Smoothed quantile regression analysis of competing risks

Censored quantile regression models, which offer great flexibility in assessing covariate effects on event times, have attracted considerable research interest. In this study, we consider flexible estimation and inference procedures for competing risks quantile regression, which not only provides meaningful interpretations by using cumulative incidence quantiles but also extends the conventional accelerated failure time model by relaxing some of the stringent model assumptions, such as global linearity and unconditional independence. Current method for censored quantile regressions often involves the minimization of the L₁‐type convex function or solving the nonsmoothed estimating equations. This approach could lead to multiple roots in practical settings, particularly with multiple covariates. Moreover, variance estimation involves an unknown error distribution and most methods rely on computationally intensive resampling techniques such as bootstrapping. We consider the induced smoothing procedure for censored quantile regressions to the competing risks setting. The proposed procedure permits the fast and accurate computation of quantile regression parameter estimates and standard variances by using conventional numerical methods such as the Newton–Raphson algorithm. Numerical studies show that the proposed estimators perform well and the resulting inference is reliable in practical settings. The method is finally applied to data from a soft tissue sarcoma study.     

Effect of Soil Chemical and Physical Properties on Sorption and Desorption Behavior of Lead in Different Soils of India

Lead (Pb) is a non-biodegradable contaminant, present in the environment, especially near lead-based industrial sites, agricultural lands, and roadside soils. Bioavailability of Pb in the soil is controlled by the sorption and desorption behavior of Pb, which are further controlled by the soil chemical and physical properties. In this study, sorption and desorption amounts of Pb in soil were compared with soil physical (sand, silt, clay content) and chemical (pH; electrical conductivity, EC; percent organic carbon, (%OC); cation exchange capacity, CEC) properties. Twenty-six surface soils (0–5cm), expected to vary in physical and chemical properties, were collected from different parts of India and were treated with known concentration of Pb solution (40 μg/L). The amount of Pb sorbed and desorbed were measured and correlated with soil properties using simple linear regressions. Sorption was significantly (p ≤ 0.05) and positively correlated with pH, and %OC; desorption was significantly (p ≤ 0.05) negatively correlated with the same two factors. Stepwise multiple regressions were performed for better correlations. Predicted sorption and desorption amounts, based on multiple regression equations, showed reasonably good fit (R² = 0.79 and 0.83, respectively) with observed values. This regression model can be used for estimation of sorption and desorption amounts at contaminated sites.     

Spectra in low-rank localized layers (SpeLLL) for interpretable time–frequency analysis

The time-varying frequency characteristics of many biomedical time series contain important scientific information. However, the high-dimensional nature of the time-varying power spectrum as a surface in time and frequency limits its direct use by applied researchers and clinicians for elucidating complex mechanisms. In this article, we introduce a new approach to time–frequency analysis that decomposes the time-varying power spectrum in to orthogonal rank-one layers in time and frequency to provide a parsimonious representation that illustrates relationships between power at different times and frequencies. The approach can be used in fully nonparametric analyses or in semiparametric analyses that account for exogenous information and time-varying covariates. An estimation procedure is formulated within a penalized reduced-rank regression framework that provides estimates of layers that are interpretable as power localized within time blocks and frequency bands. Empirical properties of the procedure are illustrated in simulation studies and its practical use is demonstrated through an analysis of heart rate variability during sleep.     

Path analysis of standing crop and environmental variables in the field layer of two Belgian riverine forests

Seasonal variation in standing crop, litter, pH and relative light intensity was measured in the field layer of two riverine forests near Bruges, Belgium. At each site the living fraction in 10 randomly selected 0.25 m² quadrats was separated into various components and graphed in relation to the environmental variables. The effect of the environmental variables on standing crop was assessed using path analysis, based on the standardized partial regression coefficients obtained in separate stepwise multiple regressions. In order to linearize the relation between the standing crop and the environmental variables, and to meet other statistical assumptions, a log-transformation was applied to the standing crop data. On an annual basis, 44% of the total variation in log-standing crop was explained by the variables litter, relative light intensity and pH, while seasonally the coefficient of determination ranged from 0.23 (November) to 0.72 (April). A general path diagram, based on all data, indicated predominant direct effect of litter (path coefficient: ?0.55) and pH (0.26). Relative light intensity had only an indirect effect through its impact on litter and pH. Considerable seasonal changes occurred in the importance of litter, relative light intensity and pH.     

