Robust ascertainment-adjusted parameter estimation

Nonrandom ascertainment is commonly used in genetic studies of rare diseases, since this design is often more convenient than the random-sampling design. When there is an underlying latent heterogeneity, Epstein et al. ([2002] Am. J. Hum. Genet. 70:886-895) showed that it is possible to get unbiased or consistent estimation of population parameters under ascertainment adjustment, but Glidden and Liang ([2002] Genet. Epidemiol. 23:201-208) showed in a simulation study that the resulting estimates are highly sensitive to misspecification of the latent components. To overcome this difficulty, we consider a heavy-tailed model for latent variables that allows a robust estimation of the parameters. We describe a hierarchical-likelihood approach that avoids the integration used in the standard marginal likelihood approach. We revisit and extend the previous simulation, and show that the resulting estimator is efficient and robust against misspecification of the distribution of latent variables.