Supporting Text. Technical appendix to “The burden of seasonal influenza: using statistical models to inform targets for risk-based immunisation policy” (Cromer et al.)
1Technical description of model construction, fitting and selection
1.1 Model construction
The proportion of each health care outcome (hospitalisations, deaths in hospital and episodes leading to consultations in general practice) attributable to various respiratory pathogens was estimated using generalised linear models of the form.Here, represents the number of reported outcomes (eg. hospitalisations) for age group j and risk group r in week i. The right hand side is made up of constant term () representing outcomes attributed to causes other than the pathogens recorded in microbiological surveillance, a linear trend term that takes into account the change in outcomes over time (i.e. a coefficient, , multiplied by the week number, w, which starts at 0 in the first week of the series), and the sum of the product of the number of laboratory reports reported in microbiological surveillance for each pathogen p in week i() and their coefficient
(). The coefficients are estimated by negative binomial regression using an identity link function. If the coefficients are estimated to be negative, the term for the corresponding pathogen is removed for reasons of biological implausibility, and the model is re-run to obtain new estimates for the other coefficients. Backwards stepwise regression is used, this means that the least significant pathogens issequentially removed from the modelprovidedit is deemed to have a significance level above 0.05 and the model is re-run to obtain new estimates for the other coefficients. The total non-pathogen related coefficient (sum of the baseline coefficient and the linear trend term, ) is also required to be greater than zero for all values of w in the data series.
1.2Model variants and fittingprocedure
We fit the 9 models presented in Table S1 to data on each outcome (episodes leading to consultations in general practice, hospital admissions and deaths in hospital) data, and analyse the fitting results across all age and risk groups to determine the best fitting model.
Model Num / Name / 3 week moving average / Linear trend in outcomes over time / Division of influenza A into H1/H3 subtypes / Interactions between pathogens / Delays to test or to effect1 / Basic / / / / /
2 / Moving Average / / / / /
3* / Linear Trend / / / / /
4 / Subtypes / / / / /
5 / Interactions / / / / /
6 / 2 wk delay to test / / / / / (-2 weeks)
7 / 1 wk delay to test / / / / / (-1 week)
8 / 1 wk delay to effect / / / / / (+1 week)
9 / 2 wk delay to effect / / / / / (+2 weeks)
Supporting Table S1 Summary of the different models considered
The modelsare able to describe the size and frequency of the winter peaks in outcomesand were fitted to data from each age, risk group and clinical outcome separately. We found that the same model consistently gave either the best fit, or very close to the best fit across all groups. The residuals appear to be normally distributed and there is little evidence of heteroskedacicity or autocorrelation, suggesting that the negative binomial model is reasonable. The only correlation is between the residuals and the data itself. This suggests that low target values are over-estimated and high target values are under-estimated.
In selecting the best fitting model, we first select the best fitting model that does not include a delay (models 1 – 5). The best fitting of those 5 models (based on the Akaike Information Criterion or AIC) is then modified to incorporate a delay varying length (models 6-9).
Each of models 2-5 have a lower AIC value than the basic model (model 1) for all age and clinical risk groups (Supporting Figure S1, left hand side) indicating that the model variations we include all improved the quality of the model fit and hence are appropriate.For both hospitalisations and deathsincluding both a moving average and a linear trend term (model 3) substantially decreases the AICfor almost all age and risk groups. Separating influenza A into its component strains or including interactions between pathogensconfers little further (if any) improvement to AIC. For GP consultations all of models 2-5 provide similar improvements over the basic model. Combining this information, we conclude that model 3, which incorporates a moving average of the pathogen values from LabBase and a Linear Trend term consistently gave either the best, or very close to the best fit to the data. We then comparedit with similar models (all incorporating a moving average and linear trend) that also incorporate delays of different lengths (models 6-9) (Supporting Figure S1, right hand side).In most risk and age groups the inclusion of any delay either increases the AIC value associated with the model, or does not significantly decrease it. We therefore do not incorporate a delay in the final model, and use model 3 in our subsequent analysis.
