Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 Elsevier B V All rights reserved

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.

Intra- and interspecific divergence in the nuclear sequences of the clock gene period in species of the Drosophila buzzatii cluster

We have measured nucleotide variation in the CLOCK/CYCLE heterodimer inhibition domain (CCID) of the clock X-linked gene period in seven species belonging to the Drosophila buzzatii cluster, namely D. buzzatii, Drosophila koepferae, Drosophila antonietae, Drosophila serido, Drosophila gouveai, Drosophila seriema and Drosophila borborema. We detected that the purifying selection is the main force driving the sequence evolution in period, in agreement with the important role of CCID in clock machinery. Our survey revealed that period provides valuable phylogenetic information that allowed to resolve phylogenetic relationships among D. gouveai, D. borborema and D. seriema, which composed a polytomic clade in preliminary studies. The analysis of patterns of intraspecific variation revealed two different lineages of period in D. koepferae, probably reflecting introgressive hybridization from D. buzzatii, in concordance with previous molecular data.

Evolutionary History of Arabidopsis thaliana Aminoacyl-tRNA Synthetase Dual-Targeted Proteins

Aminoacyl-transfer RNA (tRNA) synthetases (aaRS) are key players in translation and act early in protein synthesis by mediating the attachment of amino acids to their cognate tRNA molecules. In plants, protein synthesis may occur in three subcellular compartments (cytosol, mitochondria, and chloroplasts), which requires multiple versions of the protein to be correctly delivered to its proper destination. The organellar aaRS are nuclear encoded and equipped with targeting information at the N-terminal sequence, which enables them to be specifically translocated to their final location. Most of the aaRS families present organellar proteins that are dual targeted to mitochondria and chloroplasts. Here, we examine the dual targeting behavior of aaRS from an evolutionary perspective. Our results show that Arabidopsis thaliana aaRS sequences are a result of a horizontal gene transfer event from bacteria. However, there is no evident bias indicating one single ancestor (Cyanobacteria or Proteobacteria). The dual-targeted aaRS phylogenetic relationship was characterized into two different categories (paralogs and homologs) depending on the state recovered for both dual-targeted and cytosolic proteins. Taken together, our results suggest that the dual-targeted condition is a gain-of-function derived from gene duplication. Selection may have maintained the original function in at least one of the copies as the additional copies diverged.

THE TEMPO AND MODE OF EVOLUTION OF TRANSPOSABLE ELEMENTS AS REVEALED BY MOLECULAR PHYLOGENIES RECONSTRUCTED FROM MOSQUITO GENOMES

Although many mathematical models exist predicting the dynamics of transposable elements (TEs), there is a lack of available empirical data to validate these models and inherent assumptions. Genomes can provide a snapshot of several TE families in a single organism, and these could have their demographics inferred by coalescent analysis, allowing for the testing of theories on TE amplification dynamics. Using the available genomes of the mosquitoes Aedes aegypti and Anopheles gambiae, we indicate that such an approach is feasible. Our analysis follows four steps: (1) mining the two mosquito genomes currently available in search of TE families; (2) fitting, to selected families found in (1), a phylogeny tree under the general time-reversible (GTR) nucleotide substitution model with an uncorrelated lognormal (UCLN) relaxed clock and a nonparametric demographic model; (3) fitting a nonparametric coalescent model to the tree generated in (2); and (4) fitting parametric models motivated by ecological theories to the curve generated in (3).

Models for genetic evaluation of Nelore cattle mature body weight

Records of 18,770 Nelore animals, born from 1975 to 2002, in 8 herds participating in the Nelore Cattle Breeding Program, were analyzed to estimate genetic parameters for mature BW. The mature BW were analyzed as a single BW taken closest to 4.5 yr of age for each cow in the data file, considering BW starting from 2 (W2Y_S), 3 (W3Y_S), or 4 (W4Y_S) yr of age or as repeated records, including all BW starting from 2 (W2Y_R), 3 (W3Y_R), or 4 (W4Y_R) yr of age. The variance components were estimated by restricted maximum likelihood, fitting univariate and bivariate animal models, including weaning weight. The heritability estimates were 0.29, 0.34, 0.36, 0.41, 0.44, and 0.46 for W2Y_S, W3Y_S, W4Y_S, W2Y_R, W3Y_R, and W4Y_R, respectively. The repeatability estimates for W2Y_R, W3Y_R, and W4Y_R were 0.59, 0.64, and 0.72, respectively. Larger accuracy values associated with the EBV were obtained in the repeated records models. The results indicated the bivariate repeated records model as the most appropriate for analyzing mature BW.

