Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data

Summary .  We study quantile regression (QR) for longitudinal measurements with nonignorable intermittent missing data and dropout. Compared to conventional mean regression, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. We account for the within-subject correlation by introducing a   ℓ₂   penalty in the usual QR check function to shrink the subject-specific intercepts and slopes toward the common population values. The informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects. We assess the performance of the proposed method using simulation studies, and illustrate it with data from a pediatric AIDS clinical trial.     

Ontogenic study of the brachiopod Dicoelosia by geometric morphometrics and morphing techniques

The distinctive brachiopod Dicoelosia King 1850 is characterized by a strongly bilobed outline. To date, studies have concentrated on its functional morphology, taxonomy and evolution; little attention has been paid to its ontogeny. Here, we map population variation by principal component analysis for over 80 specimens distributed across five species of Dicoelosia. Using geometric morphometrics with landmarks for some 40 specimens, the ontogenic trends in D. sp. nov. are compared with those of Dicoelosia biloba. In addition, the ontogenic pathway in D. sp. nov. is investigated by morphing with control points, a new technique introduced here to palaeontology. Combining the results above, the ontogeny of the key character of the genus, emargination, is modelled. Within single populations, taxa may develop from broad weakly emarginate forms into those that are elongate and deeply emarginate. As the identification of the genus and its species depends on external morphological characters, the definition of ontogenetic trends in each species is essential for taxonomic discrimination. Substantial population variation exists in many of its species; however, the morphing technique provides a method of simulation, predicting the full range of ontogenetic variation in given populations.     

A varying‐coefficient generalized odds rate model with time‐varying exposure: An application to fitness and cardiovascular disease mortality

Varying‐coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time‐varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying‐coefficient generalized odds rate model that allows flexible estimation of age‐modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed‐effects model, and its associated age‐varying coefficient function is represented by cubic B‐splines. An expectation‐maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian‐Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E‐step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.     

Approximate standard errors in semiparametric models

We consider semiparametric models with p regressor terms and q smooth terms. We obtain an explicit expression for the estimate of the regression coefficients given by the back-fitting algorithm. The calculation of the standard errors of these estimates based on this expression is a considerable computational exercise. We present an alternative, approximate method of calculation that is less demanding. With smoothing splines, the method is exact, while with loess, it gives good estimates of standard errors. We assess the adequacy of our approximation and of another approximation with the help of two examples.     

Empirical Bayes estimation of random effects parameters in mixed effects logistic regression models

We extend an approach for estimating random effects parameters under a random intercept and slope logistic regression model to include standard errors, thereby including confidence intervals. The procedure entails numerical integration to yield posterior empirical Bayes (EB) estimates of random effects parameters and their corresponding posterior standard errors. We incorporate an adjustment of the standard error due to Kass and Steffey (KS; 1989, Journal of the American Statistical Association 84, 717-726) to account for the variability in estimating the variance component of the random effects distribution. In assessing health care providers with respect to adult pneumonia mortality, comparisons are made with the penalized quasi-likelihood (PQL) approximation approach of Breslow and Clayton (1993, Journal of the American Statistical Association 88, 9-25) and a Bayesian approach. To make comparisons with an EB method previously reported in the literature, we apply these approaches to crossover trials data previously analyzed with the estimating equations EB approach of Waclawiw and Liang (1994, Statistics in Medicine 13, 541-551). We also perform simulations to compare the proposed KS and PQL approaches. These two approaches lead to EB estimates of random effects parameters with similar asymptotic bias. However, for many clusters with small cluster size, the proposed KS approach does better than the PQL procedures in terms of coverage of nominal 95% confidence intervals for random effects estimates. For large cluster sizes and a few clusters, the PQL approach performs better than the KS adjustment. These simulation results agree somewhat with those of the data analyses.     

Bayesian survival analysis using a MARS model

A Bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring. The possible models contain the proportional hazards model as a subclass and automatically detect departures from this. A reversible jump Markov chain Monte Carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve.     

Phylogenetic and biogeographic diversification of Rhus (Anacardiaceae) in the Northern Hemisphere

Sequences of internal transcribed spacers (ITS) of nuclear ribosomal DNA, the chloroplast ndhF gene, and chloroplast trnL-F regions (trnL intron, and trnL [UAA] 3' exon-trnF [GAA] intergenic spacer) were used for phylogenetic analyses of Rhus, a genus disjunctly distributed in Asia, Europe, Hawaii, North America, and Northern Central America. Both ITS and cpDNA data sets support the monophyly of Rhus. The monophyly of subgenus Rhus was suggested by the combined cpDNA and ITS data, and largely supported in the cpDNA data except that Rhus microphylla of subgenus Lobadium was nested within it. The monophyly of subgenus Lobadium was strongly supported in the ITS data, whereas the cpDNA data revealed two main clades within the subgenus, which formed a trichotomy with the clade of subgenus Rhus plus R. microphylla. The ITS and cpDNA trees differ in the positions of Rhus michauxii, R. microphylla, and Rhus rubifolia, and hybridization may have caused this discordance. Fossil evidence indicates that Rhus dates back to the early Eocene. The penalized likelihood method was used to estimate divergence times, with fossils of Rhus subgenus Lobadium, Pistacia and Toxicodendron used for age constraints. Rhus diverged from its closest relative at 49.1+/-2.1 million years ago (Ma), the split of subgenus Lobadium and subgenus Rhus was at 38.1+/-3.0 Ma. Rhus most likely migrated from North America into Asia via the Bering Land Bridge during the Late Eocene (33.8+/-3.1 Ma). Rhus coriaria from southern Europe and western Asia diverged from its relatives in eastern Asia at 24.4+/-3.2 Ma. The Hawaiian Rhus sandwicensis diverged from the Asian Rhus chinensis at 13.5+/-3.0 Ma. Subgenus Lobadium was inferred to be of North American origin. Taxa of subgenus Lobadium then migrated southward to Central America. Furthermore, we herein make the following three nomenclatural combinations: (1) Searsia leptodictya (Diels) T. S. Yi, A. J. Miller and J. Wen, comb. nov., (2) Searsia pyroides (A. Rich.) T. S. Yi, A. J. Miller and J. Wen, comb. nov., and (3) Searsia undulata (Jacq.) T. S. Yi, A. J. Miller and J. Wen, because our analyses support the segregation of Searsia from Rhus.     

Semiparametric estimation of tag loss and reporting rates for tag-recovery experiments using exact time-at-liberty data

We present a semiparametric likelihood approach to estimating reporting rates and tag-loss rates from the tags returned from capture-recapture studies. Such studies are commonly used to estimate critical population parameters. Tag loss rates are estimated using double-tagged animals, while reporting rates are estimated using information from high-reward tags. A likelihood function is constructed based on the conditional distribution of the type of tag returned (low or high reward, single or double tag), given that a tag has been returned. This involves many sparse 5 x 1 tag-return contingency tables, and choosing a good functional form for the tag loss rate is difficult with such data. We model tag-loss rates using monotone-smoothing splines, and use these nonparametric estimates to diagnose the parametric form of the tag-loss rate. The nonparametric methods can also be used directly to model tag-loss rates.