SUPPLEMENTARY DIGITAL CONTENT
To accompany the Epidemiology article:
An evidence synthesis approach to estimating the proportion of true influenza among influenza‐like illness patients in the Netherlands
Scott A. McDonald1, Michiel van Boven1, Jacco Wallinga1
1 Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands
Supplementary analyses
1. Assumptions regarding test sensitivity
The default value for the sensitivity of ILI symptoms as a test for influenza was derived from the age‐group‐specific values presented in Patterson‐Lomba et al. (2014), which were based on a Hong Kong household transmission study (Lau et al., 2010) (see main text, Methods). Sensitivity was specified separately for the <15 years and 15+ years age‐groups. The question addressed in this supplementary analysis concerns the effect of estimates of the posterior predictive value (PPV) on the ‘default’ values for ILI test sensitivity, given that these were derived from a Hong Kong‐based study, and therefore could differ for the Netherlands context. We therefore set plausible lower and higher values for test sensitivity, and re‐estimated the posterior PPV.
eTable 1 shows the results (posterior median PPV and 95% credible intervals) if the sensitivity of ILI as a test for influenza is varied, compared with the default test sensitivity assumptions.
Compared with the default values and considering the PPV aggregated over the nine peak ILI weeks only, assuming a 15% lower test sensitivity decreased the median PPV only slightly, from
50.2%, to 49.1%, and assuming a 15% higher test sensitivity increased median PPV for the peak weeks by 0.9%, to 51.1%.
2. Impact of random‐walk priors specified for P(ILI+), P(Infl) and P(ILI–|Infl–)
The effect of specifying random‐walk prior distributions on the prevalence of ILI, P(ILI+), and the prevalence of influenza, P(Infl), was to smooth the time‐series of these variables while recognising the temporal autocorrelation in the underlying count data. We evaluated the impact of these priors (and of the random‐walk prior on specificity, P(ILI–|Infl–)) on the principal results by running a variant of the evidence synthesis model with conventionally specified vague priors for these parameters:
Time‐series for the PPV and P(Infl) for two example seasons are shown in eFig. 7. By comparing this figure with Fig. 2b, the specification of random‐walk priors clearly smooths the weekly PPV and prevalence estimates, and the precision of these estimates increased (smaller 95% CrIs in Fig. 2b compared with eFig. 7). However, in terms of the aggregate PPV outcomes there was very little difference. The posterior median PPV over the 11‐week periods surrounding the peak ILI weeks of each season was 39.0.% (95% CrI: 37.8–40.2%) using the vague priors, which is indistinguishable from the value estimated using the version of the model specifying random‐
walk priors (38.9%). For the summer period only, the PPV was estimated slightly higher, at 9.9% (95% CrI: 8.5–11.9%) , compared with 5.8% in the preferred model. The average annual number of GP consultations with ILI that are attributable to influenza was also slightly higher;
this was estimated at 64,600 (95% CrI: 44,600–103,700). In summary, although the aggregate estimates were only marginally affected by the smoothing, the precision of these estimates, and of the weekly PPV estimates, was increased through specification of the random‐walk priors.
3. Contribution of virological testing data
Time‐series for the posterior median PPV for three example seasons are shown in eFig. 8, overlaying the ‘standard’ model in which the PPV is informed by virological testing data and a model variant in which these data were excluded completely. Differences between model variants were apparent surrounding and including the peaks, the periods for which generally
more virological testing samples were available, but also in the inter‐peak period of the first and second depicted seasons.
4. Comparison of H3 and H1 dominant seasons
We observed a small difference in estimated PPV associated with the dominant influenza strain circulating in a given season. Comparing the six H3N2 dominant seasons (2003/4, 2004/5,
2005/6, 2006/7, 2008/9, and 2011/12) with the three H1N1 dominant seasons (2007/8, 2009/10, and 2010/11 [in 2007/8 influenza B was dominant, but among the influenza A specimens that were subtyped, H1N1 was dominant]), the PPV over the 11‐week peak period was 35.8% (95% CrI:
34.2–37.5%), compared with 45.0% (95% CrI: 43.5–46.6%). The lower estimated PPV obtained for the six H3N2‐dominant seasons compared with the three H1/N1 dominant seasons –may be due to the fact that the 2007/8 season was the first H1N1 dominant season in almost a decade (Dijkstra et al., 2009), whereas the 2009/10 and 2010/11 seasons were caused by a novel,
pandemic H1N1 subtype to which less immunity may have been present. Thus, the lower PPV for H3N2‐dominant seasons may reflect the lower severity associated with a greater build‐up of immunity at the population level for the more frequently occurring H3N2 compared with the H1N1 subtype. However, this numerical difference should be interpreted with caution, because season‐aggregated values ignore autocorrelation in the data and precision is consequently artifically high.
