• Open Access

Estimates of US influenza-associated deaths made using four different methods

Authors

  • William W. Thompson,

    1. Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA
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  • Eric Weintraub,

    1. Immunization Safety Office, Office of the Chief Science Officer, Centers for Disease Control and Prevention, Atlanta, GA, USA
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  • Praveen Dhankhar,

    1. Division of Emerging Infections and Surveillance Services, National Center for Preparedness, Detection and Control of Infectious Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA.
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  • Po-Yung Cheng,

    1. Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA
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  • Lynnette Brammer,

    1. Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA
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  • Martin I. Meltzer,

    1. Division of Emerging Infections and Surveillance Services, National Center for Preparedness, Detection and Control of Infectious Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA.
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  • Joseph S. Bresee,

    1. Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA
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  • David K. Shay

    1. Influenza Division, National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA
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Dr David K. Shay, Influenza Division, US Centers for Disease Control and Prevention, Mailstop A32, 1600 Clifton RD, NE, Atlanta, GA 30333, USA. E-mail: dks4@cdc.gov

Abstract

Background  A wide range of methods have been used for estimating influenza-associated deaths in temperate countries. Direct comparisons of estimates produced by using different models with US mortality data have not been published.

Objective  Compare estimates of US influenza-associated deaths made by using four models and summarize strengths and weaknesses of each model.

Methods  US mortality data from the 1972–1973 through 2002–2003 respiratory seasons and World Health Organization influenza surveillance data were used to estimate influenza-associated respiratory and circulatory deaths. Four models were used: (i) rate-difference (using peri-season or summer-season baselines), (ii) Serfling least squares cyclical regression, (iii) Serfling–Poisson regression, (iv) and autoregressive integrated moving average models.

Results  Annual estimates of influenza-associated deaths made using each model were similar and positively correlated, except for estimates from the summer-season rate-difference model, which were consistently higher. From the 1976/1977 through the 2002/2003 seasons the, the Poisson regression models estimated that an annual average of 25 470 [95% confidence interval (CI) 19 781–31 159] influenza-associated respiratory and circulatory deaths [9·9 deaths per 100 000 (95% CI 7·9–11·9)], while peri-season rate-difference models using a 15% threshold estimated an annual average of 22 454 (95% CI 16 189–28 719) deaths [8·6 deaths per 100 000 (95% CI 6·4–10·9)].

Conclusions  Estimates of influenza-associated mortality were of similar magnitude. Poisson regression models permit the estimation of deaths associated with influenza A and B, but require robust viral surveillance data. By contrast, simple peri-season rate-difference models may prove useful for estimating mortality in countries with sparse viral surveillance data or complex influenza seasonality.

Introduction

For several decades, the Centers for Disease Control and Prevention (CDC) has made annual estimates of influenza-associated deaths in the US.1–4 We use the term influenza-associated death herein to refer to a death for which influenza infection was likely a contributor to mortality, but not necessarily the sole reason for the acute illness that led to the death. Estimates of influenza-associated deaths have been used to determine costs and benefits associated with influenza prevention and control strategies (including vaccination) and in preparing for both seasonal epidemics and future pandemics.5–7

Influenza infections result in morbidity and mortality nearly every season in the US.4,8 Mortality associated with influenza varies by age group, by chronic disease status, and by influenza virus type and subtype.4,9–11 Introductions of a novel efficiently transmitted influenza A virus into the population can result in pandemics, which are often associated with more deaths than annual influenza epidemics. Primarily because the US population of those aged ≥65 years has increased substantially since the last pandemic in 1968–1969, current annual estimates of influenza-associated deaths exceed the annual estimates of deaths associated with that pandemic.4

Previous estimates for both pandemic and epidemic influenza-associated deaths have varied, based on outcomes modeled and the specific statistical methods used.4,9,12,13 Four classes of models have been used by CDC to estimate influenza-associated deaths in the US: (i) rate-difference models,14–17 (ii) Serfling least squares cyclical regression models which do not incorporate influenza viral surveillance data,1,2,18 (iii) Serfling–Poisson regression models which do incorporate influenza viral surveillance data,4,19 and (iv) autoregressive integrated moving average (ARIMA) models which do not use influenza surveillance data.13,20,21 In this study, we used these four classes of models to estimate underlying respiratory and circulatory deaths that were associated with influenza among persons aged <65 or ≥65 years. Our objectives were to compare estimates made by using each of the models, to assess similarities and differences among the estimates produced by using each model, and to suggest several strengths and weakness of each model. We believe these results will be of interest not only to researchers and health officials in countries that currently use these models, but also to those in countries that are considering methods to estimate the mortality burden of influenza.

