Testing the heritability and parent-of-origin hypotheses for ages at onset of psoriatic arthritis under biased sampling

The heritability and parent-of-origin effect hypotheses for chronic diseases can be evaluated by estimating and conducting inference about the parameters that measure the within-family dependences in disease onset times. We model the within-family associations in these times using a Gaussian copula whose correlation matrix accommodates the different pairwise family relationships. We derive score-type statistics to test the heritability and parent-of-origin effect hypotheses when the families selection protocol induces a sampling bias. We illustrate the use of the developed methods through an application to a motivating family study in Psoriatic arthritis and provide strong evidence of excessive paternal transmission of risk.