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The authors have declared that no competing interests exist.

Conceived and designed the experiments: DS CS BW TM. Critical review of the methods and manuscript: DS CS BW TM. Responsible for the statistical analysis: DS. Acquisition and interpretation of the FluWatch data: BW CS TM. Drafted the manuscript: DS. Critically reviewed the manuscript for intellectual content: BW CS TM.

Poisson regression modelling has been widely used to estimate the disease burden attributable to influenza, though not without concerns that some of the excess burden could be due to other causes. This study aims to provide annual estimates of the mortality and hospitalization burden attributable to both seasonal influenza and the 2009 A/H1N1 pandemic influenza for Canada, and to discuss issues related to the reliability of these estimates.

Weekly time-series for all-cause mortality and regression models were used to estimate the number of deaths in Canada attributable to influenza from September 1992 to December 2009. To assess their robustness, the annual estimates derived from different parameterizations of the regression model for all-cause mortality were compared. In addition, the association between the annual estimates for mortality and hospitalization by age group, underlying cause of death or primary reason for admission and discharge status is discussed.

The crude influenza-attributed mortality rate based on all-cause mortality and averaged over 17 influenza seasons prior to the 2009 A/H1N1 pandemic was 11.3 (95%CI, 10.5 - 12.1) deaths per 100 000 population per year, or an average of 3,500 (95%CI, 3,200 - 3,700) deaths per year attributable to seasonal influenza. The estimated annual rates ranged from undetectable at the ecological level to more than 6000 deaths per year over the three A/Sydney seasons. In comparison, we attributed an estimated 740 deaths (95%CI, 350–1500) to A(H1N1)pdm09. Annual estimates from different model parameterizations were strongly correlated, as were estimates for mortality and morbidity; the higher A(H1N1)pdm09 burden in younger age groups was the most notable exception.

With the exception of some of the Serfling models, differences in the ecological estimates of the disease burden attributable to influenza were small in comparison to the variation in disease burden from one season to another.

Regression modelling is widely used to estimate the disease burden attributable to seasonal and pandemic influenza

The emergence of a novel influenza A H1N1 strain in the spring of 2009 has resulted in a renewed interest in better understanding the reliability of annual estimates of the number of deaths attributable to influenza

This study aims to provide annual estimates of the mortality and hospitalization burden attributable to seasonal influenza and the 2009 A/H1N1 pandemic for Canada and discuss issues related to the robustness of these estimates to the choice of statistical model. We applied a variety of Serfling and Poisson regression models incorporating over-dispersion to all-cause mortality and then compared the annual estimates of the number of deaths attributable to influenza. We also estimated and compared the annual estimates for mortality and morbidity stratified by age group, underlying cause of death, hospital discharge status, and primary reason for admission, with the hypothesis that disease severity might be similar enough to induce a strong degree of correlation between these annual measures of disease burden.

For the 2009 pandemic, a total of 428 laboratory-confirmed deaths were reported to the Public Health Agency of Canada

_{m}_{y}_{4} parameters account for a general trend with more flexibility than the linear, quadratic and cubic trend terms used in the Serfling model below. The variables ^{th}, or Christmas day). The variable _{8,} β_{9,} and β_{10, y} parameters are multipliers for the proxy variables for RSV, influenza B and influenza A respectively. Separate annual multipliers for each flu season are necessary for any meaningful discussion of the annual estimates. Unfortunately, statistical power was insufficient to estimate the annual effects of RSV or influenza B. The

Influenza-attributed deaths were calculated as the difference between model-predicted deaths and the model-predicted deaths under the hypothetical absence of influenza, with the latter referred to as the seasonal baseline. Equivalently, the annual estimate can also be calculated by summing the proxy variable over the year/season and multiplying by the corresponding estimated parameter. The former (sum of weekly estimates) is easier to visualise, while the latter approach of working with estimated parameters ensures that the correlation structure induced by the regression model is accounted for. Hence, only disease burden estimates corresponding to an estimated parameter were reported, and confidence intervals for estimates of influenza-attributed rates were calculated from the coefficient of variation of the corresponding multiplier parameter.