Methods

Data and analyses

United States laboratory-based surveillance for influenza viruses was conducted from October through mid-May (calendar week 40 through week 20). During the 1976–1977 through 2002–2003 respiratory seasons, we obtained weekly influenza test results from 50 to 75 World Health Organization (WHO) collaborating virology laboratories in the US. The laboratories provided weekly numbers of total respiratory specimens tested for influenza and the number of positive influenza tests by virus type and subtype.22

National mortality data were obtained from the National Center for Health Statistics.23 Deaths were categorized using the International Classification of Diseases eighth revision (ICD-8), ninth revision (ICD-9) 24 or tenth revision (ICD-10), as appropriate. We modeled underlying respiratory and circulatory deaths (ICD-8 codes 390–519; ICD-9 codes 390–519; ICD-10 codes I00–I99, J00–J99). Underlying respiratory and circulatory deaths provide an estimate of death-associated respiratory infections that is more sensitive than underlying pneumonia and influenza deaths and more specific than all-cause deaths.4

We used four types of models to estimate influenza-associated deaths: (i)rate-difference models,16 (ii) Serfling least squares cyclical regression models,18 (iii) Serfling–Poisson regression models,4 and (iv) autoregressive integrated moving average models.20 Human subject review was not required for this study as only aggregate national data without personal identifiers were used in analyses.

Peri- and summer-season rate-difference models

Incidence rate-difference models have been used frequently to estimate influenza-associated hospitalizations and deaths.14,16,17,25 We defined five periods for each season: (i) a period when ≥10% of specimens tested were positive for influenza, (ii) a period when ≥15% of specimens were positive, (iii) a peri-season baseline period when <10% of specimens were positive, (iv) a peri-season baseline period when <15% of specimens were positive, and (v) a summer-season baseline period. The summer-season baseline period was defined as the weeks from July through September at the beginning of each season and May and June at the end of each season when there is little influenza activity.

The peri-season excess mortality rates were defined as the difference in the average weekly mortality rates between an influenza period and a peri-season period for a particular season. The summer-season excess mortality rates were defined as the difference in the average weekly rates between an influenza period and a summer-season period.

Weekly excess mortality rates were converted to annual excess numbers of deaths by using the number of weeks that were above an epidemic threshold, and available US census data: annual excess deaths = (excess weekly rate) × (number of epidemic weeks) × (population).

Serfling least squares cyclical regression model

A previously published Serfling least squares cyclical regression model was used to estimate annual numbers of influenza-associated deaths.18 In this model

image

where Yi represented the number of deaths in a particular week i, β0 represented the intercept, β1 represented a coefficient for the linear time trend, β2 represented a coefficient for the quadratic time trend, β3 and β4 represented coefficients associated with seasonal fluctuations in deaths, and ei represented the error term. Epidemic thresholds were defined for the first 5 years of data for each age-group based primarily on visual inspection of the data. These thresholds were based on the 1978/1979 influenza season, when influenza A(H1N1) viruses predominated and other evidence suggested that few deaths were attributable to influenza.18,26 For subsequent seasons, annual baselines were forecasted using the prior 5-year non-epidemic data.

Serfling–Poisson regression model

Poisson regression models which incorporated weekly influenza circulation data were used to estimate influenza-associated deaths by age group.4,27,28 The models included coefficients similar to those described for the least squares regression models as well as additional terms corresponding to the circulation of influenza A(H3N2), A(H1N1), and B viruses.4 The three terms represented the percentages of specimens testing positive by subtype during a particular week. The age-specific population size was used as an offset term. Weekly estimates of the US population by age group were obtained from the US Census Bureau.29

In each Poisson regression model,

image

where, Yi represented the number of deaths at week i, α was the population offset, β0 represented the intercept, β1 through β3 represented coefficients associated with secular trends, β4 and β5 represented coefficients associated with seasonal changes in deaths, and β6–β8 represented coefficients associated with the percentages of specimens testing positive for each influenza virus type and sub-type during a given week. We did not have data for respiratory syncytial virus (RSV) before 1990 so an RSV term was not included in the model. Previous estimates of influenza-associated deaths have suggested that the total estimates of influenza-associated deaths are not significantly influenced by the inclusion of a RSV term.30 However, it is possible that if we made age-specific estimates for young children that the inclusion of RSV in the model could lead to significant differences in death estimates.

Predicted values for the full model for a given week were estimated and then predicted values for models that excluded one viral term were subtracted to estimate influenza-associated deaths associated with that viral type/subtype. The weekly influenza-associated deaths were summed for each viral term across the influenza season.

Autoregressive integrated moving average (ARIMA) models

Previously published methods developed by Choi and Thacker 13,20,31,32 were used to estimate influenza-associated deaths. For each age group, a Fourier equation was used to estimate baseline, non-influenza deaths during the influenza epidemic weeks of 1972–1973 and 1973–1974; epidemic weeks were defined as two or more consecutive weeks when mortality was greater than two standard deviations (SD) above the mean. Influenza-related excess deaths were defined as the difference between actual deaths and estimated non-influenza deaths. During epidemic weeks, total deaths were replaced with estimates of non-influenza deaths. Following Box-Jenkins procedures,33 we removed seasonal patterns from the data by taking the difference in weekly deaths one year apart (e.g., deaths week 40 in 1974–deaths week 40 in 1973). We used the actual deaths during non-epidemic weeks and the Fourier-estimated non-influenza deaths to build the model to estimate deaths for the next 52 weeks. Influenza epidemic weeks were defined as two or more consecutive weeks when actual mortality was greater than the upper bound of a 95% confidence interval (CI) around the non-influenza deaths. We replaced actual deaths for epidemic weeks with estimated non-influenza deaths, and repeated the process for each subsequent season, re-estimating the coefficients from the ARIMA equation. Goodness-of-fit was tested by using the Ljung modification of the Box-Pierce Q statistic. 39

Comparisons of annual numbers of influenza-associated deaths by age group

We compared the annual numbers of deaths for each model by age group using Wilcoxon signed-rank tests with a Bonferroni adjustment for multiple comparisons; an adjusted P-value of <0·05 was considered statistically significant.

