Adjusting for Nonignorable Missingness When Estimating Generalized Additive Models

Generalized additive models (GAMs) have been widely used for flexible modeling of various types of outcomes. When the outcome in a GAM is subject to missing, practical analyses often assume that missingness is missing at random (MAR). This assumption can be of suspicion when the missingness is not by design. Evaluating the potential effects of alternative nonignorable missing data mechanism on the MAR inference from a GAM can be important but often challenging due to the complicatedness of alternative nonignorable models. We apply the index approach to local sensitivity (Troxel, Ma, and Heitjan 2004 (2004). Statistica Sinica 14 , 1221–1237) to evaluate the potential changes of the GAM estimates in the neighborhood of the MAR model. The approach avoids fitting any complicated nonignorable GAM. Only MAR estimates are required to calculate the resulting sensitivity index and adjust the GAM estimates to account for nonignorable missingness. Thus the proposed approach is considerably simpler to conduct, as compared with the alternative methods. The simulation study shows that the index provides valid assessment of the local sensitivity of the GAM estimates to nonignorable missingness. We then illustrate the method using a rheumatoid arthritis clinical trial data set.     

Holocephalan (Chondrichthyes) dental plates with hypermineralized dentine as a substitute for missing teeth through developmental plasticity

All extant holocephalans (Chimaeroidei) have lost the ability to make individual teeth, as tooth germs are not part of the embryonic development of the dental plates or of their continuous growth. Instead, a hypermineralized dentine with a unique mineral, whitlockin, is specifically distributed within a dentine framework into structures that give the dental plates their distinctive, species-specific morphology. Control of the regulation of this distribution must be cellular, with a dental epithelium initiating the first outer dentine, and via contact with ectomesenchymal tissue as the only embryonic cell type that can make dentine. Chimaeroids have three pairs of dental plates within their mouth, two in the upper jaw and one in the lower. In the genera Chimaera, Hydrolagus and Harriotta, the morphology and distribution of this whitlockin within each dental plate differs both between different plates in the same species and between species. Whitlockin structures include ovoids, rods and tritoral pads, with substantial developmental changes between these. For example, rods appear before the ovoids and result from a change in the surrounding trabecular dentine. In Harriotta, ovoids form separately from the tritoral pads, but also contribute to tritor development, while in Chimaera and Hydrolagus, tritoral pads develop from rods that later are perforated to accommodate the vasculature. Nevertheless, the position of these structures, secreted by the specialized odontoblasts (whitloblasts), appears highly regulated in all three species. These distinct morphologies are established at the aboral margin of the dental plate, with proposed involvement of the outer dentine. We observe that this outer layer forms into serially added lingual ridges, occurring on the anterior plate only. We propose that positional, structural specificity must be contained within the ectomesenchymal populations, as stem cells below the dental epithelium, and a coincidental occurrence of each lingual, serial ridge with the whitlockin structures that contribute to the wear-resistant oral surface.     

How do Araucaria angustifolia trees grow in overstocked stands?

The objective of this study was to evaluate growth along the stem of Araucaria angustifolia (Bertol.) Kuntze trees competing in overstocked stands, in order to identify periods when growth and trunk shape are differentiated during the trees' lifespan. The research was carried out in a planted forest of Araucaria angustifolia established in 1946 in the Açungui National Forest in Campo Largo, Paraná, Brazil, when these trees were 65 years old. One thinning was recorded, at some time between 1970 and 1980. Forty-six trees were selected and divided into three development classes (DC) at 65 years of age; these classes considered diameter at 1.30 m (breast height, dbh) with a range of 20 cm (from 10 cm to 70 cm). In addition to dbh, total tree height, and crown height and diameter were measured in the field. From each tree, 14 disks were removed to analyze growth rings and confirm the age of the stand. Some trees in the smallest DC (10 ≤ dbh < 30 cm) were the product of natural regeneration (younger trees that grew after the initial planting). In 63% of the trees, at least one growth ring was missing at breast height. Missing rings at breast height were more common in trees with smaller dbh and crown diameters. The need for more growing space was observed at different periods during the studied lifespan of the trees from three DCs. It resulted in changes in stems shape from conical to cylindrical. Different growth patterns could be observed during the lives of some trees as they outgrew their competition.     

Multiple imputation for multivariate data with missing and below-threshold measurements: time-series concentrations of pollutants in the Arctic

Many chemical and environmental data sets are complicated by the existence of fully missing values or censored values known to lie below detection thresholds. For example, week-long samples of airborne particulate matter were obtained at Alert, NWT, Canada, between 1980 and 1991, where some of the concentrations of 24 particulate constituents were coarsened in the sense of being either fully missing or below detection limits. To facilitate scientific analysis, it is appealing to create complete data by filling in missing values so that standard complete-data methods can be applied. We briefly review commonly used strategies for handling missing values and focus on the multiple-imputation approach, which generally leads to valid inferences when faced with missing data. Three statistical models are developed for multiply imputing the missing values of airborne particulate matter. We expect that these models are useful for creating multiple imputations in a variety of incomplete multivariate time series data sets.     