Genetic associations between accumulated productivity, and reproductive and growth traits in Nelore cattle

The total meat yield in a beef cattle production cycle is economically very important and depends on the number of calves born per year or birth season, being directly related to reproductive potential. Accumulated Productivity (ACP) is an index that expresses a cow`s capacity to give birth regularly at a young age and to wean animals of greater body weight. Using data from cattle participating in the ""Program for Genetic Improvement of the Nelore Breed"" (PMGRN - Nelore Brasil), bi-trait analyses were performed using the Restricted Maximum Likelihood method based on an ACP animal model and the following traits: age at first calving (AFC), female body weight adjusted for 365 (BW365) and 450 (BW450) days of age, and male scrotal circumference adjusted for 365 (SC365), 450 (SC450), 550 (SC550) and 730 (SC730) days of age. Median estimated ACP heritability was 0.19 and the genetic correlations with AFC, BW365, BW450, SC365, SC450, SC550 and SC730 were 0.33, 0.70, 0.65, 0.08, 0.07, 0.12 and 0.16, respectively. ACP increased and AFC decreased over time, revealing that the selection criteria genetically improved these traits. Selection based on ACP appears to favor the heaviest females at 365 and 450 days of age who showed better reproductive performance as regards AFC. Scrotal circumference was not genetically associated with ACP. (C) 2007 Elsevier B.V. All rights reserved.

A general hazard model for lifetime data in the presence of cure rate

Historically, the cure rate model has been used for modeling time-to-event data within which a significant proportion of patients are assumed to be cured of illnesses, including breast cancer, non-Hodgkin lymphoma, leukemia, prostate cancer, melanoma, and head and neck cancer. Perhaps the most popular type of cure rate model is the mixture model introduced by Berkson and Gage [1]. In this model, it is assumed that a certain proportion of the patients are cured, in the sense that they do not present the event of interest during a long period of time and can found to be immune to the cause of failure under study. In this paper, we propose a general hazard model which accommodates comprehensive families of cure rate models as particular cases, including the model proposed by Berkson and Gage. The maximum-likelihood-estimation procedure is discussed. A simulation study analyzes the coverage probabilities of the asymptotic confidence intervals for the parameters. A real data set on children exposed to HIV by vertical transmission illustrates the methodology.

Genetic associations between age at first calving and heifer body weight and scrotal circumference in Nelore cattle

P>Age at first calving (AFC) measures the entry of heifers into the beef cattle production system. This trait can be used as a selection criterion for earlier reproductive performance. Using data from Nelore cattle participating in the `Program for Genetic Improvement of the Nelore Breed` (PMGRN-Nelore Brazil), bi-trait analyses were performed using the restricted maximum likelihood method, based on an AFC animal model and the following traits: female body weight adjusted to 365 (BW365) and 450 (BW450) days of age, and male scrotal circumference adjusted to 365 (SC365), 450 (SC450), 550 (SC550) and 730 (SC730) days of age. The heritability estimates for AFC ranged from 0.02 +/- 0.02 to 0.04 +/- 0.02. The estimates of additive direct heritabilities (with standard error) for BW365, BW450, SC365, SC450, SC550 and SC730 were 0.36 +/- 0.07, 0.38 +/- 0.07, 0.48 +/- 0.07, 0.65 +/- 0.07, 0.64 +/- 0.07 and 0.42 +/- 0.07, respectively, and the genetic correlations with AFC were -0.38, -0.33, 0.10, -0.13, -0.13 and 0.06, respectively. In the herds studied, selection for SC365, SC450, SC550 or SC730 should not cause genetic changes in AFC. Selection based on BW365 or BW450 would favor smaller AFC breeding values. However, the low magnitude of direct heritability estimates for AFC in these farms indicates that changes in phenotypical expression depend mostly on non-genetic factors.