The Serfling model was only used in the sensitivity analysis. The annual number of deaths attributable to influenza was calculated for the Serfling models by summing the weekly excess (actual less estimated baseline) over a period that only included the excluded weeks. Both positive and negative ‘excesses’ were included in the sum in order to avoid biasing the estimate upward. For each Serfling model we reported the number of excluded weeks per season, the annual number of excess deaths and the annual baseline for the full year, averaged over 17 seasons (1992/93-2008/April 2009).

For the sensitivity analysis for all-cause mortality, selected thresholds for the Serfling model and various parameterizations of the Poisson regression model were used to assess the impact of model choice on the point estimate of influenza mortality and its standard error. All parameters included in the main Poisson model described above were statistically significant (with p-values from the type 3 analysis often less than 0.0001).

The average number of deaths attributable to seasonal influenza over the 17 seasons prior to the 2009 pandemic was estimated at 3,500 (95% CI 3,200 - 3,700) for an average crude mortality rate of 11.3 (95% CI, 10.5 - 12.1) deaths per 100,000 population per year. These estimates were based on the impact of influenza activity on all-cause mortality. The annual estimates ranged from undetectable to an average of more than 6000 deaths per year over the three A/Sydney seasons (

Season | Predominant A Strain and Sub-type | Influenza –Attributed Deaths Canada (95% CI) |
Influenza -Attributed Admissions with a Respiratory Dx (95% CI) |
||||

1992/93 | A/Beijing/32/92 (H3N2) | 3,000 | (2,200 – 3,800) | ||||

1993/94 | A/Beijing/32/92 (H3N2) | 3,900 | (3,000 – 4,700) | ||||

1994/95 | A/Shangdong/09/93(H3N2) | 2,500 | (1,700 – 3,300) | 12,800 | (8,700 – 16,800) | ||

1995/96 | A/TEXAS/36/91(H1N1) | 1,500 | (200 – 2,700) | 1,200 | (–4,100 – 6,600) | ns | |

1996/97 | A/Wuhan/359/ 95(H3N2) | 4,800 | (3,900 – 5,700) | 15,500 | (11,900 – 19,100) | ||

1997/98 | A/Sydney/05/97(H3N2) | 6,500 | (5,700 – 7,400) | 27,300 | (22,900 – 31,700) | ||

1998/99 | A/Sydney/05/97(H3N2) | 5,700 | (4,800 – 6,700) | 13,800 | (6,100 – 21,400) | ||

1999/00 | A/Sydney/05/97(H3N2) | 6,700 | (5,800 – 7,600) | 37,000 | (32,900 – 41,100) | ||

2000/01 | A/New Caledonia/20/99 (H1N1) | 1,400 | (500 – 2,200) | 3,300 | (–750 – 7,400) | ns | |

2001/02 | A/Panama/2007/99 (H3N2) | 1,800 | (700 – 2,900) | 8,300 | (2,600 – 14,100) | ||

2002/03 | A/New Caledonia/20/99 (H1N1) | 1,000 | (–300 – 2,400) | ns | 3,100 | (–5,700 – 11,900) | ns |

2003/04 | A/Fujian/411/02 (H3N2) | 5,200 | (4,000 – 6,300) | 16,000 | (11,900 – 20,100) | ||

2004/05 | A/Fujian/411/02 (H3N2) | 5,100 | (4,000 – 6,100) | 17,400 | (11,900 – 22,800) | ||

2005/06 | A/California/7/2004(H3N2) | 1,100 | (30 – 2,200) | 4,300 | (–1,100 – 9,700) | ns | |

2006/07 | A/Wisconsin/67/2005 (H3N2) | 4,600 | (3,400 – 5,700) | 5,100 | (380 – 9,700) | ||

2007/08 | A/Solomon Islands/3/2006 (H1N1) | 4,100 | (2,800 – 5,400) | 11,400 | (5,200 – 17,700) | ||

2008/09 | A/Brisbane/59/2007 (H1N1) | 300 | (–800 – 1,400) | ns | 6,200 | (720 – 11,700) | |

2009p | A/California/7/2009 (A(H1N1)pdm09) | 740 | (350 – 1,500) | ns |
16,600 | (14,100 – 19,000) | |

Seasonal Average | 3,500 | (3,200 – 3,700) | 12,200 | (10,800 – 13,600) | |||

Crude Rate/100,000 | 11.3 | (10.5 – 12.1) | 39.5 | (34.9 – 44.1) | |||

Influenza B (average) |
391 | (50–770) | 1,700 | (–270 – 3,580) | ns |

Though the model estimate for the 2009 pandemic was not statistically significant based on all-cause mortality, the estimate based on respiratory deaths was statistically significant. Hence, the lower 95%CI was adjusted based on the results of the respiratory model (see Table2).