THE DUAL ROLE OF SELECTION AND EVOLUTIONARY HISTORY AS REFLECTED IN GENETIC CORRELATIONS

The patterns of genetic correlations between a series of eye and antenna characters were compared among two sets of spring-dwelling and cave-dwelling populations of Gammarus minus. The two sets of populations originate from different drainages and represent two separate invasions of cave habitats from surface-dwelling populations. Matrix correlations, using permutation tests, indicated significant correlations both between populations in the same basin and from the same habitat. The technique of biplot, which allows for the simultaneous consideration of relationships between different genetic correlations and different populations, was used to further analyze the correlation structure. A rank-3 biplot indicated that spring and cave populations were largely differentiated by eye-antennal correlations, whereas basins were differentiated by both eye-antennal and antennal-antennal correlations. Eye-antennal correlations, which are likely to be subject to selection, were most similar within habitats, which are likely to have similar selective regimes.     

Assessing three methods for identification of desirable genotypes in white cabbage (Brassica oleracea L. var. capitata)

Summary A desirable genotype is a genotype performing well in a chosen set of environments. Three methods for identification of desirable genotypes were assessed in two cabbage data sets: regression analysis, multidimensional scaling of dissimilarity matrices, and biplot of deviation matrices. Using the regression approach is not recommended mainly for two reasons: (1) it is difficult to identify the desirable genotypes since one has to unify three parameters into one decision; (2) the regression method failed to identify the most desirable genotypes in one of the data sets. Multidimensional scaling and the biplot method were in accordance with each other and with the mean tables when different subsets where compared. Consequently, they were considered more adequate for identifying desirable genotypes. In cases where rank 2 approximation of the analysed matrix was justified, the biplot revealed more information in one display and was, therefore, considered particularly useful in plant breeding for larger target areas.     

Rejoinder to Use of Principal Component Analysis and the GE -Biplot for the Graphical Exploration of Gene Expression Data

Summary This note is in response to Wouters et al. (2003, Biometrics 59, 1131–1139) who compared three methods for exploring gene expression data. Contrary to their summary that principal component analysis is not very informative, we show that it is possible to determine principal component analyses that are useful for exploratory analysis of microarray data. We also present another biplot representation, the GE‐biplot (Gene Expression biplot), that is a useful method for exploring gene expression data with the major advantage of being able to aid interpretation of both the samples and the genes relative to each other.     

Genome-Wide Regression and Prediction with the BGLR Statistical Package

Many modern genomic data analyses require implementing regressions where the number of parameters (p, e.g., the number of marker effects) exceeds sample size (n). Implementing these large-p-with-small-n regressions poses several statistical and computational challenges, some of which can be confronted using Bayesian methods. This approach allows integrating various parametric and nonparametric shrinkage and variable selection procedures in a unified and consistent manner. The BGLR R-package implements a large collection of Bayesian regression models, including parametric variable selection and shrinkage methods and semiparametric procedures (Bayesian reproducing kernel Hilbert spaces regressions, RKHS). The software was originally developed for genomic applications; however, the methods implemented are useful for many nongenomic applications as well. The response can be continuous (censored or not) or categorical (either binary or ordinal). The algorithm is based on a Gibbs sampler with scalar updates and the implementation takes advantage of efficient compiled C and Fortran routines. In this article we describe the methods implemented in BGLR, present examples of the use of the package, and discuss practical issues emerging in real-data analysis.     

Tree mortality of five major species on Hokkaido Island, northern Japan

The mortality rates of five major tree species (Abies sachalinensis, Acer mono, Magnolia obovata, Quercus crispula, Tilia japonica) on Hokkaido Island, northern Japan were modeled using logistic regressions based on the long-term observation of 8929 individuals in 65 permanent plots. Individual size, recent growth, one-sided and two-sided interactions with neighbors, climatic and topographic factors were used as independent variables in the logistic regressions, and relevant variables were selected using the stepwise method. For all species analyzed, the final models significantly explained tree mortality rates. The regression analyses indicated that individual size and/or recent growth had effects on tree mortality. A significant effect of one-sided interaction on tree mortality was detected for three species, and a significant effect of two-sided interaction was detected for two species. The interactions with neighbors were not necessarily competitive. For all species analyzed, climatic and topographic factors affected tree mortality. The mortality models obtained can be used for forest dynamics simulations. One ecological question was examined using these models. Species that can grow fast in forest stands with smaller basal areas tended to have high mortality rates in forest stands with larger basal areas. Some ecological characteristics of the analyzed species are described based on the results of the regressions.     