Results

Estimates of influenza-associated deaths using rate-difference models with a 15% threshold

Among persons aged <65 years, the average annual excess death rate using the peri-season baseline was 0·15 (95% CI 0·11–1·8) deaths per 100 000 person-weeks and ranged from 0 to 0·42 deaths per 100 000 person-weeks (Appendix S1). The annual average summer-season excess rate was 0·27 deaths per 100 000 person-weeks (95% CI 0·22–0·31). Among persons aged ≥65 years, excess mortality rates were substantially higher. Using the peri-season baseline, there were 8·00 (95% CI 6·16–9·84) deaths per 100 000 person-weeks with substantial variation by seasons (0–18·5 deaths per 100 000 person-weeks). The average annual excess rate using the summer-season baseline was 15·1 deaths per 100 000 person-weeks (95% CI 12·9–17·3).

The annual average number of epidemic weeks (when >15% of specimens tested were positive for influenza) was 7·4 (range 0–15 weeks) (Table 1). Among persons aged <65 years, the estimated number of influenza-associated deaths for the peri-season model ranged from 0 to 6574 deaths with an annual average of 2507 deaths. Similarly, using the summer-season model, the number of deaths ranged from 0 to 9264 deaths with an annual average of 4509 deaths. Among those aged ≥65 years, the estimated number of influenza-associated deaths for the peri-season model ranged from 0 to 51 122 deaths with an annual average of 19 954 deaths. Using the summer-season model, the number of deaths ranged from 0 to 74 821 deaths with an annual average of 36 430 deaths. Eighty-nine percent of all deaths occurred among persons aged 65 and older. Among all persons, the peri-season model estimated an annual average of 22 454 (95% CI 16 189–28 179) influenza-associated deaths.

Table 1.   Incidence rate-difference model annual estimates for underlying respiratory and circulatory deaths using a 15% threshold*.
SeasonEpi weeksAge < 65 yearsAge >65 yearsTotal
Annual excess numbersAnnual excess ratesAnnual excess numbersAnnual excess ratesAnnual excess numbers
Peri**Summer***Peri**Summer***Peri**Summer***Peri**Summer***PeriSummer
  1. *The 15% threshold represent weeks in which the number of positive influenza isolates exceeded 15% of the total specimen tested.

  2. **The Peri-season model estimates are calculated by multiplying the peri-season rates in Appendix S1 times the number of epiweeks times the population divided by 100 000.

  3. ***The summer-season model estimates are calculated by multiplying the summer-season rates in Appendix S1 times the number of epiweeks times the population divided by 100 000.

1976308440·00·4057490·024·206593
19775416961072·13·118 65829 27277·3121·222 82735 379
1978498522280·51·1333710 00213·540·4432212 230
19794127526160·61·3789617 46131·268·9917120 077
19803207231701·01·614 33421 75355·484·116 40624 923
19810000·00·0000·00·000
19826103827140·51·3759120 12228·074·2862922 836
198312108047880·52·3819733 70429·6121·6927738 492
19849331163601·63·129 96050 028106·0176·933 27156 388
19857202241471·02·016 45433 59057·0116·418 47637 737
19868266447891·32·317 10732 70958·3111·419 77137 498
1987350214880·20·7528513 88617·646·3578715 374
198811251150591·22·319 31441 82363·2136·921 82546 882
19897142938970·71·817 74336 46157·1117·319 17240 358
1990596323610·41·1557517 39317·655·0653819 754
19918326950801·52·325 55542 43479·8132·428 82447 514
19928244047671·12·120 44240 63162·7124·722 88245 398
19937419356471·82·535 97251 450109·0155·940 16557 097
19947145733190·61·414 79531 67044·294·616 25234 989
19957263145651·12·016 43434 26548·6101·319 06538 830
199610352262011·52·635 80661 385104·7179·539 32867 586
19979449865931·92·845 43166 220131·5191·649 92972 813
199811394567771·62·843 39870 799124·4203·047 34377 576
199912657492642·73·851 12274 821145·7213·257 69684 085
200010348659241·42·421 17143 35859·9122·724 65749 282
200115505076652·03·041 80167 143117·7189·146 85174 808
200210261453841·02·115 37435 48243·299·617 98840 866
Average during the 1976/77 through the 2002/03 seasons7·4250745091·22·119 95436 43064·7119·322 46140 939

Estimates of influenza-associated deaths using rate-difference models with a 10% threshold

