Joint analysis of time-to-event and multiple binary indicators of latent classes

Multiple categorical variables are commonly used in medical and epidemiological research to measure specific aspects of human health and functioning. To analyze such data, models have been developed considering these categorical variables as imperfect indicators of an individual's "true" status of health or functioning. In this article, the latent class regression model is used to model the relationship between covariates, a latent class variable (the unobserved status of health or functioning), and the observed indicators (e.g., variables from a questionnaire). The Cox model is extended to encompass a latent class variable as predictor of time-to-event, while using information about latent class membership available from multiple categorical indicators. The expectation-maximization (EM) algorithm is employed to obtain maximum likelihood estimates, and standard errors are calculated based on the profile likelihood, treating the nonparametric baseline hazard as a nuisance parameter. A sampling-based method for model checking is proposed. It allows for graphical investigation of the assumption of proportional hazards across latent classes. It may also be used for checking other model assumptions, such as no additional effect of the observed indicators given latent class. The usefulness of the model framework and the proposed techniques are illustrated in an analysis of data from the Women's Health and Aging Study concerning the effect of severe mobility disability on time-to-death for elderly women.     

Penalized estimating equations

Penalty models--such as the ridge estimator, the Stein estimator, the bridge estimator, and the Lasso-have been proposed to deal with collinearity in regressions. The Lasso, for instance, has been applied to linear models, logistic regressions, Cox proportional hazard models, and neural networks. This article considers the bridge penalty model with penalty sigma(j)/beta(j)/gamma for estimating equations in general and applies this penalty model to the generalized estimating equations (GEE) in longitudinal studies. The lack of joint likelihood in the GEE is overcome by the penalized estimating equations, in which no joint likelihood is required. The asymptotic results for the penalty estimator are provided. It is demonstrated, with a simulation and an application, that the penalized GEE potentially improves the performance of the GEE estimator, and enjoys the same properties as linear penalty models.     

Effects of residual smoothing on the posterior of the fixed effects in disease-mapping models

Disease-mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive (CAR) prior to account for spatial clustering. In such spatial regressions, the objective may be to estimate the fixed effects while accounting for the spatial correlation. But adding the CAR random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model. This article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance. Diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the CAR random effects and to measure each region's influence on the change in the fixed effect's estimates by adding the CAR random effects. A new model that alleviates the collinearity between the fixed effect covariates and the CAR random effects is developed and extensions of these methods to point-referenced data models are discussed.     

Whole genome duplication of intra- and inter-chromosomes in the tomato genome

Whole genome duplication(WGD)events have been proven to occur in the evolutionary history of most angiosperms.Tomato is considered a model species of the Solanaceae family.In this study,we describe the details of the evolutionary process of the tomato genome by detecting collinearity blocks and dating the WGD events on the tree of life by combining two different methods:synonymous substitution rates(Ks)and phylogenetic trees.In total,593 collinearity blocks were discovered out of 12 pseudo-chromosomes constructed. It was evident that chromosome 2 had experienced an intra-chromosomal duplication event.Major inter-chromosomal duplication occurred among all the pseudo-chromosome.We calculated the Ks value of these collinearity blocks.Two peaks of Ks distribution were found,corresponding to two WGD events occurring approximately 36-82 million years ago(MYA)and 148-205 MYA.Additionally, the results of phylogenetic trees suggested that the more recent WGD event may have occurred after the divergence of the rosidasterid clade,but before the major diversification in Solanaceae.The older WGD event was shown to have occurred before the divergence of the rosid-asterid clade and after the divergence of rice-Arabidopsis(monocot-dicot).     

Multiple Linear Regression on Canonical Correlation Variables

When the explanatory variables of a linear model are split into two groups, two notions of collinearity are defined: a collinearity between the variables of each group, of which the mean is called residual collinearity, and a collinearity between the two groups called explained collinearity. Canonical correlation analysis provides information about the collinearity: large canonical correlation coefficients correspond to some small eigenvalues and eigenvectors of the correlation matrix and characterise the explained collinearity. Other small eigenvalues of this matrix correspond to the residual collinearity. A selection of predictors can be performed from the canonical correlation variables, according to their partial correlation coefficient with the explained variable. In the proposed application, the results obtained by the selection of canonical variables are better than those given by classical regression and by principal component regression.     

A regulatory 'landscape effect' over the HoxD cluster

Faithful expression of Hox genes in both time and space is essential for proper patterning of the primary body axis. Transgenic approaches in vertebrates have suggested that this collinear activation process is regulated in a largely gene cluster-autonomous manner. In contrast, more recently co-opted expression specificities, required in other embryonic structures, depend upon long-range enhancer sequences acting from outside the gene clusters. This regulatory dichotomy was recently questioned, since gene activation along the trunk seems to be partially regulated by signals located outside of the cluster. We investigated these alternative regulatory strategies by engineering a large inversion that precisely separates the murine HoxD complex from its centromeric neighborhood. Mutant animals displayed posterior transformations along with subtle deregulations of Hoxd genes, indicating an impact of the centromeric landscape on the fine-tuning of Hoxd gene expression. Proximal limbs were also affected, suggesting that this ‘landscape effect’ is generic and impacts upon regulatory mechanisms of various qualities and evolutionary origins.     

