Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures

<div><p>We propose a Bayesian nonparametric instrumental variable approach under additive separability that allows us to correct for endogeneity bias in regression models where the covariate effects enter with unknown functional form. Bias correction relies on a simultaneous equations specification with flexible modeling of the joint error distribution implemented via a Dirichlet process mixture prior. Both the structural and instrumental variable equation are specified in terms of additive predictors comprising penalized splines for nonlinear effects of continuous covariates. Inference is fully Bayesian, employing efficient Markov chain Monte Carlo simulation techniques. The resulting posterior samples do not only provide us with point estimates, but allow us to construct simultaneous credible bands for the nonparametric effects, including data-driven smoothing parameter selection. In addition, improved robustness properties are achieved due to the flexible error distribution specification. Both these features are challenging in the classical framework, making the Bayesian one advantageous. In simulations, we investigate small sample properties and an investigation of the effect of class size on student performance in Israel provides an illustration of the proposed approach which is implemented in an R package <i>bayesIV</i>. Supplementary materials for this article are available online.</p></div

P-Splines for Longitudinal Data. Application to the Study of Children Growth with Phenylketonuria

Abstract Phenylketonuria (PKU) is a rare disease that affects the growth of children and Hyperphenylalaninemia (HPA) is a medical condition which mostly results in PKU. The objective of this study is to compare the long-term growth of children with PKU and HPA. To this aim, we model the growth of children on the basis of a flexible mixed model including subject -specific curves and factor by curve interactions (Durban et al, 2005)

Post-operative stress hyperglycemia is a predictor of mortality in liver transplantation

Abstract Background A significant association is known between increased glycaemic variability and mortality in critical patients. To ascertain whether glycaemic profiles during the first week after liver transplantation might be associated with long-term mortality in these patients, by analysing whether diabetic status modified this relationship. Method Observational long-term survival study includes 642 subjects undergoing liver transplantation from July 1994 to July 2011. Glucose profiles, units of insulin and all variables with influence on mortality are analysed using joint modelling techniques. Results Patients registered a survival rate of 85% at 1 year and 65% at 10 years, without differences in mortality between patients with and without diabetes. In glucose profiles, however, differences were observed between patients with and without diabetes: patients with diabetes registered lower baseline glucose values, which gradually rose until reaching a peak on days 2–3 and then subsequently declined, diabetic subjects started from higher values which gradually decreased across the first week. Patients with diabetes showed an association between mortality and age, Model for End-Stage Liver Disease score (MELD) score and hepatitis C virus; among non-diabetic patients, mortality was associated with age, body mass index, malignant aetiology, red blood cell requirements and parenteral nutrition. Glucose profiles were observed to be statistically associated with mortality among patients without diabetes (P = 0.022) but not among patients who presented with diabetes prior to transplantation (P = 0.689). Conclusions Glucose profiles during the first week after liver transplantation are different in patients with and without diabetes. While glucose profiles are associated with long-term mortality in patients without diabetes, after adjusting for potential confounding variables such as age, cause of transplantation, MELD, nutrition, immunosuppressive drugs, and units of insulin administered, this does not occur among patients with diabetes