Supporting Figure S1Overview of the AIC improvements of the various model fits over either the basic model (left hand side fits) or model 3 (right hand side fits). Not that since improvement in AIC is plotted, a positive value represents a better model fit and a negative value represents a poorer model fit.
2Impact of model choice
In order todetermine the effect of the model selection undertaken above, we considered the percentage of all hospitalisations estimated to be attributable to influenza by each of the nine different models. We anticipate that models providing a similar quality of fit to the data, should also estimate a similar percentage of influenza attributable hospitalisations and by comparing the estimates we can determine whether the choice of model impacts on the estimated number of influenza attributable hospitalisations.
We therefore calculated the percentage of all respiratory hospitalisations that were attributed to influenza by each of the nine models, and compared these percentages for any model with an AIC value within 10 of the chosen best fitting model (model 3). These results are shown in Supporting Figure S2 below. We observe that across almost all age and risk groups the estimated percentage of influenza attributable hospitalisations is not affected by our model choice (provided the model fit is similar).
We conclude that though our model selection was effective at choosing a model that provided a good fit to the data, similar fitting models will provide similar estimates for the number of influenza attributable hospitalisations, and so the results presented in this paper are robust to our choice of model.
Supporting Figure S2.Estimated percentage of all respiratory hospitalisations that are attributed to influenza by each of the nine models with an AIC value within 10 of the best fitting model.
3Model fits by Age and Risk Group
A 6 months – 4 years (non-risk) / B ≥65 years (non-risk) / C ≥65 years (risk)Hospitalisations / / /
D 6 months – 4 years / E ≥65 years
GP consultations (1000s) / / /
F ≥65 years (non-risk) / G ≥65 years (risk)
Deaths / /
Supporting Figure S3.Model fits for estimated number of (A-C) hospitalisations, (D,E) GP consultations and (F,G) deaths. Also shown are the number of each outcome attributed by the model to influenza, other respiratory pathogens and unattributed for selected age and risk groups. Legend for all panels is identical.
4Overview of regression results using model 3
Hospitalisations / Not at Clinical Risk / Clinical Risk< 6m / 6m - 4y / 5y - 14y / 15 - 44y / 45 - 64y / 65+y / All Ages / < 6m / 6m - 4y / 5y - 14y / 15 - 44y / 45 - 64y / 65+y / All Ages
Observed / 24,743 / 83,977 / 42,649 / 87,985 / 39,353 / 53,254 / 331,960 / 1,408 / 12,008 / 9,874 / 29,337 / 99,337 / 368,489 / 520,453
Total (Model) / 24,956 / 84,103 / 42,637 / 87,978 / 39,352 / 53,238 / 332,264 / 1,409 / 12,008 / 9,870 / 29,309 / 99,219 / 368,165 / 519,980
Unattributed / 3,906 / 31,694 / 36,094 / 76,074 / 34,624 / 40,079 / 222,470 / 507 / 6,633 / 6,764 / 17,152 / 58,346 / 220,380 / 309,783
Linear trend / 1,391 / 8,278 / 0 / 6,993 / 1,501 / 0 / 18,163 / 365 / 1,296 / 1,322 / 8,520 / 28,899 / 96,341 / 136,744
Remains / 19,659 / 44,131 / 6,543 / 4,911 / 3,227 / 13,159 / 91,630 / 537 / 4,079 / 1,784 / 3,637 / 11,973 / 51,444 / 73,453
Explained by:
Influenza A / 575 / 3,673 / 547 / 1,664 / 1,082 / 2,040 / 9,581 / 0 / 214 / 218 / 807 / 1,645 / 3,029 / 5,913
Influenza B / 383 / 684 / 0 / 0 / 552 / 0 / 1,619 / 19 / 0 / 121 / 0 / 0 / 0 / 140
Adenovirus / 1,125 / 0 / 0 / 0 / 0 / 0 / 1,125 / 0 / 0 / 0 / 0 / 0 / 0 / 0
Rhinovirus / 748 / 2,797 / 0 / 651 / 0 / 0 / 4,196 / 60 / 502 / 0 / 425 / 928 / 0 / 1,915
RSV / 12,930 / 12,143 / 0 / 0 / 701 / 3,402 / 29,176 / 343 / 1,088 / 198 / 0 / 1,397 / 12,473 / 15,500
Parainfluenza / 2,038 / 8,193 / 765 / 0 / 0 / 0 / 10,996 / 114 / 587 / 323 / 0 / 0 / 3,548 / 4,572
S. pneumoniae / 1,741 / 13,657 / 1,557 / 0 / 0 / 7,717 / 24,671 / 0 / 1,688 / 924 / 2,405 / 8,002 / 17,545 / 30,564
M. pneumoniae / 118 / 0 / 3,674 / 2,597 / 893 / 0 / 7,282 / 0 / 0 / 0 / 0 / 0 / 0 / 0
H. influenza / 0 / 2,984 / 0 / 0 / 0 / 0 / 2,984 / 0 / 0 / 0 / 0 / 0 / 14,849 / 14,849
Supporting Table S4 The absolute number of observed hospitalisations in England, the model estimate for the number of hospitalisations and the number of these estimated to be attributed to the seasonal fluctuations of infectious diseases, the linear trend, and disease which cannot be attributed to the seasonal fluctuations of infectious diseases included in the analysis. The average annual number of cases is shown.
