Structure, attachment, replacement and growth of teeth in bluefish, Pomatomus saltatrix (Linnaeus, 1776), a teleost with deeply socketed teeth

Tooth replacement poses many questions about development, pattern formation, tooth attachment mechanisms, functional morphology and the evolution of vertebrate dentitions. Although most vertebrate species have polyphyodont dentitions, detailed knowledge of tooth structure and replacement is poor for most groups, particularly actinopterygians. We examined the oral dentition of the bluefish, Pomatomus saltatrix, a pelagic and coastal marine predator, using a sample of 50 individuals. The oral teeth are located on the dentary and premaxillary bones, and we scored each tooth locus in the dentary and premaxillary bones using a four-part functional classification: absent (A), incoming (I), functional (F=fully ankylosed) or eroding (E). The homodont oral teeth of Pomatomus are sharp, deeply socketed and firmly ankylosed to the bone of attachment. Replacement is intraosseus and occurs in alternate tooth loci with long waves of replacement passing from rear to front. The much higher percentage of functional as opposed to eroding teeth suggests that replacement rates are low but that individual teeth are quickly lost once erosion begins. Tooth number increases ontogenetically, ranging from 15–31 dentary teeth and 15–39 premaxillary teeth in the sample studied. Teeth increase in size with every replacement cycle. Remodeling of the attachment bone occurs continuously to accommodate growth. New tooth germs originate from a discontinuous dental lamina and migrate from the lingual (dentary) or labial (premaxillary) epithelium through pores in the bone of attachment into the resorption spaces beneath the existing teeth. Pomatomus shares unique aspects of tooth replacement with barracudas and other scombroids and this supports the interpretation that Pomatomus is more closely related to scombroids than to carangoids.     

Bayesian analysis for generalized linear models with nonignorably missing covariates

We propose Bayesian methods for estimating parameters in generalized linear models (GLMs) with nonignorably missing covariate data. We show that when improper uniform priors are used for the regression coefficients, phi, of the multinomial selection model for the missing data mechanism, the resulting joint posterior will always be improper if (i) all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism, or (ii) at least one of the covariates is continuous and unbounded. This impropriety will result regardless of whether proper or improper priors are specified for the regression parameters, beta, of the GLM or the parameters, alpha, of the covariate distribution. To overcome this problem, we propose a novel class of proper priors for the regression coefficients, phi, in the selection model for the missing data mechanism. These priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a Gibbs sampling scheme that leads to accelerated convergence. In addition, we extend the model assessment criterion of Chen, Dey, and Ibrahim (2004a, Biometrika 91, 45-63), called the weighted L measure, to GLMs and missing data problems as well as extend the deviance information criterion (DIC) of Spiegelhalter et al. (2002, Journal of the Royal Statistical Society B 64, 583-639) for assessing whether the missing data mechanism is ignorable or nonignorable. A novel Markov chain Monte Carlo sampling algorithm is also developed for carrying out posterior computation. Several simulations are given to investigate the performance of the proposed Bayesian criteria as well as the sensitivity of the prior specification. Real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods.     

Bayesian inference for stochastic kinetic models using a diffusion approximation

This article is concerned with the Bayesian estimation of stochastic rate constants in the context of dynamic models of intracellular processes. The underlying discrete stochastic kinetic model is replaced by a diffusion approximation (or stochastic differential equation approach) where a white noise term models stochastic behavior and the model is identified using equispaced time course data. The estimation framework involves the introduction of m- 1 latent data points between every pair of observations. MCMC methods are then used to sample the posterior distribution of the latent process and the model parameters. The methodology is applied to the estimation of parameters in a prokaryotic autoregulatory gene network.     

Nonparametric estimation of ROC curves in the absence of a gold standard

In the evaluation of diagnostic accuracy of tests, a gold standard on the disease status is required. However, in many complex diseases, it is impossible or unethical to obtain such a gold standard. If an imperfect standard is used, the estimated accuracy of the tests would be biased. This type of bias is called imperfect gold standard bias. In this article we develop a nonparametric maximum likelihood method for estimating ROC curves and their areas of ordinal-scale tests in the absence of a gold standard. Our simulation study shows that the proposed estimators for the ROC curve areas have good finite-sample properties in terms of bias and mean squared error. Further simulation studies show that our nonparametric approach is comparable to the binormal parametric method, and is easier to implement. Finally, we illustrate the application of the proposed method in a real clinical study on assessing the accuracy of seven specific pathologists in detecting carcinoma in situ of the uterine cervix.     

