination against deaths from any cause (4–6).
Deaths caused by influenza must be estimated indirectly
because most influenza infections are not confirmed virologically (7). Moreoever, deaths triggered by influenza may
occur as a result of a number of final causes, including
pneumonia and a wide variety of respiratory and circulatory

causes, and may occur weeks after initial infection (1,8–11). Serfling (12) developed a method to infer influenza
deaths based on seasonal patterns in the deaths attributed topneumonia and influenza. Serfling’s approach has beenfurther developed by Simonsen et al. (13, 14). Influenza
deaths are estimated as the number of deaths (either among
all deaths or among pneumonia and influenza deaths) above
an epidemic threshold based on a sinusoidal function fitted
to summer deaths. Simonsen et al. (13) estimated that influenza caused approximately 21,000 deaths per year in the
United States for the period 1972–1992. More recently,
Simonsen et al. (14) estimated influenza deaths by use of
winter excess mortality, controlling for changes in age

Correspondence to Dr. Jonathan Dushoff, Department of Ecology and Evolutionary Biology, Princeton University, Guyot Hall, Princeton,
NJ 08544 (e-mail: dushoff@eno.princeton.edu).

181

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182 Dushoff et al.

TABLE 1. Mean monthly deaths from 1979 to 2001 for the US mortality time series investigated in this study
NameDeﬁnition

Deaths/month

All deaths

All deaths

Pneumonia and inﬂuenza deaths

Any ICD-9* cause 480–487, any ICD-10* cause J10–J18

181,721
16,405

Respiratory and circulatory deaths

Any ICD-9 cause 390–519, any ICD-10 category I or J

129,275

Underlying pneumonia and inﬂuenza deaths

Underlying ICD-9 cause 480–487, underlying ICD-10 cause J10–J18

5,849

Underlying respiratory and circulatory deaths

Underlying ICD-9 cause 390–519, underlying ICD-10 category I or J

95,313* ICD-9, International Classiﬁcation of Diseases, Ninth Revision; ICD-10, International Classiﬁcation of Diseases, Tenth Revision.

structure and for dominant viral subtype, and argued thatthe population-level burden of influenza is not consistent
with the high protective values of vaccination found in cohort studies.
In a recent paper, Thompson et al. (11) introduced a new
approach for estimating deaths attributable to influenza:
They fit a regression model to death time series that combined a sinusoidal function with weekly virologic surveillance data from the United States. They attributed anaverage of 34,000 deaths per year to influenza for the period
1976–1999, consistent with the 37,500 deaths per year estimated by Serfling-type models for this period (14).
Thompson et al. also estimated deaths due to both influenza
and respiratory syncytial virus for the period 1990–1999.
This work by Thompson et al. (11) represents an advanceover baseline methods, because it quantifies the relation
between deaths attributed to influenza infection and virologic surveillance data. The work also has significant limitations. Both influenza prevalence and mortality are highly
seasonal. Therefore, fitting a weekly regression between
deaths and influenza virus surveillance has the potential
to produce spurious correlations: Even if the annual patternof deaths were exactly the same every year, unaffectedby changes in influenza prevalence, a weekly regression
against influenza prevalence would likely indicate a significant correlation. Thompson et al. address this problem byincluding sinusoidal terms in their regression. Since noninfluenza-related mortality is not expected to follow an exact exponentiated sinusoidal pattern, this reduces, but does
not eliminate, the potential for spurious correlation and spurious attribution of deaths to influenza.
Another limitation of the weekly approach is the difficultyof correctly adjusting for time delays. It has been shown thatpeak mortality lags roughly 2 weeks behind the peak of
influenza activity (8). This is likely the result of several
different time delays from different influenza mortality
pathways (1). The model of Thompson et al. (11) does not
attempt to correct for these lags.
Nicholson (15) included viral and clinical surveillancedata in a model of mortality in England and Wales using
a 4-week timescale. This model, built on earlier models by
Tillett et al. (16), used dummy variables for some time
periods (but not others) to control for seasonal trends. Interpretation of the results is complicated by the complexityof the model (27 independent variables overall).
Sophisticated time-series methods attempt to separate
seasonal components, by use of autoregressive integrated

moving average models, for example (17), before applying
regression. Carrat and Valleron (18) fit such models to timeseries of noninfluenza deaths and modeled the residuals
against influenza deaths, in an attempt to attribute the total
number of deaths caused by influenza in France. The usefulness of this approach is limited by the unreliability of
attribution of influenza deaths on death certificates, however(19). Recently, increasingly sophisticated methods including generalized additive modeling (20), hierarchical modeling (21), and distributed-lag modeling (22) have been
applied to mortality time series to assess the impact of air
pollution on deaths (21, 22), with the work of Braga et al.
(20) explicitly attempting to control for epidemics of respiratory disease. Removing seasonal confounding remains
a complex issue, however (22). Further, influenza surveillance data for this time period at daily, weekly, or evenmonthly scales are not available in the public domain.
In this paper, we take a robust, conservative approach tothe problem of seasonal confounding by investigating therelation between influenza virus surveillance data and mortality at an annual timescale. We aggregate excess deaths
and prevalence measures over an entire influenza season andestimate the number of deaths attributable to influenza infection in the United States. Additionally, we applied our
method to two regions of the United States to investigate thecontribution of cold temperatures to seasonal excess mortality on an annualized basis.