GP consultations / < 6m / 6m - 4y / 5y - 14y / 15 - 44y / 45 - 64y / 65+y / All AgesObserved / 349,858 / 1,867,501 / 1,371,638 / 3,398,517 / 1,722,038 / 1,476,338 / 10,185,890
Total (Model) / 353,402 / 1,879,737 / 1,380,909 / 3,402,510 / 1,725,321 / 1,477,431 / 10,219,310
Unattributed / 137,799 / 445,200 / 870,071 / 2,346,207 / 906,996 / 672,100 / 5,378,373
Linear trend / 0 / 0 / 0 / 0 / 0 / 0 / 0
Remains / 215,603 / 1,434,537 / 510,838 / 1,056,303 / 818,325 / 805,331 / 4,840,937
Explained by:
Influenza A / 14,479 / 102,352 / 131,747 / 278,309 / 179,133 / 46,629 / 752,649
Influenza B / 7,384 / 57,434 / 107,435 / 115,333 / 44,048 / 0 / 331,634
Adenovirus / 20,442 / 0 / 0 / 0 / 0 / 0 / 20,442
Rhinovirus / 11,680 / 64,407 / 0 / 0 / 0 / 0 / 76,088
RSV / 64,568 / 288,002 / 102,000 / 349,143 / 209,265 / 176,394 / 1,189,372
Parainfluenza / 34,673 / 202,228 / 0 / 0 / 0 / 0 / 236,900
S. pneumoniae / 59,235 / 553,637 / 169,657 / 0 / 226,836 / 582,308 / 1,591,673
M. pneumoniae / 3,142 / 0 / 0 / 313,517 / 159,043 / 0 / 475,702
H. influenza / 0 / 166,477 / 0 / 0 / 0 / 0 / 166,477
Supporting Table S5 The absolute number of recoded GP consultations in England, the model estimate for the number of GP consultations and the number of these estimated to be attributed to the seasonal fluctuations of infectious diseases, the linear trend, and disease which cannot be attributed to the seasonal fluctuations of infectious diseases included in the analysis. The average annual number of cases is shown.