Toxicity and bioaccumulation of chromium in some freshwater fish

Chromium (Cr) is a common pollutant of freshwater bodies in India, and is frequently detected in high concentrations in edible fish. Bioassays were carried out in the laboratory to determine acute the toxicity and pattern of accumulation of Cr in three species of freshwater fish. The 96-h LC₅₀ value of Cr for Labeo bata, Puntius sarana, and Catla catla was found respectively as 7.33, 10.37, and 31.61 mg/L. Concentrations of Cr in water, sediments, and fish, during a period of 28 d of exposure to 0, 0.73, and 2.19 mg/L of Cr, varied with exposure period, concentration of Cr, presence of weed, and species of fish exposed. Polynomial regressions obtained by drawing polynomial curves revealed that the aquatic weed Eichhornia crassipes prevented gradual decrease of Cr concentrations in water, but reduced the accumulation of Cr in L. bata and Catla catla. However, the effect of the weed on Puntius sarana was not apparent. The pattern of Cr deposition on sediments was also inconsistent. To explain interactions between environment and fish in a very precise manner, polynomial and multiple regression curves were simultaneously used. When polynomial curves were replaced by multiple regression curves, it was revealed that the aquatic weed E. crassipes could reduce Cr accumulation in Puntius sarana also.     

On nonlinear beta regression residuals

We proposed a new residual to be used in linear and nonlinear beta regressions. Unlike the residuals that had already been proposed, the derivation of the new residual takes into account not only information relative to the estimation of the mean submodel but also takes into account information obtained from the precision submodel. This is an advantage of the residual we introduced. Additionally, the new residual is computationally less intensive than the weighted residual. Recall that the computation of the latter involves an matrix, where n is the sample size. Obviously, that can be a problem when the sample size is very large. In contrast, our residual does not suffer from that. It can be easily computed even in large samples. Finally, our residual proved to be able to identify atypical observations as well as the weighted residual. We also propose new thresholds for residual plots and a scheme for the choice of starting values to be used in maximum likelihood point estimation in the class of nonlinear beta regression models. We report Monte Carlo simulation results on the behavior of different residuals. We also present and discuss two empirical applications; one uses the proportion of killed grasshoppers in an assay on the grasshopper Melanopus sanguinipes with the insecticide carbofuran and the synergist piperonyl butoxide, which enhances the toxicity of the insecticide, and the other uses simulated data. The results favor the new methodology we introduce.     

Rotifers,cladocerans and planktivorous fish: What are the major interactions?

Results of ten outdoor tank experiments on the effects of two kinds of planktivorous fish (Dorosoma cepedianum and Menidia beryllina) on phytoplankton and zooplankton were reviewed for evidence of rotifer-cladoceran interactions. Correlation and multiple regression analyses of the responses of populations of six rotifer species in ten experiments were examined for evidence of interference competition with daphnids, resource exploitation, or invertebrate predation by crustaceans associated with daphnid-dominated communities. A separate enclosure experiment was conducted to assess the potential for short-term effects of dense daphnid populations on four rotifer populations. Indirect resource-mediated effects on rotifer populations associated with manipulations of planktivorous fish were more numerous and consistently expressed than direct negative effects of cladocerans or copepods on rotifer populations.     

Interpreting genotype-by-environment interaction using redundancy analysis

Summary Methods for the interpretation of genotype-by-environment interaction in the presense of explicitly measured environmental variables can be divided into two groups. Firstly, methods that extract environmental characterizations from the data itself, which are subsequently related to measured environmental variables, e.g., regression on the mean or singular value decomposition of the matrix of residuals from additivity, followed by correlation, or regression, methods. Secondly, methods that incorporate measured environmental variables directly into the model, e.g., multiple regression of individual genotypical responses on environmental variables, or factorial regression in which a genotype-by-environment matrix is modelled in terms of concomitant variables for the environmental factor. In this paper a redundancy analysis is presented, which can be derived from the singular-value decomposition of the residuals from additivity by imposing the restriction on the environmental scores of having to be linear combinations of environmental variables. At the same time, redundancy analysis is derivable from factorial regression by rotation of the axes in the space spanned by the fitted values of the factorial regression, followed by a reduction of dimensionality through discarding the least explanatory axes. Redundancy analysis is a member of the second group of methods, and can be an important tool in the interpretation of genotype-by-environment interaction, especially with reference to concomitant environmental information. A theoretical treatise of the method is given, followed by a practical example in which the results of the method are compared to the results of the other methods mentioned.     