As expected, estimates of numbers and rates of influenza-associated deaths were higher with this model than the model using a 15% threshold (Appendices S2 and S3). The annual average number of epidemic weeks (when >10% of specimens tested positive for influenza) was 11·8 (range 2–20 weeks). For persons aged <65 years, the estimated number of influenza-associated deaths for the peri-season model ranged from 0 to 7084 deaths with an annual average of 3819 deaths. Using the summer-season model, the number of deaths ranged from 436 to 10 069 deaths with an annual average of 6574 deaths. For persons aged ≥65 years, the estimated number of influenza-associated deaths for the peri-season model ranged from 0 to 57 844 deaths with an annual average of 29 971 deaths. Using the summer-season model, the number of deaths ranged from 4072 to 93 789 deaths with an annual average of 52 795 deaths.

Estimates of influenza-associated deaths using Serfling least squares regression models

Among persons aged <65 or ≥65 years, the average annual number of epidemic weeks estimated during the 19761977 through 20022003 seasons was 3·6 and 9·7, respectively (Table 2). Among persons aged ≥65 years during the 2000/2001 season, the model estimated 28 epidemic weeks, which represented an outlier. Among persons aged <65 or ≥65 years, the model estimated annual averages of 1475 (95% CI 855–2095) and 20 161 (95% CI 14 90725 415) influenza-associated deaths, respectively. The average annual rates of influenza-associated deaths among those aged <65 or ≥65 years were 0·7 (range 0–2·7) and 65·0 (range 0–134·2) per 100 000 person-weeks, respectively. The total number of influenza-associated deaths annually was 21 636 (95% CI 15 91427 358). More than 90% of influenza-associated pneumonia and influenza deaths occurred among persons aged ≥65 years.

Table 2.   Linear regression model annual estimates using underlying respiratory and circulatory deaths*
SeasonAge < 65 yearsAge ≥ 65 yearsTotal
Epi weeksAnnual excess numbers L 95% CI U 95% CIAnnual excess rate**Epi weeksAnnual excess numbers L 95% CI U 95% CIAnnual excess rate**Annual excess numbers L 95% CI U 95% CI
  1. *Model estimates are based on the linear regression model used in Simonsen et al. (1997).

  2. **Deaths per 100 000 person years.

197295206221282002·7612 174576318 58556·917 380797526 785
197300000·000000·0000
1974283617514970·4712 140469319 58754·112 976486821 084
197500000·0822 54314 04731 03998·022 54314 04731 039
197600000·000000·0000
197775299290476952·7930 38720 48540 289125·935 68723 38947 984
197800000·000000·0000
197900000·0714 494767321 31457·314 494767321 314
198074035223358372·01134 72625 29244 159134·238 76127 52549 996
198100000·077758194713 56829·37758194713 568
198200000·068600337313 82731·88600337313 827
1983274326712200·4234671707522612·5421019756446
198472595104441471·2921 90813 84329 97277·624 50314 88734 119
1985274230011850·41220 426879832 05570·921 169909733 240
198625301269340·2710 974511716 83137·411 504524317 765
198700000·01626 85715 51838 19789·826 85715 51838 197
198800000·043446848604311·334468486043
198952495150334871·1927 01620 42633 60687·229 51021 92837 093
1990264225410300·31820 881763234 13066·321 523788735 160
199152085110130690·92036 65821 85551 461114·538 74322 95654 530
1992388528314870·42135 30220 13250 472108·636 18720 41551 959
199342026126627850·9830 90824 86036 95693·832 93426 12639 742
199400000·0810 569425916 87931·710 569425916 879
19953144987220270·6613 408880518 01139·714 857967720 037
19964154275523290·7926 84119 70233 98078·528 38320 45736 309
199782604113040771·11133 90126 05841 74498·236 50427 18845 821
19987229098335970·91541 10629 93452 279117·943 39630 91755 875
199984157269856161·71037 80531 37944 230107·641 96234 07749 847
2000154303147571311·72834 19515 01053 38096·638 49816 48560 511
20015140343823680·6812 712666518 76035·714 116710321 128
200200000·000000·0000
Average during the 1976/77 through the 2002/03 seasons3·6147585520950·79·720 161 14 90725 41565·021 636 15 91427 358

Estimates of influenza-associated deaths using Serfling Poisson regression models

Among persons aged <65 years, the models estimated an annual average of 2680 (95% CI 2188–3171) deaths annually (Table 3). The annual rates of influenza-associated deaths ranged from 0·29 to 2·06 deaths per 100 000 person years. Among persons aged ≥65 years, the models estimated an annual average of 22 790 (95% CI 17 565–28 033), and annual rates of influenza-associated deaths ranged from 11·7 to 144·7 deaths per 100 000 person years. The average annual total number of influenza-associated deaths estimated from this model was 25 470 (95% CI 19 781–31 159). Eighty-nine percent of the estimated deaths occurred among persons aged ≥65 years.