Deaths / Not at Clinical Risk / Clinical Risk0 - 14y / 15 - 44y / 65+ / All Ages / 0 - 14y / 15 - 44y / 65+ / All Ages
Observed / 39 / 476 / 7,729 / 8,244 / 127 / 6,132 / 54,933 / 61,192
Total (Model) / 39 / 476 / 7,723 / 8,238 / 127 / 6,130 / 54,900 / 61,157
Unattributed / 29 / 412 / 5,330 / 5,771 / 55 / 3,930 / 33,232 / 37,217
Linear trend / 0 / 0 / 0 / 0 / 22 / 1,046 / 8,465 / 9,533
Remains / 10 / 64 / 2,393 / 2,467 / 50 / 1,154 / 13,203 / 14,407
Explained by:
Influenza A / 0 / 20 / 378 / 398 / 10 / 98 / 1,298 / 1,406
Influenza B / 3 / 0 / 0 / 3 / 0 / 0 / 0 / 0
Adenovirus / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0
Rhinovirus / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0
RSV / 8 / 44 / 833 / 885 / 25 / 311 / 4,104 / 4,440
Parainfluenza / 0 / 0 / 0 / 0 / 16 / 170 / 774 / 960
S. pneumoniae / 0 / 0 / 1,182 / 1,182 / 0 / 574 / 4,179 / 4,754
M. pneumoniae / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0
H. influenza / 0 / 0 / 0 / 0 / 0 / 0 / 2,848 / 2,848
Supporting Table S6 The absolute number of recorded deaths in hospital in England, the model estimate for the number of deaths in hospital and the number of these estimated to be attributed to the seasonal fluctuations of infectious diseases, the linear trend, and disease which cannot be attributed to the seasonal fluctuations of infectious diseases included in the analysis. The average annual number of cases is shown.
5Annual variations in influenza-attributable outcomes
Hospitalisation / Not at clinical risk / Clinical riskFlu A / <6m / >6m-4y / 5-14y / 15-44y / 45-64y / 65y+ / <6m / >6m-4y / 5-14y / 15-44y / 45-64y / 65y+
2000/01 / 395 / 1915 / 705 / 1798 / 1031 / 1684 / 0 / 112 / 281 / 872 / 1569 / 2501
2001/02 / 750 / 4621 / 608 / 1585 / 1152 / 1907 / 0 / 270 / 242 / 769 / 1752 / 2831
2002/03 / 110 / 1294 / 136 / 681 / 480 / 866 / 0 / 76 / 54 / 330 / 730 / 1286
2003/04 / 1546 / 11282 / 951 / 2945 / 1799 / 3534 / 0 / 658 / 379 / 1428 / 2737 / 5248
2004/05 / 523 / 3209 / 700 / 2192 / 1605 / 4271 / 0 / 187 / 279 / 1063 / 2441 / 6342
2005/06 / 328 / 1483 / 435 / 1008 / 748 / 1271 / 0 / 87 / 174 / 489 / 1137 / 1888
2006/07 / 441 / 2733 / 457 / 1845 / 1047 / 2008 / 0 / 159 / 182 / 894 / 1592 / 2982
2007/08 / 508 / 2850 / 382 / 1254 / 792 / 777 / 0 / 166 / 152 / 608 / 1205 / 1154
Supporting Table S7 The estimated number of influenza A attributable hospitalisations in England by season, age and risk group.
Hospitalisation / Not at clinical risk / Clinical riskFlu B / <6m / >6m-4y / 5-14y / 15-44y / 45-64y / 65y+ / <6m / >6m-4 / 5-14y / 15-44y / 45-64y / 65y+
2000/01 / 1110 / 1484 / 0 / 0 / 1432 / 0 / 55 / 0 / 198 / 0 / 0 / 0
2001/02 / 358 / 108 / 0 / 0 / 254 / 0 / 18 / 0 / 31 / 0 / 0 / 0
2002/03 / 524 / 1035 / 0 / 0 / 324 / 0 / 26 / 0 / 189 / 0 / 0 / 0
2003/04 / 131 / 156 / 0 / 0 / 116 / 0 / 7 / 0 / 16 / 0 / 0 / 0
2004/05 / 96 / 479 / 0 / 0 / 305 / 0 / 5 / 0 / 28 / 0 / 0 / 0
2005/06 / 585 / 1346 / 0 / 0 / 966 / 0 / 29 / 0 / 412 / 0 / 0 / 0
2006/07 / 26 / 42 / 0 / 0 / 138 / 0 / 1 / 0 / 28 / 0 / 0 / 0
2007/08 / 236 / 820 / 0 / 0 / 880 / 0 / 12 / 0 / 68 / 0 / 0 / 0
Supporting Table S8 The estimated number of influenza B attributablehospitalisations in England by season, age and risk group.