MATERIALS AND METHODS

Using public-use mortality data files for the United States,
obtained from the Centers for Disease Control and Protection’s National Center for Health Statistics, we created a database of all US deaths from 1979 to 2001 that can bequeried by age, gender, underlying cause of death, andcontributing cause of death, among other variables. Using
this database, we generated several monthly time series of
US mortality (available at http://mortality.princeton.edu/
annualflu/) by use of different disease categories from theInternational Classification of Diseases, Ninth Revision
and Tenth Revision, that were based on either the underlying
cause of death or the underlying and contributing cause ofdeath (table 1). We divide the calendar into ‘‘flu years,’’ eachcontaining a single influenza season, that run from July toJune. Deaths were corrected multiplicatively to a standard
month length of 1,461/48  30.44 days.
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An Annualized Approach to US Inﬂuenza Mortality

183

FIGURE 1. Reported respiratory and circulatory (A) and pneumonia and inﬂuenza (B) deaths, by underlying cause and by multiple causes, UnitedStates, 1979–2001.The sharp drop in underlying pneumonia and inﬂuenza deaths in 1999 is due to the change in coding under the International
Classiﬁcation of Diseases system from the Ninth Revision to the Tenth Revision. In general, the series that consider multiple causes are expected
to be less sensitive to changes in coding methodologies.

Estimates based on mortality data depend on the consistency of mortality reports. This study takes a novel approachwithin the influenza epidemiology literature to the categorization of causes of death. Instead of using only the listed‘‘underlying’’ cause of death, we tabulate all deaths witha specific cause—either pneumonia and influenza causesor all respiratory and circulatory causes—listed anywhereon the death certificate. We expect these ‘‘multiple-cause’’data series to be more robust, both because more deaths areincluded and because considering all causes on the deathcertificate should make these series less sensitive to coding
and nosologic changes (figure 1).
Annual virologic surveillance data (aggregated by influenza season) for the United States were obtained from
Thompson et al. (11) and Morbidity and Mortality Weekly
Report (23, 24). Following Thompson et al., we use theproportion of tested samples positive as a proxy for prevalence of each influenza subtype. Although this proportion is
an imperfect measure of prevalence, we feel that it is thebest influenza-specific measure available. The model ofThompson et al. makes use of weekly virus surveillancedata, but these data have not been made available in the
public domain.
To remove long-term trends from our mortality data, we fit
a least-squares quadratic model to the time series of alldeaths in each age category studied and divided the numberof deaths in each category by this quadratic fit to all deaths to
obtain ‘‘normalized’’ deaths by month and category. This
form of normalization is an alternative to dividing by population estimates, and it has the advantages of being robust tochanges in population estimation methods and of allowing
us to conveniently divide our population by age and region.
Annual excess deaths were defined as the total number ofdeaths in a selected set of ‘‘influenza months’’ above the
Am J Epidemiol 2006;163:181–187

monthly average of a disjoint set of ‘‘baseline months.’’ For
the main analysis, we used November to April as the flu
months and the remaining 6 months as the baseline months(figure 2).
The main statistical model used was as follows:
NAD ¼ a þ bH3 H3 þ bH1 H1 þ bB B;
where ‘‘NAD’’ is any normalized annual death series;‘‘H3,’’ ‘‘H1,’’ and ‘‘B’’ refer to the proportions of samples
positive for influenza A subtypes H3N2 and H1N1 andinfluenza B; a is the intercept; and the bs are regression
coefficients.
Regional studies used deaths from 16 large counties in the
New York metropolitan area, linked to temperature datafrom Newark International Airport, and deaths from thestates of Illinois and Indiana, linked to temperature datafrom O’Hare International Airport. We chose regions that aredensely populated, were expected to have similar weather
across the region, and had complete monthly temperatureseries available at the International Research Institute for
Climate Prediction (25). Cold was measured on a monthly
basis as the average number of degrees below a threshold
temperature (Tthresh) or cold (C) ¼ min(Tthresh  T, 0), where
T is the mean monthly temperature. Cold was measured foreach flu year as the average of monthly cold values from
November through April. The statistical model used was asfollows:
NAD ¼ a þ bH3 H3 þ bH1 H1 þ bB B þ bC C:
Because virus surveillance data were not available with age
structure or regional breakdowns, we used national virus
surveillance data for all regressions involving surveillancedata.

