Comparison of hierarchical likelihood versus orthodox best linear unbiased predictor approaches for frailty models

Hierarchical likelihood provides a statistically efficient procedure for frailty models. Recently, a method using the computationally attractive orthodox best linear unbiased predictor has been proposed; this uses Pearson-type estimation. We compare both approaches and discuss their relative merits. With semiparametric frailty models difficulties can arise for the orthodox method, if the number of nuisance parameters increases with the sample size. This difficulty is avoided by the use of the hierarchical-likelihood method.