Origin and evolution of gnathostome dentitions: a question of teeth and pharyngeal denticles in placoderms

The fossil group Placodermi is the most phylogenetically basal of the clade of jawed vertebrates but lacks a marginal dentition comparable to that of the dentate Chondrichthyes, Acanthodii and Osteichthyes (crown-group Gnathostomata). The teeth of crown-group gnathostomes are part of an ordered dentition replaced from, and patterned by, a dental lamina, exemplified by the elasmobranch model. A dentition recognised by these criteria has been previously judged absent in placoderms, based on structural evidence such as absence of tooth whorls and typical vertebrate dentine. However, evidence for regulated tooth addition in a precise spatiotemporal order can be observed in placoderms, but significantly, only within the group Arthrodira. In these fossils, as in other jawed vertebrates with statodont, non-replacing dentitions, new teeth are added at the ends of rows below the bite, but in line with biting edges of the dentition. The pattern is different on each gnathal bone and probably arises from single odontogenic primordia on each, but tooth rows are arranged in a distinctive placoderm pattern. New teeth are made of regular dentine comparable to that of crown-gnathostomes, formed from a pulp cavity. This differs from semidentine previously described for placoderm gnathalia, a type present in the external dermal tubercles. The Arthrodira is a derived taxon within the Placodermi, hence origin of teeth in placoderms occurs late in the phylogeny and teeth are convergently derived, relative to those of other jawed vertebrates. More basal placoderm taxa adopted other strategies for providing biting surfaces and these vary substantially, but include addition of denticles to the growing gnathal plates, at the margins of pre-existing denticle patches. These alternative strategies and apparent absence of regular dentine have led to previous interpretations that teeth were entirely absent from the placoderm dentition. A consensus view emerged that a dentition, as developed within a dental lamina, is a synapomorphy characterising the clade of crown-group gnathostomes. Recent comparisons between sets of denticle whorls in the pharyngeal region of the jawless fish Loganellia scotica (Thelodonti) and those in sharks suggest homology of these denticle sets on gill arches. Although the placoderm pharyngeal region appears to lack denticles (placoderm gill arches are poorly known), the posterior wall of the pharyngeal cavity, formed by a bony flange termed the postbranchial lamina, is covered in rows of patterned denticle arrays. These arrays differ significantly, both in morphology and arrangement, from those of the denticles located externally on the head and trunkshield plates. Denticles in these arrays are homologous to denticles associated with the gill arches in other crown-gnathostomes, with pattern similarities for order and position of pharyngeal denticles. From their location in the pharynx these are inferred to be under the influence of a cell lineage from endoderm, rather than ectoderm. Tooth sets and tooth whorls in crown-group gnathostomes are suggested to derive from the pharyngeal denticle whorls, at least in sharks, with the patterning mechanisms co-opted to the oral cavity. A comparable co-option is suggested for the Placodermi.     

Optimal design of experiments with anticipated pattern of missing observations

We propose a general method of designing an experiment when there are potentially failing trials. We use polynomial models and the Michaelis-Menten model as examples and construct different types of optimal designs under a broad class of response probability functions. We show that the usual optimal designs, that assume all observations are available at the end of the experiment, can be quite inefficient if the anticipated missingness pattern is not accounted for at the design stage. We also investigate robustness properties of the proposed designs to specification of their nominal values and the response probability functions.     

Multiple augmentation with partial missing regressors

In large cohort studies, it is common that a subset of the regressors may be missing for some study subjects by design or happenstance. In this article, we apply the multiple data augmentation techniques to semiparametric models for epidemiologic data when a subset of the regressors are missing for some subjects, under the assumption that the data are missing at random in the sense of Rubin (2004) and that the missingness probabilities depend jointly on the observable subset of regressors, on a set of observable extraneous variables and on the outcome. Computational algorithms for the Poor Man's and the Asymptotic Normal data augmentations are investigated. Simulation studies show that the data augmentation approach generates satisfactory estimates and is computationally affordable. Under certain simulation scenarios, the proposed approach can achieve asymptotic efficiency similar to the maximum likelihood approach. We apply the proposed technique to the Multi-Ethic Study of Atherosclerosis (MESA) data and the South Wales Nickel Worker Study data.     

