Robust rank estimation for transformation models with random effects

Summary

Semiparametric transformation models with random effects are useful in analysing recurrent and clustered data. With specified error and random effect distributions, Zeng & Lin (2007a) proved that nonparametric maximum likelihood estimators are semiparametric efficient. In this paper we consider a more general class of transformation models with random effects, under which an unknown monotonic transformation of the response is linearly related to the covariates and the random effects with unspecified error and random effect distributions. This includes many popular models. We propose an estimator based on the maximum rank correlation, which relies on symmetry of the random effect distribution, and establish its consistency and asymptotic normality. A random weighting resampling scheme is employed for inference. The proposed method can be extended to censored and clustered data. Numerical studies demonstrate that the proposed method performs well in practical situations. Application of the method is illustrated with the Framingham cholesterol data.

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