Figures have been rounded.

Annual estimates for the burden attributed to influenza B were not specifically reported, as only one influenza B multiplier parameter was estimated for whole study period.

Annual estimates of the number of deaths and hospital admissions attributable to influenza are shown as a) an annual time-series with the influenza season identified on the x-axis and b) as a scatter graph of influenza-attributable deaths (x-axis) by hospital admissions (y-axis) with a linear trend identified by the solid black line. Open symbols indicate that the estimate was not statistically significant (95% CI includes 0). In the scatter graph, the A(H1N1)pdm09 estimates are indicated with a red square. c) Annual estimates of influenza-attributed deaths from the death and hospitalization databases are compared in time-series format and d) scatter graph format.

Of the 428 deaths with laboratory-confirmed A(H1N1)pdm09 reported to the Agency, 73% were in persons under 65 years of age and 72% were certified as due to influenza as the underlying cause of death. We estimated that 561 (95% CI, 347-775) deaths certified as due to an underlying respiratory cause were attributable to the pandemic. An additional 179 deaths certified as due to other causes were attributed to the pandemic, though this estimate was not statistically significant and the confidence intervals are quite wide. We assumed that the pandemic did not result in fewer deaths from circulatory or other causes, and as a result, set the lower 95% confidence interval (CI) for all-cause deaths attributed to influenza to the lower 95% CI from the respiratory underlying causes model. The resulting estimate is 740 deaths for a rate of 2.2 (95% CI, 1.0, 4.5) deaths per 100,000 population. (For any subsequent analysis, such as for a meta-analysis to assess the pandemic burden on a global scale, the model estimated standard error (coefficient of variation is 0.543) should be used.) The lower 95%CI at 1.0 deaths/100,000 population is close to the figure for deaths certified through ICD-10 coding as due to laboratory-confirmed influenza of 0.9 (

Source | Age | # Deaths | Influenza Mortality Rate per 100,000 Population | 95% CI (Lower, Upper) | % 65 yrs or older | |

Laboratory confirmed deaths reported to Public Health Agency of Canada | ||||||

All ages | 428 | 1.27 | ||||

<65 | 312 | 1.07 | 27% | |||

65+ years | 116 | 2.47 | ||||

Underlying cause of death, Vital Statistics Database: Influenza, J09, J10 | ||||||

All ages | 310 | 0.92 | ||||

<65 | 216 | 0.74 | 30% | |||

65+ years | 94 | 2.00 | ||||

Influenza-attributed Respiratory Deaths (Regression model estimate) |
||||||

All ages | 561 | 1.7 | 1.0 | 2.3 | ||

<65 | 254 | 0.9 | 0.7 | 1.1 | 55% | |

65+ years | 311 | 6.6 | 2.5 | 10.7 | ||

Influenza-attributed All cause Deaths |
||||||

All ages | 740 | 2.2 | 1.0 | 4.5 | ||

<65 | 195 | 0.7 | 0.7 | 1.5 | 74% | |

65+ years | 540 | 11.5 | 2.5 | 26.1 |

The number of influenza-attributed respiratory deaths was calculated from the regression model for deaths certified as due to an underlying respiratory cause.

The estimated number deaths that were attributable to A(H1N1)pdm2009 based on the all-cause model was not statistically significant. However, the estimate based on the respiratory model was statistically significant. Hence, the lower 95% CI for the number of deaths attributed to influenza was set to the lower 95% CI for respiratory deaths attributed to H1N1/p2009, a figure that is close to the number of deaths certified through ICD-10 coding as due to laboratory-confirmed influenza as the underlying cause of death (rates of 1.0 vs 0.92).

Early reports of laboratory-confirmed A(H1N1)pdm09 associated deaths to the Agency suggested that most deaths (73%) had occurred among persons under the age of 65 years of age. However, the results of the regression models suggest that this early estimate was too high as under-ascertainment of the role of influenza was more significant for persons 65 years of age or older (

Estimates of respiratory and circulatory influenza-attributable deaths were closely correlated (

a) Annual time-series with influenza season identified on the x-axis. b) Scatter graph with a linear trend shown in solid black. Annual estimates based on respiratory and circulatory underlying causes are highly correlated, while in c) a comparison of respiratory to other causes shows a significant change with the conversion from ICD-9 to ICD-10 (denoted by an x). Open symbols indicate that the estimate was not statistically significant (95% CI includes 0). The A(H1N1)pdm09 estimates are indicated with a red square.

