Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

Isolation and characterization of actinobacteria ectosymbionts from Acromyrmex subterraneus brunneus (Hymenoptera, Formicidae)

The ectosymbiont actinobacterium Pseudonocardia was isolated from the integument of Acromyrmex leaf-cutter ants and seems to play a crucial role in maintaining asepsis of the nest. Currently, there has been an intensive search for Pseudonocardia associated with several attine species, but few studies have indicated that other actinobacteria may be associated with these ants as well. We therefore characterized the culturable actinobacteria community associated with the integument of the fungus-growing ant Acromyrmex subterraneus brunneus Forel, 1893 (Hymenoptera: Formicidae). Ectosymbionts were isolated using four different media and characterized by morphological and molecular (16S rDNA) methods. A total of 20 strains were isolated, of which 17 were characterized as Streptomyces spp., and one isolate each as Pseudonocardia, Kitassatospora and Propionicimonas. Unlike other Acromyrmex species, A. subterraneus brunneus is associated with a diversity of actinobacteria. Even though Pseudonocardia is present on this leaf-cutting ant`s integument, the number and diversity of Streptomyces spp. found differs from those of previous studies with other attine ants and suggest that different culturing approaches are needed to characterize the true diversity of microbes colonizing the integument of attine ants. Moreover, understanding the diversity of the culturable actinobacteria associated with A. subterraneus brunneus should increase our knowledge of the evolutionary relationship of this intricate symbiotic association. (C) 2010 Elsevier GmbH. All rights reserved.

Random regression models to estimate test-day milk yield genetic parameters Holstein cows in Southeastern Brazil

A total of 152,145 weekly test-day milk yield records from 7317 first lactations of Holstein cows distributed in 93 herds in southeastern Brazil were analyzed. Test-day milk yields were classified into 44 weekly classes of DIM. The contemporary groups were defined as herd-year-week of test-day. The model included direct additive genetic, permanent environmental and residual effects as random and fixed effects of contemporary group and age of cow at calving as covariable, linear and quadratic effects. Mean trends were modeled by a cubic regression on orthogonal polynomials of DIM. Additive genetic and permanent environmental random effects were estimated by random regression on orthogonal Legendre polynomials. Residual variances were modeled using third to seventh-order variance functions or a step function with 1, 6,13,17 and 44 variance classes. Results from Akaike`s and Schwarz`s Bayesian information criterion suggested that a model considering a 7th-order Legendre polynomial for additive effect, a 12th-order polynomial for permanent environment effect and a step function with 6 classes for residual variances, fitted best. However, a parsimonious model, with a 6th-order Legendre polynomial for additive effects and a 7th-order polynomial for permanent environmental effects, yielded very similar genetic parameter estimates. (C) 2008 Elsevier B.V. All rights reserved.

Positive selection on an acrosomal sperm protein, M7 lysin, in three species of the mussel genus Mytilus

Marine invertebrate sperm proteins are particularly interesting because they are characterized by positive selection and are likely to be involved in prezyogotic isolation and, thus, speciation. Here, we present the first survey of inter and intraspecific variation of a bivalve sperm protein among a group of species that regularly hybridize in nature. M7 lysin is found in sperm acrosomes of mussels and dissolves the egg vitelline coat, permitting fertilization. We sequenced multiple alleles of the mature protein-coding region of M7 lysin from allopatric populations of mussels in the Mytilus edulis species group (M. edulis, M. galloprovincialis, and M. trossulus). A significant McDonald-Kreitman test showed an excess of fixed amino acid replacing substitutions between species, consistent with positive selection. In addition, Kolmogorov-Smirnov tests showed significant heterogeneity in polymorphism to divergence ratios for both synonymous variation and combined synonymous and non-synonymous variation within M. galloprovincialis. These results indicate that there has been adaptive evolution at M7 lysin and, furthermore, shows that positive selection on sperm proteins can occur even when post-zygotic reproductive isolation is incomplete.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Distinguishing species and populations of Rhipicephaline ticks with its 2 ribosomal RNA