GP Consultations / Flu A / Flu B<6m / >6m-4y / 5-14y / 15-44y / 45-64y / 65y+ / <6m / >6m-4 / 5-14y / 15-44y / 45-64y / 65y+
2000/01 / 9942 / 53352 / 169901 / 300844 / 170770 / 38497 / 21374 / 124671 / 175802 / 354849 / 114302 / 0
2001/02 / 18882 / 128746 / 146467 / 265177 / 190730 / 43586 / 6900 / 9049 / 27547 / 54169 / 20246 / 0
2002/03 / 2774 / 36069 / 32809 / 113979 / 79471 / 19804 / 10098 / 86968 / 167287 / 98164 / 25884 / 0
2003/04 / 38920 / 314351 / 229074 / 492748 / 297923 / 80788 / 2525 / 13070 / 14525 / 18148 / 9226 / 0
2004/05 / 13179 / 89421 / 168730 / 366750 / 265765 / 97630 / 1851 / 40217 / 25043 / 62418 / 24347 / 0
2005/06 / 8246 / 41329 / 104870 / 168643 / 123827 / 29058 / 11276 / 113109 / 364626 / 228225 / 77141 / 0
2006/07 / 11098 / 76146 / 110143 / 308597 / 173357 / 45900 / 505 / 3519 / 24542 / 20073 / 11020 / 0
2007/08 / 12793 / 79402 / 91981 / 209738 / 131219 / 17768 / 4544 / 68871 / 60103 / 86616 / 70221 / 0
Supporting Table S9 The estimated number of influenza attributable GP consultations in England by season and age group.
Deaths / Not at clinical risk / Clinical risk0-14y / 15-64y / 65y+ / <6m / >6m-4y / 65y+
2000/01 / 4.93 / 20.59 / 312.01 / 7.33 / 101.07 / 1071.47
2001/02 / 0.77 / 19.96 / 353.26 / 11.70 / 97.97 / 1213.13
2002/03 / 3.85 / 8.47 / 160.51 / 2.74 / 41.56 / 551.19
2003/04 / 0.48 / 34.55 / 654.77 / 24.95 / 169.57 / 2248.54
2004/05 / 0.96 / 27.70 / 791.28 / 9.46 / 135.93 / 2717.31
2005/06 / 6.92 / 12.81 / 235.51 / 5.23 / 62.86 / 808.75
2006/07 / 0.40 / 21.04 / 372.01 / 7.38 / 103.28 / 1277.52
2007/08 / 1.93 / 14.90 / 144.00 / 7.42 / 73.15 / 494.52
Supporting Table S9 The estimated number of influenza attributable deaths in England by season, age and risk group.
6ICD-10 codes used to identify risk groups
Condition / ICD-10 codes usedChronic respiratory disease / J4, J6, J7, J8, Q30, J31, Q32, Q33Q34, Q35, Q36, Q37
Chronic heart disease / I05, I06, I07, I08, I09, I11, I12, I13, I20, I21, I22, I25, I27, I28, I3, I40, I41, I42, I43, I44, I45, I47, I48, I49, I5, I6, Q2
Chronic kidney disease / N0, N11, N12, N14, N15, N16, N18, N19, N25, Q60, Q61
Chronic liver disease / K7, P78.8, Q44
Chronic Neurological disease / G1, G2, G3, G4, G5, G6, G7, G8, G9
Diabetes / E10, E11, E12, E13, E14, E24, G59.0, G63.2, G73.0, G99.0, N08.3, O24,
P70.0, P70.1, P70.2
Immunosuppression / Malignancies affecting the immune system:All C-codes and D37, D38, D39, D4
HIV:B20, B21, B22, B23, B24
Transplantations:Z94, Z85(Bone marrow transplants: Z94.8)
Conditions affecting the immune system:D56.1, D57.8, D57.0, D57.D61, D70, D71, D72, D73, D76, D80, D81, D82, D83, D84, 1, K90.0
Asplenia or dysfunction of the spleen / D73, D56.1, D57.8, D57.0, D57.1, K90.0
Cochlear implants / Z96.1
Cerebrospinal fluid leaks / G96.0
Supporting Table S10 ICD-10 codes used to identify risk groups. Where a two digit code is given this will include all ICD-10 codes beginning with that code.