Open symbols indicate that the estimate was not statistically significant (95% CI includes 0). The A(H1N1)pdm09 estimates are indicated with a red square. A linear trend line is shown in solid black.

Annual estimates of influenza-attributed respiratory admissions for a) the 65+ age group versus 20–64 years age group; b) the 65+ age group versus 0–19 years age group; and c) by discharge status. Open symbols indicate that the estimate was not statistically significant (95% CI includes 0). The A(H1N1)pdm09 estimates are plotted with a red square. A linear trend line is shown in solid black.

In applying different parameterizations of Poisson regression models to the weekly time-series of all-cause mortality, we found minimal differences in the average number of deaths attributed to influenza and the annual estimates were closely correlated (

a) Poisson regression and Serfling model estimates of influenza-attributable deaths by influenza season. Three parameterizations of the Poisson regression model are shown in solid lines and 4 choices of thresholds for periods of influenza activity for the Serfling model are shown with dashed lines. Serfling models use regression to estimate a cyclical baseline, but exclude weeks with influenza activity. b) Average Number of Deaths (all cause) by Week with the Estimated Baselines for Selected Models. Despite an additional 150–200 deaths occurring in week 1, the averages of the weekly baseline for the full model (dashed line) and the Simple Serfling-like Poisson model (solid red) for January through mid-March were similar. Use of 53 indicator variables – 1 for each week of the year to account for seasonality resulted in a similar weekly baseline (dotted line). The Serfling baseline for a 10% influenza positive threshold is shown in green. The average weekly number of deaths attributed to influenza is shown on the secondary y-axis.

Model Parameterization | Average Number of Influenza-attributable Deaths | Standard Error | Average Annual Baseline |

Full model | 3,486 | 128 | 216,518 |

Removed |
3,474 | 131 | 216,506 |

Removed |
3,190 | 131 | 216,793 |

Removed |
3,122 | 135 | 216,850 |

Removed sine and cosine terms | 3,700 | 130 | 216,285 |

Removed |
3,528 | 127 | 216,498 |

Full model + Annual multipliers for |
3,306 | 189 | 216,590 |

Simple Serfling-like Poisson model( |
3,517 | 123 | 216,530 |

Simple Serfling-like Poisson model ( |
3,227 | 121 | 216,825 |

Week-of-year Baseline | 3,759 | 121 | 216,432 |

Single multipler for |
3,082 | 301 | 217,043 |

Though the annual estimates from various Serfling models were closely correlated with the results from the Poisson models (

Threshold | Average Number of Influenza-attributable Deaths | Average Number of excluded weeks | Average Annual Baseline | |

0.03% | 2,864 | 33 | 217,256 | |

0.05% | 2,767 | 24 | 217,300 | |

0.10% | 2,416 | 14 | 217,638 | |

0.15% | 2,130 | 10 | 217,910 | |

0.20% | 1,911 | 8 | 218,135 | |

0.25% | 1,901 | 7 | 218,139 | |

0.30% | 1,782 | 6 | 218,256 | |

0.5% | 2,858 | 31 | 217,189 | |

1% | 3,292 | 27 | 216,785 | |

5% | 2,894 | 17 | 217,145 | |

10% | 1,894 | 10 | 218,120 | |

15% | 1,370 | 6 | 218,674 |

Influenza-attributable deaths are deaths that occur in people for whom an influenza infection contributed to the actual death, or at least the time of death, regardless of whether or not influenza was identified as the underlying cause of death. Because of the limitations of an ecological study design, these models have been be given much scrutiny

As a measure of external consistency, we assessed the correlation between the annual mortality estimates by cause of death and the annual morbidity estimates by age, reason for admission, and discharge status. Most estimates of the disease burden attributable to influenza were well correlated with only a few exceptions. A notable exception is that the severity of an influenza season among persons under the age of 20 years was found to be a relatively poor predictor of the severity among adults (

For persons over the age of 65 years, the estimated A(H1N1)pdm09-attributed burden was considerably less than for seasonal influenza (

Though no obvious trend was observed over the study period, a full trend analysis was limited by the significant year-to-year variation in the influenza-attributable mortality rate, together with increased virological testing over the study period, and significant coding differences of the underlying cause of death introduced with the conversion to ICD-10.