184 Dushoff et al.

FIGURE 2. A normalized, detrended annual time series of excess deaths from monthly mortality data, United States, 1979–2001. Respiratory andcirculatory (R&C) deaths for the whole population are used in this example. In A, a quadratic is ﬁt to all deaths for a given age class (or the whole
population); in B, deaths from a given cause are normalized by dividing by this quadratic ﬁt; in C and D, normalized annualized winter deaths aredeﬁned as normalized deaths in ‘‘inﬂuenza’’ months above the monthly average for ‘‘baseline’’ months in the same season.

Statistical analyses were performed using the statisticalpackage R (26). Deaths attributed to an independent variable
in a regression model were calculated by the difference
between the number of normalized deaths predicted by the
regression model and the number predicted when the independent variable is set to zero. Normalized deaths attributedin each year were then multiplied by the appropriate normalization factor. Because this method assumes that eachcofactor has the same effect each year (e.g., no strain ofa given subtype is more virulent than any other), estimatesof attributable deaths in a particular season are less reliable
than the estimates of average annual deaths over the entire
time period. R scripts used in the analysis are available at
http://mortality.princeton.edu/annualflu/.

RESULTSWe find positive correlations between excess deaths andthe annual prevalence of each of the three influenza subtypes, for each category of deaths that we study. Using these
correlations, we can estimate the average number of deaths
in each category caused by influenza over a 20-year period(table 2) (Web table 1). (This latter tabular material is described in the first of seven supplementary tables; each isreferred to as ‘‘Web table’’ in the text and is posted on the
Journal’s website (http://aje.oxfordjournals.org/).) The regression model attributes an annual average of 41,400 (95percent confidence interval: 27,100, 55,700) deaths to influenza over the period 1979–2001.
To investigate the effects of cold, we compared deathrecords for two regions of the United States with wintertemperature records from these regions. We found associations between normalized excess regional pneumonia andinfluenza deaths and the national prevalence of H3 and B
viruses in both regions (table 3). Pneumonia and influenza
deaths were used with these smaller samples because they
showed more robust correlations with surveillance data in
all analyses. No consistent relations were found between
various combinations of monthly mean temperatures andnormalized excess deaths, however, whether or not nationwide influenza virus surveillance data were used in the regression models (the example of cold over the whole winterseason is shown in table 3).
Confidence intervals on the number of deaths attributed tocold weather are large, so we cannot conclude that influenza
is a more important cause of winter mortality on an annual
timescale than is cold weather. The result is suggestive,
however, because the weather data used are more localized
and more precise than the influenza surveillance data, so we
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An Annualized Approach to US Inﬂuenza Mortality

185

TABLE 2. Annual deaths attributed by the surveillance regression model, categorized by pneumonia andinﬂuenza or by all respiratory and circulatory causes appearing anywhere in the death record, UnitedStates, 1979–2001
Cause

Pneumonia andinﬂuenza deaths

Other respiratory andcirculatory deaths

All respiratory andcirculatory deaths

Non-respiratory andcirculatory deaths

All deaths

H3N2

10,266***

13,331**

H1N1

1,045

1,731

23,597***

5,282***

28,878***2,775

1,184yB

3,165*

3,960

3,562

6,727y1,821y8,547*

Total

14,475***

18,624**33,099***8,287**

41,386**** p < 0.05; **p < 0.01; ***p < 0.001.
y p < 0.1.

might have expected more statistical power in weather analyses. Results in table 3 are for Tthresh ¼ 10C. Results setting
Tthresh to the mean temperature for each month, or to 20C,
are similar, but with much smaller and much larger confidence intervals, respectively.
We performed a sensitivity analysis to test our expectation that attributing deaths using annualized regression
would be relatively insensitive to our choice of influenza
months and baseline months, by examining several different
such choices (Web tables 2, 3, 4, 5, and 6). For all choices,each of the 15 estimates of deaths in a category attributed toa subtype was positive, and all produced estimated totals
within 10 percent of the estimate in the main text.
Over the time span that we studied, the average surveyed
prevalence of influenza increases through time, possibly because of better prescreening or improved test sensitivity. We
constructed normalized surveillance time series, by fitting
a linear trend through total measured influenza prevalenceand dividing the surveillance observations for H3, H1, and B
for each year by this trend line, thus removing overall prevalence trends. These normalized data showed a qualitatively
similar pattern, with significantly positive regression coefficients for two of the three subtypes, and predicted a total
number of influenza deaths around 90 percent of the number
predicted by the raw prevalence estimates (Web table 7).
If, instead of using normalized excess deaths, we apply
our regression model to Serfling estimates generated by themethod of Simonsen et al. (14), the model attributes 33,100(95 percent confidence interval: 20,500, 45,600) annual
deaths to influenza infection.
DISCUSSION