Inappropriate analysis does not reveal the ecological causes of evolution of stickleback armour: a critique of Spence et al. 2013

In a recent paper in this journal, Spence et al. (2013) sought to identify the ecological causes of morphological evolution in three‐spined sticklebacks Gasterosteus aculeatus, by examining phenotypic and environmental variation between populations on the island of North Uist, Scotland. However, by using simple qualitative assessments of phenotype and inappropriate measures of environmental variation, Spence et al. have come to a conclusion that is diametrically opposite to that which we have arrived at in studying the same populations. Our criticisms of their paper are threefold: (1) using a binomial qualitative measure of the variation in stickleback armour (“low” versus “minimal” (i.e., “normal” low‐plated freshwater sticklebacks versus spineless and/or plateless fish)) does not represent the full range of phenotypes that can be described by quantitative measures of the individual elements of armour. (2) Their use of unspecified test kits, with a probable accuracy of 4 ppm, may not be accurate in the range of water chemistry on North Uist (1 to 30 ppm calcium). (3) Their qualitative assessment of the abundance of brown trout Salmo trutta as the major predator of sticklebacks does not accurately describe the variation in brown trout abundance that is revealed by catch‐per‐unit‐effort statistics. Repeating Spence et al.'s analysis using our own measurements, we find, in direct contradiction to them, that variation in stickleback bony armour is strongly correlated with variation in trout abundance, and unrelated to variation in the concentration of calcium in the lochs in which they live. Field studies in ecology and evolution seldom address the same question in the same system at the same time, and it is salutary that in this rare instance two such studies arrived at diametrically opposite answers.     

Comparative analysis of Gossypium and Vitis genomes indicates genome duplication specific to the Gossypium lineage

Genetic mapping studies have suggested that diploid cotton (Gossypium) might be an ancient polyploid. However, further evidence is lacking due to the complexity of the genome and the lack of sequence resources. Here, we used the grape (Vitis vinifera) genome as an out-group in two different approaches to further explore evidence regarding ancient genome duplication (WGD) event(s) in the diploid Gossypium lineage and its (their) effects: a genome-level alignment analysis and a local-level sequence component analysis. Both studies suggest that at least one round of genome duplication occurred in the Gossypium lineage. Also, gene densities in corresponding regions from Gossypium raimondii, V. vinifera, Arabidopsis thaliana and Carica papaya genomes are similar, despite the huge difference in their genome sizes and the different number of WGDs each genome has experienced. These observations fit the model that differences in plant genome sizes are largely explained by transposon insertions into heterochromatic regions.     

Desaturase multigene families of Brassica napus arose through genome duplication

 This paper reports the estimated gene copy number and restriction fragment length polymorphism (RFLP) map locations of five different desaturase cDNA clones from Brassica napus (oilseed rape). The desaturase enzymes encoded by four of these genes catalyze successive reactions that insert double bonds into lipid-linked fatty acid residues. Delta-12 (e2) and delta-15 (e3) desaturases are active in the endoplasmic reticulum, while omega-6 (p2) and omega-3 (p3) desaturases catalyze analogous desaturation reactions via a parallel pathway located in plastids. The fifth cDNA clone (b5) contains a desaturase-like domain bound to a cytochrome b₅ segment. Estimates of gene copy number based on Southern blot analysis of 16 oilseed rape varieties and three different resynthesized Brassica napus lines indicated that e2 had 4–6 gene copies and e3, p2, p3 and b5 each had 6–8 gene copies per haploid genome. Estimates of the gene copy number for the two progenitor species, Brassica oleracea and Brassica rapa, supported the premise that all these genes were at least duplicated or triplicated in the two progenitor species before they combined to form B. napus. RFLP mapping results showed that the e2 probe detected 4 distinct loci, the e3 probe 6 loci and p2, p3 and b5 each detected 8 loci, with pairs of loci often mapping to homoeologous regions on 2 different linkage groups. The 28 mappable loci were distributed across 12 linkage groups of the B. napus map (Parkin et al. 1995) and were usually represented by single RFLP fragments. A collinear segment containing the e2 and p3 loci was positioned on B. napus linkage groups N1, N11, N3, N13, N5 and N15. This segment was collinear with a 30-cM region of Arabidopsis thaliana chromosome 3 that contains the homologous fad2 (e2) and fad7(p3) genes. This suggests that the desaturase multigene families arose as the result of duplication of large chromosome segments rather than duplication of individual genes. Received: 14 August 1996 / Accepted: 18 October 1996