Table 3.   Poisson regression model annual estimates using underlying respiratory and circulatory deaths*
SeasonAge < 65 yearsAge ≥ 65 yearsTotal
Annual excess numbers L 95% CI U 95% CIAnnual excess rate**Annual excess numbers L 95% CI U 95% CIAnnual excess rate**Annual excess numbers L 95% CI U 95% CIAnnual excess rate**
  1. *The Poisson regression model is based on the methods described in Thompson et al. (2003).

  2. **Deaths per 100 000 person years.

19761549147416280·7910 88910,68611 09545·912 43812 22112 6595·7
19773618350237381·8421 37021 08521 65888·524 98824 68025 30011·3
19781504143015820·7633183207343313·44822468849602·2
19799068499670·4591078922929635·910 013981910 2114·4
19802914281030221·4517 97917 71818 24469·520 89320 61221 1789·2
19815845396330·2947024570483817·75286514554302·3
19823375326334911·6423 88123 58024 18688·027 25626 93427 58211·7
19831822174019080·8811 70611 49611 92042·213 52813 30213 7585·8
19844294416744242·0633 44833 09133 808118·337 74237 36338 12515·9
19851638156117190·7816 13915 89216 39055·917 77717 51818 0407·4
19861303123413760·6134293316354611·74732459948692·0
19872328223524251·0819 59819 32619 87465·321 92621 63822 2189·0
19882049196221400·9515 27215 03215 51650·017 32117 06517 5817·0
19893299318834141·5129 00528 67329 34193·332 30431 95432 65812·9
19901232116513030·5613 88813 65914 12143·915 12014 88115 3636·0
19913632351637521·6331 07330 72931 42097·034 70534 34235 07213·6
19922110202222020·9323 02222 72723 32170·625 13224 82325 4459·7
19933297318634111·4531 45231 10631 80295·334 74934 38635 11613·3
19942481238525811·0725 00024 69225 31274·727 48127 15827 80810·4
19952531243426321·0920 56420 28520 84760·823 09522 79923 3958·6
19963948382740731·6741 22040 82441 620120·545 16844 75345 58616·7
19974429430045611·8543 82443 41644 236126·848 25347 82448 68517·6
19983763364538851·5538 88438 49939 272111·542 64742 24443 05415·4
19994678454648141·9144 81844 40545 235127·749 49649 06249,93417·7
20001608153116890·6512 01311 80012 23034·013 62113 39413 8524·8
20015187504853302·0651 39050 94851 836144·756 577 56 11357 04519·7
20022269217823640·8918 35118 08718 61851·520 62020 34020 9037·1
Average during 1976/77 through the 2002/03 seasons2680218831711·20 22 790 17 56528 01672·425 47019 78131 1599·90

Age-specific annual estimates for the Poisson regression model were made by influenza virus type and subtype (Table 4). Among persons aged <65 years, the models estimated annual averages of 345 (range 0–1462), 2027 (range 0–4743), and 307 (range 0–825) influenza-associated deaths for A(H1), A(H3) and B viruses, respectively. Among persons aged ≥65 years, the models estimated annual averages of 887 (range 0–3241), 17 797 (range 0–45 339), and 4107 (4–10 342) influenza-associated deaths for A(H1), A(H3) and B viruses, respectively.

Table 4.   Poisson regression model annual estimates by virus type and subtype using underlying respiratory and circulatory deaths*
Age groupSeasonA(H1) virusesA(H3) virusesB virusesAll influenza
Annual excess number L 95% CI U 95% CIAnnual excess number L 95% CI U 95% CIAnnual excess number L 95% CI U 95% CIAnnual excess number L 95% CI U 95% CI
  1. *The Poisson regression model is based on the methods described in Thompson et al. (2003).

<65 years19765212110310401170441402484154914741628
19772902583253323321234385212361835023738
1978146213891539218402955150414301582
1979251737564373825771883906849967
1980382346422253224352633000291428103022
1981199173229000385348425584539633
1982250221283293728333045188163217337532633491
1983924866986228200260670621723182217401908
1984319423741114367544171429441674424
19851079779181040660612712163815611719
1986128312151355148246313130312341376
198710385125205819712149167143194232822352425
19889498911011435396478665616718204919622140
19892517373268315833826313329931883414
199011697139438399481678629731123211651303
1991369333409324331333357201331363235163752
1992655183135612861430689639742211020222202
1993951732763166339012721329731863411
1994281941220721172301246217279248123852581
1995760708816151314391591258228291253124342632
1996000352534113643423385465394838274073
19974211440442764536211432442943004561
1998161026342633133543321288358376336453885
1999153131179450643764640191230467845464814
20009859251048745993549505597160815311689
2001453460474346104880399362440518750485330
2002873817933858802917538494585226921782364
Average 1976/1977–2002/2003345169521202713882667307198416268021883171
≥65 years1976841666096452677042724146440210 88910 68611 095
197757052561920 75920 47921 04341305621 37021 08521 658
197829162812302410519392355433331832073433
1978513967377341417867984988864910789229296
198082477088217 15116 89617 410421117 97917 71818 244
1981435396478000426741414397470245704838
198256952461821 19620 91321 48321162028220823 88123 58024 186
198321732084226616741596175678597687803511 70611 49611 920
1984631332 77532 42233 13266761872033 44833 09133 808
1985421177297559790384068228858816 13915 89216 390
198632413131335511091133786297342933163546
198727324230717 10516 85117 36322202130231419 59819 32619 874
198825912493269336753558379690068822919415 27215 03215 516
198966528428 82128 49029 1561189914129 00528 67329 341
199032429136138623742398697029511989713 88813 65914 121
199110841021115029 68329 34730 02330627434231 07330 72931 420
199219116622012 48912 27212 71010 34210 14510 54323 02222 72723 321
199328194131 20930 86531 55721518824631 45231 10631 802
1994897211021 13020 84721 41737813662390325 00024 69225 312
199523192227241514 35314 12014 59038923772401620 56420 28520 847
199600034 69234 32935 05965286372668841 22040 82441 620
19971272143 48443 07743 89532829436543 82443 41644 236
199845346033 70733 34934 06951324993527438 88438 49939 272
199946242250644 03943 63044 45231728435444 81844 40545 235
200029752870308471466476883248147850512 01311 80012 230
200113411315945 33944 92445 75859175768607051 39050 94851 836
200225592462266078187647799379747801815118 35118 08718 618
Average 1976/1977–2002/2003887440133417 79711 83323 76041072660555422 79017 56528 016

