Flexible Bivariate Binary Models for Estimating the Efficacy of Phototherapy for Newborns with Jaundice

In this work we analyse the efficacy of phototherapy (treatment) on the probability of being hyperbilirubinemic (outcome) in infants. A realistic quantification of the relationship between treatment and outcome can be challenging for various reasons. First, the probability of interest might be too small. Second, confounding unmeasured variables may exist which can bias the efficacy of phototherapy at preventing significant hyperbilirubinemia. Third, relationships between covariates and the outcome variable may exhibit non-linear patterns that, if not accounted for, can bias the relationship of interest. One way of dealing with the second and third issues is to use a semiparametric recursive bivariate probit model. To address the first issue as well, we explore an extension of this model which accounts for the fact that being hyperbilirubinemic can be regarded as a rare event. The proposed approach combines the marginal distributions of treatment and outcome using copulae, and uses asymmetric link functions to deal with rare outcome events. The main features underpinning the use of asymmetric link functions within semiparametric bivariate binary models are discussed.

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