For internal consistency, we compared the annual estimates of the number of deaths attributable to influenza from different Serfling and Poisson regressions models. The Serfling estimates were dependant on the number of weeks per year that were excluded due to influenza activity, and for most exclusion rules, this method produced lower annual estimates than the Poisson models.

Concern has been expressed that as Serfling models attribute all excess deaths to influenza, that this approach would inherently over-estimated the burden attributable to influenza. It appears that, on the contrary, the fitted cyclical baseline, with only a few data points in the winter months as a guide, tended to overestimate the number of non-influenza deaths in the winter months, and hence underestimate the winter excess due to influenza. Including the proxy variable for influenza activity along with annual multipliers for independent estimates of the annual excess was sufficient to stabilize the annual estimates.

Additional parameters that allowed the baseline to adapt more closely to the weekly data had little effect on the average annual estimates for influenza mortality. For example, deaths in 1^{st} week in January were elevated by an estimated 163 deaths (95% CI 88-240). Removing this parameter from the regression model resulted in these additional deaths being absorbed into the baseline estimates for other weeks. The same was observed for the monthly indicator variables and the RSV proxy variable. Even using a week-of-year indicator variable (53 parameters) produced similar results. On the other hand, removing all parameters related to seasonality resulted in a two-fold increase in the estimated number of influenza-attributed deaths (not shown).

Some earlier models for estimating the burden of influenza mortality used the percentage of tests positive for influenza as the proxy variable for influenza activity and the same multiplier for each season

Our sensitivity analysis was limited in the breadth of comparisons included. Other options for proxy variables are emerging

Some of the annual influenza disease burden estimates (or the lower 95% confidence interval) in the tables or figures are negative. Negative estimates will occur when the true number of events (deaths or admissions) due to influenza is less than the natural variation in the total number of events (all-cause mortality or hospital admission) during periods of influenza activity. For the Serfling estimates, we summed all positive and negative weekly ‘excesses’ over the defined influenza period in order not to introduce biases by ignoring negative estimates. Technically, though plausible in a few rare instances, it is unlikely that an influenza infection ‘saved’ lives, and hence any negative ‘excess’, is most likely due to the random variation of the total number of deaths. Hence, to avoid biasing the annual total, these natural or random dips below baseline must be included to balance out the nature swings above baseline.

Though Poisson regression, or equivalently, negative binomial regression models with annual multipliers to adjust for potential year-to-year differences in the relationship between the proxy variable for the level of influenza activity and the resulting disease burden are emerging as the preferred model, various methods have been used internationally to estimate the A(H1N1)pdm09 mortality burden. A recent review article

For future estimates of influenza disease burden, increases in virological testing of hospitalized patients along with the ICD-10 coding to identify laboratory-confirmed cases will offer significant improvements in the measurement of influenza activity specific to the region and age group. With a better influenza proxy variable, the expectation is for a slight increase in the estimates of disease burden attributed to influenza. It is therefore important that estimates based on new models forms or even a new parameterization of the regression model be compared head-to-head with a Poisson regression model that includes at least seasonality, secular trend and a proxy variable for influenza or influenza A with annual multipliers and a dispersion parameter or equivalently the use of the negative binomial distribution.

In summary, differences in the ecological estimates of the disease burden attributable to influenza were small in comparison to the variation in disease burden from one season to another. Poisson regression models that included at least seasonality, a secular trend and a proxy variable for influenza or influenza A with annual multipliers and a dispersion parameter to correct for overdispersion produced reasonably consistent estimates of the annual mortality burden attributable to influenza and these estimates were highly correlated with annual estimates for the morbidity burden for adults. The annual morbidity burden for children (under the age of 20 years) was found to be a poor predictor of the corresponding adult burden. Influenza continues to be a significant contributor to mortality.

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The authors gratefully acknowledge the support of Statistics Canada and the provincial and territorial vital statistics registries in providing access to the Canadian Vital Statistics databases, the Canadian Institute for Health Information, the National