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1.  Bayesian Model Selection For Incomplete Data using the Posterior Predictive Distribution 
Biometrics  2012;68(4):1055-1063.
Summary
We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.
doi:10.1111/j.1541-0420.2012.01766.x
PMCID: PMC3890150  PMID: 22551040
DIC; Bayes Factor; Longitudinal data; MCMC; Model Selection
2.  A Note on MAR, Identifying Restrictions, Model Comparison, and Sensitivity Analysis in Pattern Mixture Models With and Without Covariates for Incomplete Data 
Biometrics  2011;67(3):810-818.
Summary
Pattern mixture modeling is a popular approach for handling incomplete longitudinal data. Such models are not identifiable by construction. Identifying restrictions are one approach to mixture model identification (Little, 1995; Little and Wang, 1996; Thijs et al., 2002; Kenward et al., 2003; Daniels and Hogan, 2008) and are a natural starting point for missing not at random sensitivity analysis (Thijs et al., 2002; Daniels and Hogan, 2008). However, when the pattern specific models are multivariate normal, identifying restrictions corresponding to missing at random may not exist. Furthermore, identification strategies can be problematic in models with covariates (e.g. baseline covariates with time-invariant coefficients). In this paper, we explore conditions necessary for identifying restrictions that result in missing at random (MAR) to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully Bayesian analysis with informative priors. In addition, we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data. We adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches. We also apply the methods to a longitudinal clinical trial. Problems caused by baseline covariates with time-invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution.
doi:10.1111/j.1541-0420.2011.01565.x
PMCID: PMC3136648  PMID: 21361893
Missing at random; Non-future dependence; Deviance information criterion
3.  Estimating the Causal Effect of Low Tidal Volume Ventilation on Survival in Patients with Acute Lung Injury† 
Summary
Acute lung injury (ALI) is a condition characterized by acute onset of severe hypoxemia and bilateral pulmonary infiltrates. ALI patients typically require mechanical ventilation in an intensive care unit. Low tidal volume ventilation (LTVV), a time-varying dynamic treatment regime, has been recommended as an effective ventilation strategy. This recommendation was based on the results of the ARMA study, a randomized clinical trial designed to compare low vs. high tidal volume strategies (The Acute Respiratory Distress Syndrome Network, 2000) . After publication of the trial, some critics focused on the high non-adherence rates in the LTVV arm suggesting that non-adherence occurred because treating physicians felt that deviating from the prescribed regime would improve patient outcomes. In this paper, we seek to address this controversy by estimating the survival distribution in the counterfactual setting where all patients assigned to LTVV followed the regime. Inference is based on a fully Bayesian implementation of Robins’ (1986) G-computation formula. In addition to re-analyzing data from the ARMA trial, we also apply our methodology to data from a subsequent trial (ALVEOLI), which implemented the LTVV regime in both of its study arms and also suffered from non-adherence.
doi:10.1111/j.1467-9876.2010.00757.x
PMCID: PMC3197806  PMID: 22025809
Bayesian inference; Causal inference; Dynamic treatment regime; G-computation formula

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