Estimates of influenza-associated deaths using ARIMA models

Using a two-SD threshold and data for persons aged <65 years, the average annual number of epidemic weeks from the 1976/1977 through 2002/2003 seasons was 1·6 (range 0–7 weeks), and the average annual number of influenza-associated deaths was 809 (95% CI 292–1326) (Table 5). Among persons aged ≥65 years, the average annual number of epidemic weeks was 9·0 and the average annual number of influenza-associated deaths were 24 856 (95% CI 19 576–30 136). Using these models, more than 96% of all influenza-associated deaths occurred among persons aged 65 and older (See Appendix S4 for ARIMA model estimates using a one standard deviation threshold).

Table 5.   Autoregressive integrated moving average (ARIMA) model annual estimates using two SD threshold using underlying respiratory and circulatory deaths*
SeasonAge < 65 yearsAge ≥ 65 yearsTotal
Epi weeksAnnual excess numbers L 95% CI U 95% CIAnnual excess rateEpi weeksAnnual excess numbers L 95% CI U 95% CIAnnual excess rateAnnual excess numbers L 95% CI U 95% CI
  1. *The ARIMA models are based on the methods described in Choi & Thacker (1982).

  2. **Excess death confidence intervals could not be estimated.

19724690NA**NA**0·443698NA**NA**17·34388NA**NA**
197300000·000000·0000
197400000·000000·0000
19752104311319740·5617 879774428 01577·718 922785729 989
197600000·000000·0000
197774702188775172·4825 24613 06437 426104·629 94814 95144 943
197800000·000000·0000
197900000·0718 582895828 20573·518 582895828 205
198063715156258691·81137 31922 49852 139144·241 03424 06058 008
1981289217216110·446376118411 56624·17268135613 177
198200000·01019 732689232 57372·919 732689232 573
198300000·0916 424510927 73959·416 424510927 739
19846310993252851·51237 53522 66352 407133·040 64423 59557 692
198500000·01227 30512 76841 84194·827 30512 76841 841
198600000·01018 252635030 15562·218 252635030 155
198700000·01437 52821 09753 960125·437 52821 09753 960
198800000·01122 96710 39835 53775·422 96710 39835 537
19894184661730760·81135 69423 20048 187115·137 54023 81751 263
199000000·0510 038443115 64531·910 038443115 645
199100000·0920 88310 87730 88965·220 88310 87730 889
19923119128520970·51336 38122 08250 681112·037 57222 36752 778
19934205888432320·91039 62428 65750 592120·341 68229 54153 824
199400000·01023 06512 97133 15869·123 06512 97133 158
1995280223113730·31022 40612 37932 43366·323 20812 61033 806
199626458012100·31436 95123 01650 887108·137 59623 09652 097
199700000·01242 92831 08454 772124·342 92831 08454 772
199826175011850·31549 09734 51863 677140·949 71434 56864 862
199942268115733780·9939 91531 25748 573113·642 18332 41451 951
200000000·0617 96710 32925 60450·717 96710 32925 604
200100000·0822 25614 56929 94462·522 25614 56929 944
200200000·0366463717957418·6664637179574
Average 1976/1977–2002/20031·680929213260·49·024 856 19 57630 13680·325 665 20 14831 182

Comparisons of annual estimates of influenza-associated deaths by age and model type

Annual estimates of influenza-associated deaths for each model by season are summarized in Table 6. Correlations between annual estimates by model type were all at least moderately correlated (r > 0·53) and statistically significant (Table 7). The lowest correlations were seen for comparisons with the Serfling linear regression model.

Table 6.   Summary of average annual numbers of influenza-associated deaths by model type
SeasonPeri-10%Sum-10%Peri-15%Sum-15%LinearPoissonARIMA 2 SD
  1. ARIMA, autoregressive integrated moving average; SD, standard deviation.

