Functional data analysis with covariate-dependent mean and covariance structures

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.     

A penalized structural equation modeling method accounting for secondary phenotypes for variable selection on genetically regulated expression from PrediXcan for Alzheimer's disease

As the global burden of mental illness is estimated to become a severe issue in the near future, it demands the development of more effective treatments. Most psychiatric diseases are moderately to highly heritable and believed to involve many genes. Development of new treatment options demands more knowledge on the molecular basis of psychiatric diseases. Toward this end, we propose to develop new statistical methods with improved sensitivity and accuracy to identify disease‐related genes specialized for psychiatric diseases. The qualitative psychiatric diagnoses such as case control often suffer from high rates of misdiagnosis and oversimplify the disease phenotypes. Our proposed method utilizes endophenotypes, the quantitative traits hypothesized to underlie disease syndromes, to better characterize the heterogeneous phenotypes of psychiatric diseases. We employ the structural equation modeling using the liability‐index model to link multiple genetically regulated expressions from PrediXcan and the manifest variables including endophenotypes and case‐control status. The proposed method can be considered as a general method for multivariate regression, which is particularly helpful for psychiatric diseases. We derive penalized retrospective likelihood estimators to deal with the typical small sample size issue. Simulation results demonstrate the advantages of the proposed method and the real data analysis of Alzheimer's disease illustrates the practical utility of the techniques. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.     

Penalized survival models for the analysis of alternating recurrent event data

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length-of-stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end-stage renal disease patients.     

High dimensional mediation analysis with latent variables

We propose a model for high dimensional mediation analysis that includes latent variables. We describe our model in the context of an epidemiologic study for incident breast cancer with one exposure and a large number of biomarkers (i.e., potential mediators). We assume that the exposure directly influences a group of latent, or unmeasured, factors which are associated with both the outcome and a subset of the biomarkers. The biomarkers associated with the latent factors linking the exposure to the outcome are considered “mediators.” We derive the likelihood for this model and develop an expectation‐maximization algorithm to maximize an L1‐penalized version of this likelihood to limit the number of factors and associated biomarkers. We show that the resulting estimates are consistent and that the estimates of the nonzero parameters have an asymptotically normal distribution. In simulations, procedures based on this new model can have significantly higher power for detecting the mediating biomarkers compared with the simpler approaches. We apply our method to a study that evaluates the relationship between body mass index, 481 metabolic measurements, and estrogen‐receptor positive breast cancer.     

Early Tertiary out-of-India dispersal of Crypteroniaceae: evidence from phylogeny and molecular dating

Abstract.— Pylogenetic analyses and molecular dating estimates based on chloroplast DNA sequences were used to establish the relationships of the southern and Southeast Asian Crypteroniaceae and elucidate their biogeographic history. Maximum parsimony and likelihood analyses of rbc L sequences suggested that Crypteroniaceae should be restricted to Crypteronia , Axinandra , and Dactylocladus and that Crypteroniaceae, so defined, are sister to a clade formed by three small African taxa (Oliniaceae, Penaeaceae, and Rhynchocalycaceae) and the monotypic Central and South American Alzateaceae. Three molecular dating approaches (maximum-likelihood under a molecular clock, Langley-Fitch, and penalized-likelihood) were used to infer the age of Crypteroniaceae using both paleobotanic and geologic calibrations. Comparisons among these three methods revealed significant lineage effects in rbc L sequences. Clock-independent dating estimates suggested that divergence of Crypteroniaceae from its African and South American relatives coincided with the breakup of Gondwana, and that India likely served as a "raft" transporting Crypteroniaceae to Asia, with later expansion to Southeast Asia. To our knowledge, Crypteroniaceae are the first plant group for which the out-of-India hypothesis is well corroborated by molecular-based estimates of divergence times.     

Response Adaptive Designs with a Variance‐penalized Criterion

We consider a response adaptive design of clinical trials with a variance‐penalized criterion. It is shown that this criterion evaluates the performance of a response adaptive design based on both the number of patients assigned to the better treatment and the power of the statistical test. A new proportion of treatment allocation is proposed and the doubly biased coin procedure is used to target the proposed proportion. Under reasonable assumptions, the proposed design is demonstrated to generate an asymptotic variance of allocation proportions, which is smaller than that of the drop‐the‐loser design. Simulation comparisons of the proposed design with some existing designs are presented.     