Most populations and some species of ticks of the genera Boophilus (5 spp.) and Rhipicephalus (ca. 75 spp.) cannot be distinguished phenotypically. Moreover, there is doubt about the validity of species in these genera. I studied the entire second internal transcribed spacer (ITS 2) rRNA of 16 populations of rhipicephaline ticks to address these problems: Boophilus,microplus from Australia, Kenya, South Africa and Brazil (4 populations); Boophilus decoloratus from Kenya; Rhipicephalus appendiculatus from Kenya, Zimbabwe and Zambia (7 populations); Rhipicephalus zambesiensis from Zimbabwe (3 populations); and Rhipicephalus evertsi from Kenya. Each of the 16 populations had a unique ITS 2, but most of the nucleotide variation occurred among species and genera. ITS 2 rRNA can be used to distinguish the populations and species of Boophilus and Rhipicephalus studied here. Little support was found for the hypothesis that B. microplus from Australia and South Africa are different species. ITS 2 appears useful for phylogenetic inference in the Rhipicephalinae because in genetic distance, maximum likelihood, and maximum parsimony analyses, most branches leading to species had >95% bootstrap support. Rhipicephalus appendiculatus and R, zambeziensis are closely related, yet their ITS 2 sequences could be distinguished unambiguously. This lends weight to a previous proposal that Rhipicephalus sanguineus and Rhipicephalus turanicus, and Rhipicephalus pumlilio and Rhipicephalus camicasi, respectively, are conspecific, because each of these pairs of species had identical sequences for ca. 250 bp of ITS 2 rRNA.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

Hemichordates and deuterostome evolution: robust molecular phylogenetic support for a hemichordate plus echinoderm clade

Hemichordates were traditionally allied to the chordates, but recent molecular analyses have suggested that hemichordates are a sister group to the echinoderms, a relationship that has important consequences for the interpretation of the evolution of deuterostome body plans. However, the molecular phylogenetic analyses to date have not provided robust support for the hemichordate + echinoderm clade. We use a maximum likelihood framework, including the parametric bootstrap, to reanalyze DNA data from complete mitochondrial genomes and nuclear 18S rRNA. This approach provides the first statistically significant support for the hemichordate + echinoderm clade from molecular data. This grouping implies that the ancestral deuterostome had features that included an adult with a pharynx and a dorsal nerve cord and an indirectly developing dipleurula-like larva.

High HIV incidence and prevalence among young women in rural South Africa: Developing a cohort for intervention trials

Objective: To measure prevalence and model incidence of HIV infection. Setting: 2013 consecutive pregnant women attending public sector antenatal clinics in 1997 in Hlabisa health district, South Africa. Historical seroprevalence data, 1992-1995. Methods: Serum remaining from syphilis testing was tested anonymously for antibodies to HIV to determine seroprevalence. Two models, allowing for differential mortality between HIV-positive and HIV-negative people, were used. The first used serial seroprevalence data to estimate trends in annual incidence. The second, a maximum likelihood model, took account of changing force of infection and age-dependent risk of infection, to estimate age-specific HIV incidence in 1997. Multiple logistic regression provided adjusted odds ratios (OR) for risk factors for prevalent HIV infection. Results: Estimated annual HIV incidence increased from 4% in 1992/1993 to 10% in 1996/1997. In 1997, highest age-specific incidence was 16% among women aged between 20 and 24 years. in 1997, overall prevalence was 26% (95% confidence interval [CI], 24%-28%) and at 34% was highest among women aged between 20 and 24 years. Young age (<30 years; odds ratio [OR], 2.1; p = .001), unmarried status (OR 2.2; p = .001) and living in less remote parts of the district (OR 1.5; p = .002) were associated with HIV prevalence in univariate analysis. Associations were less strong in multivariate analysis. Partner's migration status was not associated with HIV infection. Substantial heterogeneity of HIV prevalence by clinic was observed (range 17%-31%; test for trend, p = .001). Conclusions: This community is experiencing an explosive HIV epidemic. Young, single women in the more developed parts of the district would form an appropriate cohort to test, and benefit from, interventions such as vaginal microbicides and HIV vaccines.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Estimating HIV incidence rates from age prevalence data in epidemic situations