References
Dijkstra F, Donker GA, Wilbrink B, Van Gageldonk‐Lafeber AB, Van Der Sande MA. Long time trends in influenza‐like illness and associated determinants in The Netherlands. Epidemiol Infect 2009;137(4):473‐9
Lau LL, Cowling BJ, Fang VJ, Chan KH, Lau EH, Lipsitch M, Cheng CK, Houck PM, Uyeki TM, Peiris JS, Leung GM. Viral shedding and clinical illness in naturally acquired influenza virus infections. J Infect Dis 2010;201(10):1509‐16.
Patterson‐Lomba O, Van Noort S, Cowling BJ, Wallinga J, Gomes MG, Lipsitch M, Goldstein E.
Utilizing syndromic surveillance data for estimating levels of influenza circulation. Am J
Epidemiol 2014;179(11):1394‐401.
eTable 1. Posterior median PPV for all ages, considering the total nine‐season period 2003/4 to 2011/12, the peak ILI week of each of the nine seasons, and the 14‐week summer periods only.
Two other possible specifications of test sensitivity – 15% lower and 15% higher than the default value – are compared.
Prior for sensitivity All weeks Peak ILI weeks Summer periods
(Mean; 95% CI) Median PPV (95% CrI) Median PPV (95% CrI) Median PPV (95% CrI)
Default 14.1% (13.5–14.8%) 50.2% (47.6–52.7.%) 5.8% (5.0–7.1%) ( <15 yrs: 76%; 69–82%;
15+ yrs: 42%; 35–49%)
Lower sensitivity 13.6% (13.0‐–14.4%) 49.1% (46.6–51.8%) 5.2% (4.3–6.6%) (<15 yrs: 61%; 54–67%;
15+ yrs: 27%; 20–34%)
Higher sensitivity 14.3% (13.7–15.0%) 51.1% (48.8–53.5%) 6.2% (5.4–7.3%) (<15 yrs: 91%; 84–97%;
15+ yrs: 57%; 50–64%)
Note. PPV = positive predictive value; CI = confidence interval; CrI = credible interval
eFigure 1. Directed acyclic graph of the relationships between data sources and model
parameters. Distributional and functional relationships are indicated by solid and dashed lines, respectively. Rectangles indicated data sources. Circles indicate model parameters; double circles indicate parameters for which prior distributions are specified.
eFigure 2. Posterior median estimates of the weekly number of ILI consultations and the weekly number of ILI consultations with influenza in the <15 years age‐group only, for the nine‐season period 1993/94 to 2011/2012 (displayed as three seasons per panel). Capped lines indicate 95%
credible intervals. Note the differences in y‐axis scale between panels.
eFigure 3. Posterior median estimates of the weekly number of ILI consultations and the weekly number of ILI consultations with influenza in the 15‐64 years age‐group only, for the nine‐
season period 1993/94 to 2011/2012 (displayed as three seasons per panel). Capped lines indicate 95% credible intervals.
eFigure 4. Posterior median estimates of the weekly number of ILI consultations and the weekly number of ILI consultations with influenza in the 65+ years age‐group only, for the nine‐season period 1993/94 to 2011/2012 (displayed as three seasons per panel). Capped lines indicate 95%
credible intervals.
eFigure 5. The weekly proportion of ILI patient samples testing influenza positive for all nine seasons of the study period (2003/4 to 2011/12), overlaid with the PPV of ILI as a test for influenza derived from the evidence synthesis model, P(Infl|ILI+). Capped lines indicate 95%
credible intervals.
eFigure 6. Weekly ILI consultation rates, per 1000 persons (right axis), weekly influenza prevalence (based on weekly laboratory virological surveillance for influenza and other ILI‐
causing pathogens), and the proportion of ILI patient samples testing influenza positive, for the pH1N1 pandemic influenza season (2009/10), and the previous season (2008/09), only.
eFigure 7. Weekly posterior median estimates of influenza prevalence, P(Infl) and the positive predictive value of ILI as a test for influenza (derived from the evidence synthesis model), P(Infl|ILI+) for two example influenza seasons (2003/4 and 2004/5), with vague Beta(1,1) priors substituted for the random‐walk priors specified in the principal model. Capped lines indicate 95% CrIs.
eFigure 8. Weekly posterior median estimates of the positive predictive value (PPV) of ILI as a test for influenza for three example influenza seasons (2003/4 through 2005/6), comparing model variants informed by all available virological testing data, or with no data. The weekly number of samples submitted for virological testing (normalised to one by dividing by the maximum weekly number samples tested over this period) is overlaid.
eFigure 9. Results of posterior predictive checks of the number of influenza positives, yt, (see Eq.
2), by sampling from the posterior predictive distribution for yt (upper panel), and of the number of virological testing positives, xt, by sampling from the posterior predictive
distribution for xt (lower panel). In these plots, the data are compared with the median of the posterior predictive distribution for each parameter, for three example influenza seasons (2003/4 through 2005/6). Shaded regions indicate the 95% CrIs.