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Early estimation of the reproduction number in the presence of imported cases: pandemic influenza H1N1-2009 in New Zealand.

Roberts MG, Nishiura H - PLoS ONE (2011)

Bottom Line: Hence we show that a previous study, which did not account for these factors, overestimated R.These technical issues may compromise the usefulness of a well-known estimator of R--the inverse of the moment-generating function of the generation time given the intrinsic growth rate.Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of R, especially when one only has data covering a short time interval during the early growth phase of the epidemic.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Biology, Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand. m.g.roberts@massey.ac.nz

ABSTRACT
We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number R. We employ a renewal process which accounts for imported cases, illustrate some technical pitfalls, and propose a novel estimation method to address these pitfalls. Explicitly accounting for the infection-age distribution of imported cases and for the delay in transmission dynamics due to international travel, R was estimated to be (95% confidence interval: 107,1.47). Hence we show that a previous study, which did not account for these factors, overestimated R. Our approach also permitted us to examine the infection-age at which secondary transmission occurs as a function of calendar time, demonstrating the downward bias during the beginning of the epidemic. These technical issues may compromise the usefulness of a well-known estimator of R--the inverse of the moment-generating function of the generation time given the intrinsic growth rate. Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of R, especially when one only has data covering a short time interval during the early growth phase of the epidemic.

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Related in: MedlinePlus

Observed (black) and predicted (grey) cumulative numbers of confirmed locally transmitted cases.Predicted values represent conditional expectations given by  where  is the cumulative number of cases at day , and  is the maximum likelihood estimate of the growth rate.
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pone-0017835-g002: Observed (black) and predicted (grey) cumulative numbers of confirmed locally transmitted cases.Predicted values represent conditional expectations given by where is the cumulative number of cases at day , and is the maximum likelihood estimate of the growth rate.

Mentions: The observed and predicted cumulative numbers of local confirmed cases are shown in Figure 2. Although the earliest dates of incidence in Figure 1 have been refined and are different from those analysed in an earlier study [11], the estimated growth rate from 2–13 June is day (95% confidence interval (CI): 0.219, 0.302), which is consistent with the estimate in [11]. The mean and variance of the generation time have been estimated from contact tracing in the Netherlands to be 2.70 days and 1.21 days, respectively [25]. Assuming that the generation time follows a gamma distribution, the estimator of based on equation (2) is , leading to (95% CI: 1.76, 2.15). This is high compared with published estimates from other countries (e.g. [5], [6], [12], [16], [26], [27]), and is likely to be an overestimate.


Early estimation of the reproduction number in the presence of imported cases: pandemic influenza H1N1-2009 in New Zealand.

Roberts MG, Nishiura H - PLoS ONE (2011)

Observed (black) and predicted (grey) cumulative numbers of confirmed locally transmitted cases.Predicted values represent conditional expectations given by  where  is the cumulative number of cases at day , and  is the maximum likelihood estimate of the growth rate.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3102662&req=5

pone-0017835-g002: Observed (black) and predicted (grey) cumulative numbers of confirmed locally transmitted cases.Predicted values represent conditional expectations given by where is the cumulative number of cases at day , and is the maximum likelihood estimate of the growth rate.
Mentions: The observed and predicted cumulative numbers of local confirmed cases are shown in Figure 2. Although the earliest dates of incidence in Figure 1 have been refined and are different from those analysed in an earlier study [11], the estimated growth rate from 2–13 June is day (95% confidence interval (CI): 0.219, 0.302), which is consistent with the estimate in [11]. The mean and variance of the generation time have been estimated from contact tracing in the Netherlands to be 2.70 days and 1.21 days, respectively [25]. Assuming that the generation time follows a gamma distribution, the estimator of based on equation (2) is , leading to (95% CI: 1.76, 2.15). This is high compared with published estimates from other countries (e.g. [5], [6], [12], [16], [26], [27]), and is likely to be an overestimate.

Bottom Line: Hence we show that a previous study, which did not account for these factors, overestimated R.These technical issues may compromise the usefulness of a well-known estimator of R--the inverse of the moment-generating function of the generation time given the intrinsic growth rate.Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of R, especially when one only has data covering a short time interval during the early growth phase of the epidemic.

View Article: PubMed Central - PubMed

Affiliation: Centre for Mathematical Biology, Institute of Information and Mathematical Sciences, Massey University, Auckland, New Zealand. m.g.roberts@massey.ac.nz

ABSTRACT
We analyse data from the early epidemic of H1N1-2009 in New Zealand, and estimate the reproduction number R. We employ a renewal process which accounts for imported cases, illustrate some technical pitfalls, and propose a novel estimation method to address these pitfalls. Explicitly accounting for the infection-age distribution of imported cases and for the delay in transmission dynamics due to international travel, R was estimated to be (95% confidence interval: 107,1.47). Hence we show that a previous study, which did not account for these factors, overestimated R. Our approach also permitted us to examine the infection-age at which secondary transmission occurs as a function of calendar time, demonstrating the downward bias during the beginning of the epidemic. These technical issues may compromise the usefulness of a well-known estimator of R--the inverse of the moment-generating function of the generation time given the intrinsic growth rate. Explicit modelling of the infection-age distribution among imported cases and the examination of the time dependency of the generation time play key roles in avoiding a biased estimate of R, especially when one only has data covering a short time interval during the early growth phase of the epidemic.

Show MeSH
Related in: MedlinePlus