A Penalized-Likelihood Method to Estimate the Distribution of Selection Coefficients from Phylogenetic Data

We develop a maximum penalized-likelihood (MPL) method to estimate the fitnesses of amino acids and the distribution of selection coefficients (S = 2Ns) in protein-coding genes from phylogenetic data. This improves on a previous maximum-likelihood method. Various penalty functions are used to penalize extreme estimates of the fitnesses, thus correcting overfitting by the previous method. Using a combination of computer simulation and real data analysis, we evaluate the effect of the various penalties on the estimation of the fitnesses and the distribution of S. We show the new method regularizes the estimates of the fitnesses for small, relatively uninformative data sets, but it can still recover the large proportion of deleterious mutations when present in simulated data. Computer simulations indicate that as the number of taxa in the phylogeny or the level of sequence divergence increases, the distribution of S can be more accurately estimated. Furthermore, the strength of the penalty can be varied to study how informative a particular data set is about the distribution of S. We analyze three protein-coding genes (the chloroplast rubisco protein, mammal mitochondrial proteins, and an influenza virus polymerase) and show the new method recovers a large proportion of deleterious mutations in these data, even under strong penalties, confirming the distribution of S is bimodal in these real data. We recommend the use of the new MPL approach for the estimation of the distribution of S in species phylogenies of protein-coding genes.     

Phylogeny,diversification patterns and historical biogeography of euglossine orchid bees (Hymenoptera: Apidae)

The orchid bees constitute a clade of prominent insect pollinators distributed throughout the Neotropical region. Males of all species collect fragrances from natural sources, including flowers, decaying vegetation and fungi, and store them in specialized leg pockets to later expose during courtship display. In addition, orchid bees provide pollination services to a diverse array of Neotropical angiosperms when foraging for food and nesting materials. However, despite their ecological importance, little is known about the evolutionary history of orchid bees. Here, we present a comprehensive molecular phylogenetic analysis based on ～4.0 kb of DNA from four loci [cytochrome oxidase (CO1), elongation factor 1‐α (EF1‐α), arginine kinase (ArgK) and RNA polymerase II (Pol‐II)] across the entire tribe Euglossini, including all five genera, eight subgenera and 126 of the approximately 200 known species. We investigated lineage diversification using fossil‐calibrated molecular clocks and the evolution of morphological traits using disparity‐through‐time plots. In addition, we inferred past biogeographical events by implementing model‐based likelihood methods. Our dataset supports a new view on generic relationships and indicates that the cleptoparasitic genus Exaerete is sister to the remaining orchid bee genera. Our divergence time estimates indicate that extant orchid bee lineages shared a most recent common ancestor at 27–42 Mya. In addition, our analysis of morphology shows that tongue length and body size experienced rapid disparity bursts that coincide with the origin of diverse genera (Euglossa and Eufriesea). Finally, our analysis of historical biogeography indicates that early diversification episodes shared a history on both sides of Mesoamerica, where orchid bees dispersed across the Caribbean, and through a Panamanian connection, thus reinforcing the hypothesis that recent geological events (e.g. the formation of the isthmus of Panama) contributed to the diversification of the rich Neotropical biota. © 2010 The Linnean Society of London, Biological Journal of the Linnean Society, 2010, 100 , 552–572.     

Random regression analyses using B-splines to model growth of Australian Angus cattle

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error.     

Molecular phylogeny and diversification history of Prosopis (Fabaceae: Mimosoideae)

The genus Prosopis is an important member of arid and semiarid environments around the world. To study Prosopis diversification and evolution, a combined approach including molecular phylogeny, molecular dating, and character optimization analysis was applied. Phylogenetic relationships were inferred from five different molecular markers ( mat K- trn K, trn L- trn F, trn S- psb C, G3pdh, NIA). Taxon sampling involved a total of 30 Prosopis species that represented all Sections and Series and the complete geographical range of the genus. The results suggest that Prosopis is not a natural group. Molecular dating analysis indicates that the divergence between Section Strombocarpa and Section Algarobia plus Section Monilicarpa occurred in the Oligocene, contrasting with a much recent diversification (Late Miocene) within each of these groups. The diversification of the group formed by species of Series Chilenses, Pallidae, and Ruscifoliae is inferred to have started in the Pliocene, showing a high diversification rate. The moment of diversification within the major lineages of American species of Prosopis is coincident with the spreading of arid areas in the Americas, suggesting a climatic control for diversification of the group. Optimization of habitat parameters suggests an ancient occupation of arid environments by Prosopis species.  © 2008 The Linnean Society of London, Biological Journal of the Linnean Society , 2008, 93 , 621–640.