We present a method of estimating HIV incidence rates in epidemic situations from data on age-specific prevalence and changes in the overall prevalence over time. The method is applied to women attending antenatal clinics in Hlabisa, a rural district of KwaZulu/Natal, South Africa, where transmission of HIV is overwhelmingly through heterosexual contact. A model which gives age-specific prevalence rates in the presence of a progressing epidemic is fitted to prevalence data for 1998 using maximum likelihood methods and used to derive the age-specific incidence. Error estimates are obtained using a Monte Carlo procedure. Although the method is quite general some simplifying assumptions are made concerning the form of the risk function and sensitivity analyses are performed to explore the importance of these assumptions. The analysis shows that in 1998 the annual incidence of infection per susceptible woman increased from 5.4 per cent (3.3-8.5 per cent; here and elsewhere ranges give 95 per cent confidence limits) at age 15 years to 24.5 per cent (20.6-29.1 per cent) at age 22 years and declined to 1.3 per cent (0.5-2.9 per cent) at age 50 years; standardized to a uniform age distribution, the overall incidence per susceptible woman aged 15 to 59 was 11.4 per cent (10.0-13.1 per cent); per women in the population it was 8.4 per cent (7.3-9.5 per cent). Standardized to the age distribution of the female population the average incidence per woman was 9.6 per cent (8.4-11.0 per cent); standardized to the age distribution of women attending antenatal clinics, it was 11.3 per cent (9.8-13.3 per cent). The estimated incidence depends on the values used for the epidemic growth rate and the AIDS related mortality. To ensure that, for this population, errors in these two parameters change the age specific estimates of the annual incidence by less than the standard deviation of the estimates of the age specific incidence, the AIDS related mortality should be known to within +/-50 per cent and the epidemic growth rate to within +/-25 per cent, both of which conditions are met. In the absence of cohort studies to measure the incidence of HIV infection directly, useful estimates of the age-specific incidence can be obtained from cross-sectional, age-specific prevalence data and repeat cross-sectional data on the overall prevalence of HIV infection. Several assumptions were made because of the lack of data but sensitivity analyses show that they are unlikely to affect the overall estimates significantly. These estimates are important in assessing the magnitude of the public health problem, for designing vaccine trials and for evaluating the impact of interventions. Copyright (C) 2001 John Wiley & Sons, Ltd.

Modelling life history strategies with capture-recapture data: Evolutionary demography of the water skink Eulamprus tympanum

Matrix population models, elasticity analysis and loop analysis can potentially provide powerful techniques for the analysis of life histories. Data from a capture-recapture study on a population of southern highland water skinks (Eulamprus tympanum) were used to construct a matrix population model. Errors in elasticities were calculated by using the parametric bootstrap technique. Elasticity and loop analyses were then conducted to identify the life history stages most important to fitness. The same techniques were used to investigate the relative importance of fast versus slow growth, and rapid versus delayed reproduction. Mature water skinks were long-lived, but there was high immature mortality. The most sensitive life history stage was the subadult stage. It is suggested that life history evolution in E. tympanum may be strongly affected by predation, particularly by birds. Because our population declined over the study, slow growth and delayed reproduction were the optimal life history strategies over this period. Although the techniques of evolutionary demography provide a powerful approach for the analysis of life histories, there are formidable logistical obstacles in gathering enough high-quality data for robust estimates of the critical parameters.

Phylogeny and evolution of anomalous roots in Daviesia (Fabaceae : Mirbelieae)

The phylogeny of the Australian legume genus Daviesia was estimated using sequences of the internal transcribed spacers of nuclear ribosomal DNA. Partial congruence was found with previous analyses using morphology, including strong support for monophyly of the genus and for a sister group relationship between the clade D. pachyloma and the rest of the genus. A previously unplaced bird-pollinated species, anceps + D. D. epiphyllum, was well supported as sister to the only other bird-pollinated species in the genus, D. speciosa, indicating a single origin of bird pollination in their common ancestor. Other morphological groups within Daviesia were not supported and require reassessment. A strong and previously unreported sister clade of Daviesia consists of the two monotypic genera Erichsenia and Viminaria. These share phyllode-like leaves and indehiscent fruits. The evolutionary history of cord roots, which have anomalous secondary thickening, was explored using parsimony. Cord roots are limited to three separate clades but have a complex history involving a small number of gains (most likely 0-3) and losses (0-5). The anomalous structure of cord roots ( adventitious vascular strands embedded in a parenchymatous matrix) may facilitate nutrient storage, and the roots may be contractile. Both functions may be related to a postfire resprouting adaptation. Alternatively, cord roots may be an adaptation to the low-nutrient lateritic soils of Western Australia. However, tests for association between root type, soil type, and growth habit were equivocal, depending on whether the variables were treated as phylogenetically dependent (insignificant) or independent ( significant).