Failure of Preoperative Resting Energy Expenditure in Predicting Weight Loss after Gastroplasty

Objective: To evaluate the predictive efficacy of preoperative resting energy expenditure (REE) on weight loss after vertical banded gastroplasty (VBG). When subjected to a gastric restriction procedure of similar extent, the patients with higher energy expenditure should experience a greater negative energy balance than those with lower‐energy expenditure, and thus, lose more weight, thereby making REE a reliable predictor of weight loss after VBG. Research Methods and Procedures: This was a prospective investigation after VBG, taking into account the relationship between preoperative REE values and the results at 1‐year follow‐up in terms of weight loss and success of the procedure. The correlations were evaluated by multiple and logistic regression analysis. Results: The weight loss and the outcome at 1 year after VBG seemed to be completely independent of preoperative energy expenditure. Discussion: These findings suggest that, despite gastric restriction, patients may voluntarily adjust their energy intake, and that the weight outcome after VBG is influenced more by behavioral and cognitive variables than by biological or surgical factors.     

Exact Multiple Comparisons of Three or More Regression Lines: Pairwise Comparisons and Comparisons with a Control

The problem of finding exact simultaneous confidence bounds for differences in regression models for k groups via the union‐intersection method is considered. The error terms are taken to be iid normal random variables. Under an assumption slightly more general than having identical design matrices for each of the k groups, it is shown that an existing probability point for the multivariate studentized range can be used to find the necessary probability point for pairwise comparisons of regression models. The resulting methods can be used with simple or multiple regression. Under a weaker assumption on the k design matrices that allows more observations to be taken from the control group than from the k‐1 treatment groups, a method is developed for computing exact probability points for comparing the simple linear regression models of the k‐1 groups to that of the control. Within a class of designs, the optimal design for comparisons with a control takes the square root of (k‐1) times as many observations from the control than from each treatment group. The simultaneous confidence bounds for all pairwise differences and for comparisons with a control are much narrower than Spurrier's intervals for all contrasts of k regression lines.     

水稻多元有害生物为害特征及产量损失量化

收集了云南粳稻主产区沾益、寻甸两县106块稻田水稻有害生物为害和产量等信息,并用两种方法对其分析。第一种方法应用聚类分析和对应分析描述水稻有害生物为害类型和产量水平之间的关系,第二种方法应用主成分分析和多元逐步回归估计各为害的产量损失。聚类分析确定了7种有害生物为害类型,其中IN1、IN2和IN3为害水平较低,而IN5、IN6和IN7为害水平较高。有害生物为害类型和水稻产量水平之间的对应分析,在前两个轴构成的因子空间内绘出了各为害类型和产量水平的位置,并给出了一条与为害类型紧密联系的产量水平增加路线。该分析暗示与位于该因子平面右边的有害生物为害类型(IN1、IN2和IN3)相比,位于左边的为害类型(IN5、IN6和IN7)将引起水稻更大的产量损失。主成分多元回归分析评估了水稻各种病、虫、草害所造成的减产量及其相对重要性。分析结果表明,高于水稻冠层杂草、蛀茎害虫(白穗)、稻纵卷叶螟、白叶枯病、粘虫、叶瘟病和稻飞虱是该稻作区对水稻产量影响较大的为害因子。     

A Primer on Interpreting Regression Models

Abstract: We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x₁, x₂) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models     

Detecting change in an Australian flowering record: Comparisons of linear regression and cumulative sum analysis change point analysis

Linear regression and cumulative sum analysis (CUSUM) change point analyses were used to determine whether there had been a significant change in the first flowering date between 1983 and 2006 for 65 species. Both methods agreed that the first flowering date of 47 species did not change and that eight species had a significant change (P < 0.05) in their flowering. Three species shifted to later flowering and five species to earlier. Over the observation period, each method found that the average shift to later flowering was greater (37.4 days or approx. 1.56 days per year for CUSUM change point analysis and 51.4 days or 2.14 days per year for linear regression) than that to earlier flowering (28.4 days or approx. 1.20 days per year for change point analysis and 46.5 days or 1.97 days per year for linear regression). For the remaining 10 species the results of linear regression and change point methods differed. Each method found five species (three earlier flowering and two later) to have a significantly changed first flowering date over their observation period, where the other method did not. Some of these differences can be attributed to the fact that the CUSUM method can detect multiple change points whereas linear regression can not. Significant change points in first flowering date were identified for 13 species between the years 1987 to 1998. The most frequent year identified as a change point year was 1995. The two methods, although not interchangeable, had strong agreement (84.6%) in detecting shifts. This gives greater confidence that a change in flowering has occurred for eight species and equally importantly, that no change in first flowering date has occurred for 47 species.