The total number of deaths attributed to influenza by oursurveillance model (41,400 per year from 1979 to 2001) issimilar to that found in other studies (11, 13, 14). The factthat our estimate of the mortality burden of influenza, basedon our conservative methodology, is similar to earlier estimates provides support for classical assumptions about therole of influenza in seasonal excess mortality. Our estimates
are not consistent, however, with much lower estimates from
authors who attribute most excess winter deaths to cold (3,27) or with much higher numbers that can be inferred fromcohort studies (2, 4–6, 14).
Although our results are consistent with other ecologic
estimates, the conservative, annualized method used here
increases the certainty that deaths attributed to influenza
are in fact caused by influenza. Methods based on seasonalpattern begin from the assumption that influenza is the
major source of excess winter death. Daily, weekly, andmonthly regressions are powerful, but they are in dangerof being confounded by other seasonal factors.
The annualized approach also measures effects at a different timescale than daily or weekly regressions. A person

TABLE 3. Annual pneumonia and inﬂuenza deaths, with 95% conﬁdence intervals,
categorized by causes appearing anywhere in the death record, attributed by the regional
surveillance regression model for the New York metropolitan area and the states ofIllinois and Indiana, 1979–2001*
New York metropolitan area

Illinois and Indiana

Cause

No. ofdeaths

H3N2

1,492

H1N1

88

560, 384

127

338, 592

B

774

21, 1,571

549

173, 1,271

Cold

1,640

1,815, 5,097

1,646

2,504, 5,796

Total

3,819

66, 7,572

4,447

62, 8,832* Threshold temperature is 10C.

Am J Epidemiol 2006;163:181–187

95% conﬁdence
interval

No. ofdeaths

95% conﬁdence
interval

361, 2,624

2,126

1,004, 3,249

186 Dushoff et al.

whose death in a given week is triggered by influenza or
cold weather may be somebody who would otherwise have
lived for many more years or somebody who was unlikely tosurvive the winter anyway. Deaths in the latter category
associated with causes by time-series analysis are often referred to as the ‘‘harvesting effect,’’ meaning that a particularcause, such as cold or influenza, may be ‘‘harvesting’’ people with very short life expectancies, determining the exact
time of death but shortening lives by only a small amount(28). Weekly analyses measure deaths in both categories,
whereas an annualized analysis will omit most deaths in
the latter category. Measuring at different timescales asks
fundamentally different questions: Neither answer is morecorrect than the other. The annualized approach presented
here is, however, a substantially more conservative way of
asking whether influenza triggers a substantial proportion ofseasonal excess deaths.
By making use of multiple-cause death information, we
have more than doubled the number of pneumonia and influenza deaths available for analysis and made our analysis
less sensitive to coding choices. We suggest that, wheremultiple-cause death data are available, all pneumonia andinfluenza deaths and all respiratory and circulatory deaths
may be useful time series for investigating influenza-caused
mortality.
On an annual timescale, we find preliminary evidence thatcold weather does not predict winter deaths. A full-scalespatial analysis of influenza mortality, ideally incorporating
spatial surveillance data, remains to be done. If this result
holds up, however, it does not necessarily contradict thelarge body of evidence relating cold stress to mortality(27, 29, 30). It is likely that temperature determines thetiming of deaths on a shorter timescale; that is, people
whose deaths are triggered by a particular cold spell may
be people who are unlikely to survive until June. It is also
possible that cold weather has indirect effects on mortality,
by accelerating the spread of influenza (1, 31).
We believe that we have made a simple, robust, and conservative model of influenza deaths. The price, however, isthat our model is rather crude. The fact that we have only
one data point per year limits the power and precision of ouranalysis. Our surveillance-based regression model does notallow for the fact that different strains of a given subtype
may be more or less deadly from year to year. Additionally,
virus surveillance by the Centers for Disease Control andPrevention is based largely on contributed samples andtherefore does not reflect a systematic sampling scheme(32). On at least one occasion, the 1985–1986 season, theepidemic in the total US population was largely dominatedby the B virus, while most cases in the elderly, and thus
influenza-triggered deaths, were due to the more lethal influenza A(H3) virus (33).
In summary, a conservative, annualized analysis finds
evidence that influenza virus infections are causing mortality on an annual timescale. Our estimates support earlier
estimates of influenza burden based on direct excess deaths(13, 14) and weekly regressions (11), but they do not support
higher estimates based on cohort studies (4–6). Our results
suggest that the triggering of deaths by cold weather (3) may
be a short-term phenomenon that has much less impact onan annual timescale. Further analyses based on disaggregated, systematic viral surveillance data have the potential
to shed further light on these questions, as such data become
publicly available.

ACKNOWLEDGMENTS

The authors thank Dr. Mark Miller for helpful
conversations.
Conflict of interest: none declared.

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