  The Secondary Attack Rate (SAR) is a measure of how infectious a communicable
disease is, and is often estimated based on studies of disease transmission in
households. The Chain Binomial model is a simple model for disease outbreaks,
and the final size distribution derived from it can be used to estimate the SAR
using simple summary statistics. The final size distribution of the Chain
Binomial model assume that the outbreaks have concluded, which in some
instances may require long follow-up time. We develop a way to compute the
probability distribution of the number of infected before the outbreak has
concluded, which we call the Incomplete Chain Binomial distribution. We study a
few theoretical properties of the model. We develop Maximum Likelihood
estimation routines for inference on the SAR and explore the model by analyzing
two real world data sets.
