Title: Interval estimates of event probability from pairwise correlated data: Application in epidemiology of birth defects
Authors: Jan Klaschka - Institute of Computer Science of the Czech Academy of Sciences (Czech Republic) [presenting]
Marek Maly - Institute of Computer Science of the Czech Academy of Sciences (Czech Republic)
Antonin Sipek - Thomayer Hospital Prague (Czech Republic)
Abstract: Interval estimates of event probability are studied within a generalization of Bernoulli trials model: $n = 2m$ zero-one-valued variables consist of $m$ pairs with correlation $\phi$ between the two components. Independence between the $m$ pairs and a common expectation $\theta$ of all $n$ variables are assumed. The primary motivation and the main application field is in the epidemiology of congenital anomalies (birth defects) in twins. Occurrence of birth defects in both twins is known to be more frequent than under independence. Ignoring the fact and applying the binomial model would lead to over-liberal inferences. The focus is on the computation of exact interval estimates of $\theta$ - so far for fixed $\phi$. Numerical procedures have been designed for the calculation of confidence bounds of Clopper-Pearson, Sterne and Blaker types. The key building block is the calculation of the probability mass function (pmf) of the number of events. Several pmf calculation methods have been tested. Among them, the numerical inversion (via iFFT) of the characteristic function appears to be the most computationally effective. A quasi-symbolic calculation based on the pmf representation as a matrix of polynomial coefficients is competitive under some (but not all) settings.