Estimation of log‐odds ratio from group testing data using Firth correction

We consider the estimation of the prevalence of a rare disease, and the log‐odds ratio for two specified groups of individuals from group testing data. For a low‐prevalence disease, the maximum likelihood estimate of the log‐odds ratio is severely biased. However, Firth correction to the score function leads to a considerable improvement of the estimator. Also, for a low‐prevalence disease, if the diagnostic test is imperfect, the group testing is found to yield more precise estimate of the log‐odds ratio than the individual testing.