  2. *Excess death numbers and rates could not be estimated due to lack of viral surveillance data.

1972NA*NA*NA*NA*17 380NA*4388
1973NA*NA*NA*NA*0NA*0
1974NA*NA*NA*NA*12 976NA*0
1975NA*NA*NA*NA*22 543NA*18 922
1976016 61006593012 4380
197737 78556 32322 82735 37935 68724 98829 948
1978856523 353432212 230048220
197925 97145 929917120 07714 49410 01318 582
198047 66364 94216 40624 92338 76120 89341 034
19810450800775852867268
198222 02747 513862922 836860027 25619 732
1983955248 383927738 492421013 52816 424
198436 38966 08133 27156 38824 50337 74240 644
198523 27449 33918 47637 73721 16917 77727 305
198619 77137 49819 77137 49811 504473218 252
198723 76747 605578715 37426 85721 92637 528
198826 38656 34121 82546 882344617 32122 967
198957 26881 59019 17240 35829 51032 30437 540
199020 09046 889653819 75421 52315 12010 038
199136 34559 54228 82447 51438 74334 70520 883
199240 29374 83622 88245 39836 18725 13237 572
199350 24271 38240 16557 09732 93434 74941 682
199435 32562 60116 25234 98910 56927 48123 065
199532 45568 75819 06538 83014 85723 09523 208
199664 791103 85839 32867 58628 38345 16837 596
199761 33587 82449 92972 81336 50448 25342 928
199858 63889 91547 34377 57643 39642 64749 714
199963 11191 60257 69684 08541 96249 49642 183
200030 31157 80524 65749 28238 49813 62117 967
200155 02387 34346 85174 80814 11656 57722 256
200225 95754 60617 98840 866020 6206646
Average during the 1976/77 through the 2002/03 seasons33 79059 36922 46140 93921 63625 47025 665
SD during the 1976/77 through the 2002/03 seasons18 77823 27915 83922 05414 46214 37713 943
Table 7.   Correlations between annual estimates of influenza-associated deaths*
 Peri-10%Sum-10%Peri-15%Sum-15%LinearPoissonARIMA
  1. ARIMA, autoregressive integrated moving average; SD, standard deviation.

  2. *All correlations were statistically significant.

Peri-10%1·00      
Sum-10%0·951·00     
Peri-15%0·860·841·00    
Sum-15%0·830·880·971·00   
Linear0·720·630·620·541·00  
Poisson0·860·860·860·830·541·00 
ARIMA 2SD0·820·780·690·650·790·681·00

Estimates from each model were compared using the Wilcoxon signed-rank tests with a Bonferroni adjustment for multiple comparisons. For models that used viral surveillance data, these comparisons were limited to the 1976–1977 through the 2002–2003 seasons when viral surveillance data were available. For persons aged <65 years, the summer-season 10% rate-difference estimates were significantly higher than all other estimates. (See Appendix S5a for annual estimates) Summer-season 15% estimates were significantly lower than the summer-season 10% estimates and higher than the linear, Poisson, and ARIMA estimates. The peri-season 10% estimates were significantly higher than the linear and ARIMA estimates. The ARIMA model estimates were significantly lower than estimates from all other models, except for the linear regression estimates.

For persons aged ≥65 years, the summer-season 10% rate-difference estimates were significantly higher than all other model estimates with the exception of the summer-season 15% model. (See Appendix S5b for annual estimates).

Discussion

Annual estimates of influenza-associated deaths have been used to describe the relative severity of inter-pandemic and pandemic influenza seasons. Numbers and rates of influenza-associated deaths also have been used in economic analyses to assess the costs and benefits of public health interventions. Specifically, estimates of influenza-associated deaths have been influential in analyses of the cost-effectiveness of possible expansions of US influenza vaccination recommendations.34,35 Thus, estimates of influenza-associated deaths on a national level have been directly relevant to US influenza control policies.

The four excess death models used by CDC over the past four decades to make estimates of influenza-associated deaths produced a similar picture of the burden of influenza-associated mortality during our 31-year study period. While there is no gold standard currently available for assessing the performance of the different models, with the exception of estimates made by using the summer-season 10% rate-difference model, the models produced mortality estimates that were similar in absolute magnitude and similar across 31 influenza seasons.

While most models yielded similar excess death estimates, each model has several strengths and weaknesses. Rate-difference models have been used for many years because they are straightforward and can be used with less than five seasons of baseline data. Rate-difference models may be used in countries with more than a single peak in influenza activity each season. These models are easy to implement, they do not require the manual definition of epidemic thresholds, and they allow other factors (e.g., the circulation of RSV) to be incorporated into models, if viral data for other pathogens are available. However the many advantages of rate-difference models must be balanced against their weaknesses. While peri-season rate-difference models produce estimates of US influenza-associated deaths that are comparable with those produced by using other methods, the summer-season rate-difference models consistently produce estimates of mortality that appear inflated when compared with those obtained from other models. Rate-difference models usually cannot be used to estimate influenza type- and subtype-specific mortality, because circulation of influenza types and subtypes overlap, and overlapping viral data is difficult to incorporate in these simple models. Finally, seasonal factors other than influenza circulation are difficult to control for and therefore the results could be biased by such factors temperature and humidity.

