Bayesian variable selection for the Cox regression model with missing covariates

In this paper, we develop Bayesian methodology and computational algorithms for variable subset selection in Cox proportional hazards models with missing covariate data. A new joint semi-conjugate prior for the piecewise exponential model is proposed in the presence of missing covariates and its properties are examined. The covariates are assumed to be missing at random (MAR). Under this new prior, a version of the Deviance Information Criterion (DIC) is proposed for Bayesian variable subset selection in the presence of missing covariates. Monte Carlo methods are developed for computing the DICs for all possible subset models in the model space. A Bone Marrow Transplant (BMT) dataset is used to illustrate the proposed methodology

Bayesian variable selection and computation for generalized linear models withconjugate priors

In this paper, we consider theoretical and computational connections between six popular methods for variable subset selection in generalized linear models (GLM’s). Under the conjugate priors developed by Chen and Ibrahim (2003) for the generalized linear model, we obtain closed form analytic relationships between the Bayes factor (posterior model probability), the Conditional Predictive Ordinate (CPO), the L measure, the Deviance Information Criterion (DIC), the Aikiake Information Criterion (AIC), and the Bayesian Information Criterion (BIC) in the case of the linear model. Moreover, we examine computational relationships in the model space for these Bayesian methods for an arbitrary GLM under conjugate priors as well as examine the performance of the conjugate priors of Chen and Ibrahim (2003) in Bayesian variable selection. Specifically, we show that once Markov chain Monte Carlo (MCMC) samples are obtained from the full model, the four Bayesian criteria can be simultaneously computed for all possible subset models in the model space. We illustrate our new methodology with a simulation study and a real dataset

Bayesian inference for multivariate meta-analysis Box-Cox transformation models for individual patient data with applications to evaluation of cholesterol-lowering drugs

In this paper, we propose a class of Box-Cox transformation regression models with multidimensional random effects for analyzing multivariate responses for individual patient data (IPD) in meta-analysis. Our modeling formulation uses a multivariate normal response meta-analysis model with multivariate random effects, in which each response is allowed to have its own Box-Cox transformation. Prior distributions are specified for the Box-Cox transformation parameters as well as the regression coefficients in this complex model, and the Deviance Information Criterion (DIC) is used to select the best transformation model. Since the model is quite complex, a novel Monte Carlo Markov chain (MCMC) sampling scheme is developed to sample from the joint posterior of the parameters. This model is motivated by a very rich dataset comprising 26 clinical trials involving cholesterol lowering drugs where the goal is to jointly model the three dimensional response consisting of Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG) (LDL-C, HDL-C, TG). Since the joint distribution of (LDL-C, HDL-C, TG) is not multivariate normal and in fact quite skewed, a Box-Cox transformation is needed to achieve normality. In the clinical literature, these three variables are usually analyzed univariately: however, a multivariate approach would be more appropriate since these variables are correlated with each other. A detailed analysis of these data is carried out using the proposed methodology

A Functional Data Analysis Approach for Circadian Patterns of Activity of Teenage Girls

Background: Longitudinal or time-dependent activity data are useful to characterize the circadian activity patterns and to identify physical activity differences among multiple samples. Statistical methods designed to analyze multiple activity sample data are desired, and related software is needed to perform data analysis. Methods: This paper introduces a functional data analysis (fda) approach to perform a functional analysis of variance (fANOVA) for longitudinal circadian activity count data and to investigate the association of covariates such as weight or body mass index (BMI) on physical activity. For multiple age group adolescent school girls, the fANOVA approach is developed to study and to characterize activity patterns. The fANOVA is applied to analyze the physical activity data of three grade adolescent girls (i.e., grades 10, 11, and 12) from the NEXT Generation Health Study 2009–2013. To test if there are activity differences among girls of the three grades, a functional version of the univariate F-statistic is used to analyze the data. To investigate if there is a longitudinal (or time-dependent activity count) difference between two samples, functional t-tests are utilized to test: (1) activity differences between grade pairs; (2) activity differences between low-BMI girls and high-BMI girls of the NEXT study. Results: Statistically significant differences existed among the physical activity patterns for adolescent school girls in different grades. Girls in grade 10 tended to be less active than girls in grades 11 & 12 between 5:30 and 9:30. Significant differences in physical activity were detected between low-BMI and high-BMI groups from 8:00 to 11:30 for grade 10 girls, and low-BMI group girls in grade 10 tended to be more active. Conclusions: The fda approach is useful in characterizing time-dependent patterns of actigraphy data. For two-sample data defined by weight or BMI values, fda can identify differences between the two time-dependent samples of activity data. Similarly, fda can identify differences among multiple physical activity time-dependent datasets. These analyses can be performed readily using the fda R program

Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix

Multivariate meta-regression models are commonly used in settings where the response variable is naturally multi-dimensional. Such settings are common in cardiovascular and diabetes studies where the goal is to study cholesterol levels once a certain medication is given. In this setting, the natural multivariate endpoint is Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG) (LDL-C, HDL-C, TG). In this paper, we examine study level (aggregate) multivariate meta-data from 26 Merck sponsored double-blind, randomized, active or placebo-controlled clinical trials on adult patients with primary hypercholesterolemia. Our goal is to develop a methodology for carrying out Bayesian inference for multivariate meta-regression models with study level data when the within-study sample covariance matrix S for the multivariate response data is partially observed. Specifically, the proposed methodology is based on postulating a multivariate random effects regression model with an unknown within-study covariance matrix Σ in which we treat the within-study sample correlations as missing data, the standard deviations of the within-study sample covariance matrix S are assumed observed, and given Σ, S follows a Wishart distribution. Thus, we treat the off-diagonal elements of S as missing data, and these missing elements are sampled from the appropriate full conditional distribution in a Markov chain Monte Carlo (MCMC) sampling scheme via a novel transformation based on partial correlations. We further propose several structures (models) for Σ, which allow for borrowing strength across different treatment arms and trials. The proposed methodology is assessed using simulated as well as real data, and the results are shown to be quite promising

Designing prospective cohort studies for assessing reproductive and developmental toxicity during sensitive windows of human reproduction and development - the LIFE Study: The LIFE Study

Buck Louis GM, Schisterman EF, Sweeney AM, Wilcosky TC, Gore-Langton RE, Lynch CD, Boyd Barr D, Schrader SM, Kim S, Chen Z, Sundaram R, on behalf of the LIFE Study. Designing prospective cohort studies for assessing reproductive and developmental toxicity during sensitive windows of human reproduction and development – the LIFE Study. Paediatric and Perinatal Epidemiology 2011; 25: 413–424

Dichorionic twin trajectories: the NICHD Fetal Growth Studies

BACKGROUND: Systematic evaluation and estimation of growth trajectories in twins require ultrasound measurements across gestation, performed in controlled clinical settings. Currently there are few such data for contemporary populations. There is also controversy about whether twin fetal growth should be evaluated using the same benchmarks as singleton growth. OBJECTIVES: Our objective was to empirically define the trajectory of fetal growth in dichorionic twins using longitudinal two-dimensional ultrasonography and to compare the fetal growth trajectories for dichorionic twins with those based on a growth standard developed by our group for singletons. STUDY DESIGN: A prospective cohort of 171 women with twin gestations was recruited from eight U.S. sites from 2012 to 2013. After an initial sonogram at 11w0d–13w6d where dichorionicity was confirmed, women were randomized to one of two serial ultrasonology schedules. Growth curves and percentiles were estimated using linear mixed models with cubic splines. Percentiles were compared statistically at each gestational week between the twins and 1,731 singletons, after adjustment for maternal age, race/ethnicity, height, weight, parity, employment, marital status, insurance, income, education and infant sex. Linear mixed models were used to test for overall differences between the twin and singleton trajectories using likelihood ratio tests of interaction terms between spline mean structure terms and twin-singleton indicator variables. Singleton standards were weighted to correspond to the distribution of maternal race in twins. For those ultrasound measurements where there were significant global tests for differences between twins and singletons, we tested for week-specific differences using Wald tests computed at each gestational age. In a separate analysis, we evaluated the degree of reclassification in small for gestational age, defined as below the 10(th) percentile that would be introduced if fetal growth estimation for twins was based upon an unweighted singleton standard. RESULTS: Women underwent a median of 5 ultrasounds. The 50(th) percentile abdominal circumference and estimated fetal weight trajectories of twin fetuses diverged significantly beginning at 32 weeks, while biparietal diameter in twins was smaller from 34 through 36 weeks. There were no differences in head circumference or femur length. The mean head circumference/abdominal circumference ratio was progressively larger for twins compared with singletons beginning at 33 weeks, indicating a comparatively asymmetric growth pattern. At 35 weeks, the average gestational age at delivery for twins, the estimated fetal weights for the 10(th), 50(th) and 90(th) percentiles were 1960, 2376, and 2879 g for dichorionic twins and 2180, 2567, and 3022 g for the singletons. At 32 weeks, the initial week when the mean estimated fetal weight for twins was smaller than that of singletons, 34% of twins would be classified as small for gestational age using a singleton, non-Hispanic white standard. By 35 weeks, 38% of twins would be classified as small for gestational age. CONCLUSIONS: The comparatively asymmetric growth pattern in twin gestations, initially evident at 32 weeks, is consistent with the concept that the intrauterine environment becomes constrained in its ability to sustain growth in twin fetuses. Near term, nearly 40% of twins would be classified as small for gestational age based on a singleton growth standard