  When analysing new emerging infectious disease outbreaks one typically has
observational data over a limited period of time and several parameters to
estimate, such as growth rate, R0, serial or generation interval distribution,
latent and incubation times or case fatality rates. Also parameters describing
the temporal relations between appearance of symptoms, notification, death and
recovery/discharge will be of interest. These parameters form the basis for
predicting the future outbreak, planning preventive measures and monitoring the
progress of the disease. We study the problem of making inference during the
emerging phase of an outbreak and point out potential sources of bias related
to contact tracing, replacing generation times by serial intervals, multiple
potential infectors or truncation effects amplified by exponential growth.
These biases directly affect the estimation of e.g. the generation time
distribution and the case fatality rate, but can then propagate to other
estimates, e.g. of R0 and growth rate. Many of the traditionally used
estimation methods in disease epidemiology may suffer from these biases when
applied to the emerging disease outbreak situation. We show how to avoid these
biases based on proper statistical modelling. We illustrate the theory by
numerical examples and simulations based on the recent 2014-15 Ebola outbreak
to quantify possible estimation biases, which may be up to 20% underestimation
of R0, if the epidemic growth rate is fitted to observed data or, conversely,
up to 62% overestimation of the growth rate if the correct R0 is used in
conjunction with the Euler-Lotka equation.