A strength of the Serfling least squares regression model is that it provides estimates of influenza-associated deaths without the need for influenza virus surveillance data, at least when these models are used in temperate areas in which the seasonality of influenza has been documented. While this may be a strength for countries that are not collecting consistent influenza virus surveillance data, the lack of such data may mean that the model’s underlying assumption that essentially all excess winter mortality is associated with influenza circulation may be unreasonable. These models also are simple when compared with other regression models. Particular weaknesses of the least squares regression model are the requirement to visually examine data to define initial baseline periods and the use of arbitrary statistical thresholds (e.g., z-score cut-points) to define influenza-associated deaths.

The Serfling–Poisson regression models produce estimate of numbers and rates of deaths by influenza type and subtype, an advantage for countries like the US that have many years of robust influenza virus surveillance data. Other strengths of Poisson models include the ability to account for changes in population size over time and the ability to incorporate other variables, such as the circulation of other pathogens (e.g., RSV) or climatic variables such as temperature. Disadvantages of Poisson models as used by CDC include requirements for consistent, robust weekly viral surveillance data and for at least 5 years of mortality data before stable estimates of the effects of all three currently circulating influenza types and subtypes can be made. Nonetheless, when the necessary data are available the ability of these models to provide weekly estimates of type- and subtype-specific deaths represent a step forward in efforts to better understand the burden of influenza on mortality. Another disadvantage of this method is that it makes an assumption that a linear relationship exists between the percentage of specimens testing positive for influenza and the log of the mortality rate. This assumption is difficult to test. However, it is logical to assume that increasing intensity of influenza circulation does lead to increases in influenza-associated deaths.

The ARIMA method is a dynamic forecasting method that uses the relationship between past data to forecast future values. A strength of this method for estimating influenza-associated deaths is that virologic data and manually setting baselines are not required. Another advantage is that as more data are collected the model can be updated and re-validated (i.e., the coefficients changed) to improve model fit and accuracy. Autoregressive integrated moving average methods have several disadvantages when compared with more commonly used models. They can be complicated to implement successfully, provide relatively few advantages over the more simple linear regression models, and suffer from some of the same weaknesses as these models, including defining influenza seasons solely by the use of statistical thresholds.

Centers for Disease Control and Prevention’s most recent published estimates of influenza-associated deaths for the 1990–1991 through 1998–1999 seasons made use of Poisson regression models. The annual average number of underlying respiratory and circulatory deaths associated with influenza during those nine seasons was 36 155 deaths.4 An annual estimate for a longer period (the 1976/1977 season through the 1998/1999 season) of 25 420 deaths was also made by using the Poisson regression model.4 The mortality estimates made in this study for 1976–1977 to 2002–2003 were similar to these previous estimates. The annual average for the 1990–1991 through 1998–1999 seasons was 32 928. The average annual estimate for the 1993–1994 through the 2002–2003 seasons, the last decade of the study period, was 36 171 deaths.

While the estimates of numbers and rates of influenza-associated deaths were similar and highly correlated across models, the estimates of the numbers of epidemic weeks were less highly correlated. The beginning and end of the epidemic periods (i.e., the tails) are typically associated with small differences between expected mortality and observed mortality. Therefore, differences in epidemic weeks lead to smaller differences than might be expected in the estimated annual number of influenza-associated deaths. Understanding why differences in estimates of epidemic weeks are found using various models is an area for future research.

In summary, each of the four models we used to estimate annual influenza-associated mortality produced similar estimates, with the exception of summer baseline rate-difference and the ARIMA models. Several factors must be considered when seeking to make the most efficient and reliable estimates of influenza-associated deaths. Depending on the availability of consistent and robust surveillance data, the length of the period for which mortality estimates are being made, and the general seasonality of influenza circulation in area of the world being studied, different models might be selected for primary use. We suggest that as countries or areas that have not previously made estimates of influenza-associated mortality begin this process, that it is reasonable to compare estimates made by using several different methods to see how similar the results are, and how they vary over time. Poisson models seem well-suited for use in countries with robust viral surveillance data. In countries where viral surveillance data are limited and where the seasonality of influenza is more complex, rate-difference models represent a reasonable starting point for making estimates of influenza-associated mortality. An important area for additional research is how to apply statistical models to estimate influenza-associated mortality in those subtropical and tropical countries that include the majority of the world’s population.

Acknowledgement

We wish to thank Ericka Sinclair, Erin Murray, and Alicia Budd for assistance in organizing the WHO influenza isolate data.

Financial Support

The work presented in this manuscript was funded solely by the US Centers for Disease Control and Prevention. The findings and conclusions in this study are those of the authors and do not necessarily represent the views of the Centers for Disease Control and Prevention.

Conflict of interest

We declare that we have no conflict of interest.

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