Genetic mixed linear models for twin survival data

Frailty modelling approaches for semi-competing risks data

In the semi-competing risks situation where only a terminal event censors a non-terminal event, observed event times can be correlated. Recently, frailty models with an arbitrary baseline hazard have been studied for the analysis of such semi-competing risks data. However, their maximum likelihood estimator can be substantially biased in the finite samples. In this paper, we propose effective modifications to reduce such bias using the hierarchical likelihood. We also investigate the relationship between marginal and hierarchical likelihood approaches. Simulation results are provided to validate performance of the proposed method. The proposed method is illustrated through analysis of semi-competing risks data from a breast cancer study.

Penalized variable selection for accelerated failure time models with random effects

Accelerated failure time (AFT) models allowing for random effects are linear mixed models under the log-transformation of survival time with censoring and describe dependence in correlated survival data. It is well known that the AFT models are useful alternatives to frailty models. To the best of our knowledge, however, there is no literature on variable selection methods for such AFT models. In this paper, we propose a simple but unified variable-selection procedure of fixed effects in the AFT random-effect models using penalized h-likelihood (HL). We consider four penalty functions (ie, least absolute shrinkage and selection operator (LASSO), adaptive LASSO, smoothly clipped absolute deviation (SCAD), and HL). We show that the proposed method can be easily implemented via a slight modification to existing h-likelihood estimation procedures. We thus demonstrate that the proposed method can also be easily extended to AFT models with multilevel (or nested) structures. Simulation studies also show that the procedure using the adaptive LASSO, SCAD, or HL penalty performs well. In particular, we find via the simulation results that the variable selection method with HL penalty provides a higher probability of choosing the true model than other three methods. The usefulness of the new method is illustrated using two actual datasets from multicenter clinical trials.

Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data

Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.

Genetic analysis of age-at-onset traits based on case-control family data

Family studies are a useful alternative to twin studies for disentangling genetic and environmental effects on human diseases. However, although age-at-onset traits are often of interest, family-based quantitative genetic analysis of such data is still not commonly used. One reason is that we need multiple random components to capture the genetic and environmental contributions, so it becomes hard to use the existing frailty models for correlated survival data. In this paper we consider the alternative accelerated failure-time models with random effects. The method allows both left truncation and right censoring, and it can deal with an arbitrary family structure and multiple random components. For estimation we use the h-likelihood procedure, which avoids the integration of the random effects in the marginal likelihood approach. To deal with large cohort data, we propose a case-control scheme, where we ascertain all families with at least two events and a subsample of control families. A pseudo-h-likelihood approach is used to analyse the ascertained data. We study the performance of the method using simulated data, and provide an illustration with analysis of melanoma in the Swedish population.

Statistical inference in mixed models and analysis of twin and family data

Analysis of data from twin and family studies provides the foundation for studies of disease inheritance. The development of advanced theory and computational software for general linear models has generated considerable interest for using mixed-effect models to analyze twin and family data, as a computationally more convenient and theoretically more sound alternative to the classical structure equation modeling. Despite the long history of twin and family data analysis, some fundamental questions remain unanswered. We addressed two important issues. One is to determine the necessary and sufficient conditions for the identifiability in the mixed-effects models for twin and family data. The other is to derive the asymptotic distribution of the likelihood ratio test, which is novel due to the fact that the standard regularity conditions are not satisfied. We considered a series of specific yet important examples in which we demonstrated how to formulate mixed-effect models to appropriately reflect the data, and our key idea is the use of the Cholesky decomposition. Finally, we applied our method and theory to provide a more precise estimate of the heritability of two data sets than the previously reported estimate.