Estimating the relative recurrence risk ratio using a global cross-ratio model

The relative recurrence risk ratio lambdaR (and particularly the sibling recurrence risk ratio, lambdaS) is often of interest to those wanting to quantify the genetic contribution towards risk of disease or to discriminate between different genetic models. However, estimating lambdaR for complex diseases for which genetic and environmental risk factors are both involved is not straightforward. Ignoring environmental factors may lead to inflated estimates of lambdaR. We present a marginal model which uses a copula function to model the association in cumulative incidence rates between pairs of relatives. This model is applicable to present-state data and allows estimation of risk of disease in a pair of relatives (and hence lambdaR), given measured environmental covariates. We apply the model to leprosy among sibling pairs from the Karonga district, Malawi. If risk factors are ignored, the apparent lambdaS in this population is over 3. Accounting for known nongenetic risk factors reduces it to just under 2.