Estimating biomarker-based HIV incidence using prevalence data in high risk groups with missing outcomes

The novel two-step serologic sensitive/less sensitive testing algorithm for detecting recent HIV seroconversion (STARHS) provides a simple and practical method to estimate HIV-1 incidence using cross-sectional HIV seroprevalence data. STARHS has been used increasingly in epidemiologic studies. However, the uncertainty of incidence estimates using this algorithm has not been well described, especially for high risk groups or when missing data is present because a fraction of sensitive enzyme immunoassay (EIA) positive specimens are not tested by the less sensitive EIA. Ad hoc methods used in practice provide incorrect confidence limits and thus may jeopardize statistical inference. In this report, we propose maximum likelihood and Bayesian methods for correctly estimating the uncertainty in incidence estimates obtained using prevalence data with a fraction missing, and extend the methods to regression settings. Using a study of injection drug users participating in a drug detoxification program in New York city as an example, we demonstrated the impact of underestimating the uncertainty in incidence estimates using ad hoc methods. Our methods can be applied to estimate the incidence of other diseases from prevalence data using similar testing algorithms when missing data is present.     

The weighted generalized estimating equations approach for the evaluation of medical diagnostic test at subunit level

Sensitivity and specificity are common measures used to evaluate the performance of a diagnostic test. A diagnostic test is often administrated at a subunit level, e.g. at the level of vessel, ear or eye of a patient so that the treatment can be targeted at the specific subunit. Therefore, it is essential to evaluate the diagnostic test at the subunit level. Often patients with more negative subunit test results are less likely to receive the gold standard tests than patients with more positive subunit test results. To account for this type of missing data and correlation between subunit test results, we proposed a weighted generalized estimating equations (WGEE) approach to evaluate subunit sensitivities and specificities. A simulation study was conducted to evaluate the performance of the WGEE estimators and the weighted least squares (WLS) estimators (Barnhart and Kosinski, 2003) under a missing at random assumption. The results suggested that WGEE estimator is consistent under various scenarios of percentage of missing data and sample size, while the WLS approach could yield biased estimators due to a misspecified missing data mechanism. We illustrate the methodology with a cardiology example.     

Phase II jaw movements and masseter muscle activity during chewing in Papio anubis

It was proposed that the power stroke in primates has two distinct periods of occlusal contact, each with a characteristic motion of the mandibular molars relative to the maxillary molars. The two movements are called phase I and phase II, and they occur sequentially in that order (Kay and Hiiemae [1974] Am J. Phys. Anthropol. 40:227-256, Kay and Hiiemae [1974] Prosimian Biology, Pittsburgh: University of Pittsburgh Press, p. 501-530). Phase I movement is said to be associated with shearing along a series of crests, producing planar phase I facets and crushing on surfaces on the basins of the molars. Phase I terminates in centric occlusion. Phase II movement is said to be associated with grinding along the same surfaces that were used for crushing at the termination of phase I. Hylander et al. ([1987] Am J. Phys. Anthropol. 72:287-312; see also Hiiemae [1984] Food Acquisition and Processing, London: Academic Press, p. 257-281; Hylander and Crompton [1980] Am J. Phys. Anthropol. 52:239-251, [1986] Arch. Oral. Biol. 31:841-848) analyzed data on macaques and suggested that phase II movement may not be nearly as significant for food breakdown as phase I movement simply because, based on the magnitude of mandibular bone strain patterns, adductor muscle and occlusal forces are likely negligible during movement out of centric occlusion. Our goal is to better understand the functional significance of phase II movement within the broader context of masticatory kinematics during the power stroke. We analyze vertical and transverse mandibular motion and relative activity of the masseter and temporalis muscles during phase I and II movements in Papio anubis. We test whether significant muscle activity and, by inference, occlusal force occurs during phase II movement. We find that during phase II movement, there is negligible force developed in the superficial and deep masseter and the anterior and posterior temporalis muscles. Furthermore, mandibular movements are small during phase II compared to phase I. These results suggest that grinding during phase II movement is of minimal importance for food breakdown, and that most food breakdown on phase II facets occurs primarily at the end of phase I movement (i.e., crushing during phase I movement). We note, however, that depending on the orientation of phase I facets, significant grinding also occurs along phase I facets during phase I.