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Title: Confidence regions in a two-parameter model of congenital anomaly incidence in twins Authors:  Jan Klaschka - Institute of Computer Science of the Czech Academy of Sciences (Czech Republic) [presenting]
Jeno Reiczigel - University of Veterinary Medicine Budapest (Hungary)
Antonin Sipek - Thomayer Hospital Prague (Czech Republic)
Abstract: The focus is on $m$ mutually independent pairs of binary variables with common expectation $\theta$ and equal correlation $\phi$ within each pair. The motivation and the main application field is the epidemiology of congenital anomalies (birth defects) in twins (variable coding: 1 = defect, 0 = no defect). Simultaneous confidence regions (CRs) are considered for $\theta$ and $\phi$, based on numbers of pairs with two defects, and pairs with one defect. Fixed grid computational algorithms for CRs based on likelihood-ratio (LR) method, and Sterne (probability-based) method have been proposed and implemented in R. Both methods yield similar results in the sense that typically a CR of one type shares about 95\% of its area with CR of the other type, none of the two CR areas is uniformly smaller, and the area difference is below 2\%. The probability-based method guarantees, unlike the other method, coverage probability greater or equal to the nominal confidence level. On the other hand, advantages of the LR-based method over the Sterne method are a simpler and dramatically faster algorithm, as well as smooth CR boundaries (contrary to irregularly winding boundaries of Sterne CRs).