Semiparametric methods for multiple exposure mismeasurement and a bivariate outcome in HIV vaccine trials

Exposure to infection information is important for estimating vaccine efficacy, but it is difficult to collect and prone to missingness and mismeasurement. We discuss study designs that collect detailed exposure information from only a small subset of participants while collecting crude exposure information from all participants and treat estimation of vaccine efficacy in the missing data/measurement error framework. We extend the discordant partner design for HIV vaccine trials of Golm, Halloran, and Longini (1998, Statistics in Medicine, 17, 2335-2352.) to the more complex augmented trial design of Longini, Datta, and Halloran (1996, Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology 13, 440-447) and Datta, Halloran, and Longini (1998, Statistics in Medicine 17, 185-200). The model for this design includes three exposure covariates and both univariate and bivariate outcomes. We adapt recently developed semiparametric missing data methods of Reilly and Pepe (1995, Biometrika 82, 299 314), Carroll and Wand (1991, Journal of the Royal Statistical Society, Series B 53, 573-585), and Pepe and Fleming (1991, Journal of the American Statistical Association 86, 108-113) to the augmented vaccine trial design. We demonstrate with simulated HIV vaccine trial data the improvements in bias and efficiency when combining the different levels of exposure information to estimate vaccine efficacy for reducing both susceptibility and infectiousness. We show that the semiparametric methods estimate both efficacy parameters without bias when the good exposure information is either missing completely at random or missing at random. The pseudolikelihood method of Carroll and Wand (1991) and Pepe and Fleming (1991) was the more efficient of the two semiparametric methods.     

Generalized estimating equations for ordinal categorical data: arbitrary patterns of missing responses and missingness in a key covariate

We propose methods for regression analysis of repeatedly measured ordinal categorical data when there is nonmonotone missingness in these responses and when a key covariate is missing depending on observables. The methods use ordinal regression models in conjunction with generalized estimating equations (GEEs). We extend the GEE methodology to accommodate arbitrary patterns of missingness in the responses when this missingness is independent of the unobserved responses. We further extend the methodology to provide correction for possible bias when missingness in knowledge of a key covariate may depend on observables. The approach is illustrated with the analysis of data from a study in diagnostic oncology in which multiple correlated receiver operating characteristic curves are estimated and corrected for possible verification bias when the true disease status is missing depending on observables.     

Fitting the log-F accelerated failure time model with incomplete covariate data

Data obtained from studies in the health sciences often have incompletely observed covariates as well as censored outcomes. In this paper, we present methods for fitting the log-F accelerated failure time model with incomplete continuous and/or categorical time-independent covariates using the Gibbs sampler. A general location model that allows different covariance structures across cells is specified for the covariates, and ignorable missingness of the covariates is assumed. Techniques that accommodate standard assumptions of ignorable censoring as well as certain types of nonignorable censoring are developed. We compare our approach to traditional complete-case analysis in an application to data obtained from a study of melanoma. The comparison indicates that substantial gains in efficiency are possible with our approach.     

Selection models and pattern-mixture models for incomplete data with covariates

Most models for incomplete data are formulated within the selection model framework. This paper studies similarities and differences of modeling incomplete data within both selection and pattern-mixture settings. The focus is on missing at random mechanisms and on categorical data. Point and interval estimation is discussed. A comparison of both approaches is done on side effects in a psychiatric study.     

Taste bud form and distribution on lips and in the oropharyngeal cavity of cardinal fish species (Apogonidae, Teleostei), with remarks on their dentition

The oral dentition and type and number of taste buds (TB) on the lips and in the oropharyngeal cavity were compared by means of SEM in 11 species of cardinal fishes (Apogonidae) belonging to five genera. The occurrence of a dense cover of skin papillae on the lips of some species (e.g., Apogon frenatus), as well as differences in structure of vomer, tongue, and palatinum, expose additional morphological characters important for clarification of the taxonomy of this group of fishes. Differences are also revealed in the type of dentition, such as on the vomer and epi-hypopharyngeal bones. Strong and dense dentition of the anterior part of the oral cavity and a high number of TB on this site in species feeding on larger prey (e.g., Cheilodipterus spp) is compared to the relatively feeble jaw armor and richness of TB on the more pharyngeal site in species feeding on smaller prey (e.g., Apogon angustatus, A. frenatus). In addition to the three types of TB (Types I-III) previously described from various teleost fish, a fourth type (Type IV), comprising very small buds, was found in some cardinal fish (Apogon angustatus, A. frenatus). The various TB are distributed from the lips to the pharyngeal bones, on the breathing valves, tongue, palatinum, and pharyngeal bones; their number and type on the various sites differ in the different species. In all species studied the Types I and II TB, elevated above the surrounding epithelium, dominated the lips and anterior part of mouth, while Types III and IV, which end apically at the level with the epithelium, dominated the more posterior pharyngeal region. The highest number of TB, around 24,600, were found in Fowleria variegata, a typical nocturnal species, and the lowest in the diurnal and crepuscular Apogon cyanosoma (1,660) and Cheilodipterus quinquestriatus (2,400). Differences are also revealed in the type of dentition, such as on the vomer and epi-hypopharyngeal bones. The number of TB increased with growth of the fishes. The differences in the total number of TB and their distribution in the oropharyngeal cavity in the various species indicates possible different mechanisms of foraging and food-recognition.