Effective reproduction numbers are commonly overestimated early in a disease outbreak

Abstract

Reproduction numbers estimated from disease incidence data can give public health authorities valuable information about the progression and likely size of a disease outbreak. Here, we show that methods for estimating effective reproduction numbers commonly give overestimates early in an outbreak. This is due to many factors including the nature of outbreaks that are used for estimation, incorrectly accounting for imported cases and outbreaks arising in subpopulations with higher transmission rates. Awareness of this bias is necessary to correctly interpret estimates from early disease outbreak data.

Pandemic Influenza H1N1

“…Once the outbreak is over, seroprevalence studies provide a more reliable picture of the level of transmission in the community, as they do not suffer from many of the biases that affect calculations of the reproduction number based on outbreak data. 33,34 Given the value of population serosurveys, it would be advantageous to such serosurveys into pandemic plans. In our analysis, we had to exclude many serosurveys that did not include prepandemic data, or that were undertaken after vaccination had commenced.…”

“…5 Other high estimates of the reproduction number arose from outbreaks involving large numbers of children, 18,23 crowded locations, 2,11 or early outbreak data-all of which tend to produce higher estimates. 34 There is a single estimate below 1.0, 79 which was made from the initial 115 cases in the Netherlands, more than half of whom were imported cases. It seems likely that this estimate was made before local transmission had been established.…”

“…Changes in reporting rates can lead to inaccuracies in estimates of the reproduction number, 10,14,33 and when the reproduction number is close to one, the stochastic nature of the early stages of an outbreak can cause it to be overestimated. 34 Finally, differences in infectivity or susceptibility between population groups can lead to differences in estimates of the reproduction number if the disease is largely confined to one group. 35 For example, estimates of the reproduction number from early Japanese data (with 84% child cases) 16 were considerably higher than estimates over an extended period of time with 67% child cases, 10 suggesting a higher reproduction number in children.…”

Historical data and modern methods reveal insights in measles epidemiology: a retrospective closed cohort study

“…Measles has an R 0 of 12-18. [12][13][14][15] Serial intervals are commonly used to estimate R 0 16 and, for measles, this ranges from 6-29 days 17 with 14 days commonly applied. 18 Outbreaks linked to a single index case occurring in closed cohorts, such as island settings, 18 or entirely susceptible populations have provided informative epidemiological data.…”

Comparison of the pandemic H1N1 2009 experience in the Southern Hemisphere with pandemic expectations

“…This early higher estimate is expected from the nature of the estimation procedure and is not indicative of the population-wide reproduction number in the early stages of the outbreak. 16,22 It was not possible to estimate an unbiased R for Victoria because of undetected early transmission of pH1N1 prior to testing. …”