  The basic reproduction number, $R_0$, is a well-known quantifier of epidemic
spread. However, a class of existing methods for estimating $R_0$ from
incidence data early in the epidemic can lead to an over-estimation of this
quantity. In particular, when fitting deterministic models to estimate the rate
of spread, we do not account for the stochastic nature of epidemics and that,
given the same system, some outbreaks may lead to epidemics and some may not.
Typically, an observed epidemic that we wish to control is a major outbreak.
This amounts to implicit selection for major outbreaks which leads to the
over-estimation problem. We formally characterised the split between major and
minor outbreaks by using Otsu's method which provides us with a working
definition. We show that by conditioning a `deterministic' model on major
outbreaks, we can more reliably estimate the basic reproduction number from an
observed epidemic trajectory.
