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1.  Incorporating prior beliefs about selection bias into the analysis of randomized trials with missing outcomes 
Biostatistics (Oxford, England)  2003;4(4):495-512.
In randomized studies with missing outcomes, non-identifiable assumptions are required to hold for valid data analysis. As a result, statisticians have been advocating the use of sensitivity analysis to evaluate the effect of varying asssumptions on study conclusions. While this approach may be useful in assessing the sensitivity of treatment comparisons to missing data assumptions, it may be dissatisfying to some researchers/decision makers because a single summary is not provided. In this paper, we present a fully Bayesian methodology that allows the investigator to draw a ‘single’ conclusion by formally incorporating prior beliefs about non-identifiable, yet interpretable, selection bias parameters. Our Bayesian model provides robustness to prior specification of the distributional form of the continuous outcomes.
PMCID: PMC2748253  PMID: 14557107
Dirichlet process prior; Identifiability; MCHC; Non-parametric Bayes; Selection model; Sensitivity analysis
2.  Modelling the random effects covariance matrix in longitudinal data 
Statistics in medicine  2003;22(10):1631-1647.
A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.
PMCID: PMC2747645  PMID: 12720301
Cholesky decomposition; heterogeneity; mixed models

Results 1-2 (2)