Estimates of a Treatment Effect Based on Censored Data Rank Tests

Linear rank test statistics are applied to the problem of estimating a treatment effect if two sets of censored failure time data are compared and the distributions of the log-failure times of the two samples are assumed to differ only in location. Rank tests for this accelerated failure time model are reviewed and Hodges-Lehmann type estimates for the shift parameter are proposed. Properties of these estimates are investigated, computational aspects are discussed and an example is presented.     

Objective prior distributions for Jolly-Seber models of zero-augmented data

Statistical models of capture-recapture data that are used to estimate the dynamics of a population are known collectively as Jolly-Seber (JS) models. State-space versions of these models have been developed for the analysis of zero-augmented data that include the capture histories of the observed individuals and an arbitrarily large number of all-zero capture histories. The number of all-zero capture histories must be sufficiently large to include the unknown number N of individuals in the population that were ever alive during all sampling periods. This definition of N is equivalent to the “superpopulation” of individuals described in several JS models. To fit JS models of zero-augmented data, practitioners often assume a set of independent, uniform prior distributions for the recruitment parameters. However, if the number of capture histories is small compared to N, these uniform priors can exert considerable influence on the posterior distributions of N and other parameters because the uniform priors induce a highly skewed prior on N. In this article, I derive a class of prior distributions for the recruitment parameters of the JS model that can be used to specify objective prior distributions for N, including the discrete-uniform and the improper scale priors as special cases. This class of priors also may be used to specify prior knowledge about recruitment while still preserving the conditions needed to induce an objective prior on N. I use analyses of simulated and real data to illustrate the inferential benefits of this class of prior distributions and to identify circumstances where these benefits are most likely to be realized.     

Simultaneous Analysis of Variance Tests Using Friedman's χ Statistics

This study develops simultaneous tests for shifts in marginal distributions pertaining to complete two-way multivariate data not having Gaussian errors. Gerig's (1969) statistics based on ranks are used, a special case yielding Friedman's (1937) χ Statistics statistics for the one-dimensional marginal distributions. Exact α-level procedures are not now available. Instead, approximate but conservative tests are constructed using available tables together with suitable probability inequalities. A variational result permits unlimited tests even when these are suggested by the data. The procedures are illustrated using data from field studies with peanuts; some extensions are noted; and selected percentage points are provided to support some of the tests.     

Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status

This paper deals with the adaptive dynamics associated to a hierarchical non-linear discrete population model with a general transition matrix. In the model, individuals are categorized into n dominance classes, newborns lie in the subordinate class, and it is considered as evolutionary trait a vector eta of probabilities of transition among classes. For this trait, we obtain the evolutionary singular strategy and prove its neutral evolutionary stability. Finally, we obtain conditions for the invading potential of such a strategy, which is sufficient for the convergence stability of the latter. With the help of the previous results, we provide an explanation for the bimodal distribution of badges of status observed in the Siskin (Carduelis spinus). In the Siskin, as in several bird species, patches of pigmented plumage signal the dominance status of the bearer to opponents, and central to the discussion on the evolution of status signalling is the understanding of which should be the frequency distribution of badge sizes. Though some simple verbal models predicted a bimodal distribution, up to now most species display normal distributions and bimodality has only been described for the Siskin. In this paper, we give conditions leading to one of these two distributions in terms of the survival, fecundity and aggression rates in each dominance class.     

A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities

Estimating the risks heat waves pose to human health is a critical part of assessing the future impact of climate change. In this article, we propose a flexible class of time series models to estimate the relative risk of mortality associated with heat waves and conduct Bayesian model averaging (BMA) to account for the multiplicity of potential models. Applying these methods to data from 105 U.S. cities for the period 1987-2005, we identify those cities having a high posterior probability of increased mortality risk during heat waves, examine the heterogeneity of the posterior distributions of mortality risk across cities, assess sensitivity of the results to the selection of prior distributions, and compare our BMA results to a model selection approach. Our results show that no single model best predicts risk across the majority of cities, and that for some cities heat-wave risk estimation is sensitive to model choice. Although model averaging leads to posterior distributions with increased variance as compared to statistical inference conditional on a model obtained through model selection, we find that the posterior mean of heat wave mortality risk is robust to accounting for model uncertainty over a broad class of models.     

Commentary on Ditch,Stitch and Pitch: the niche is here to stay

A recent set of discussion papers in the Journal of Biogeography by McInerny and Etienne (henceforth M&E) questions the value of niche concepts in relation to a diverse group of practices collectively labelled species distribution modelling (SDM), and specifically the usefulness of the idea of a fundamental niche. In this Correspondence, I argue that certain types of SDM may indeed dispense with niche concepts, but that such is not the case for an important class of SDM‐based activities, including transferring predictions in space and time. Using a single term (SDM) to denote diverse objectives and practices does not help to clarify issues; I discuss this point. I also review several criticisms raised by M&E about the use of the concept of fundamental niche in the context of modelling species' distributions and their environments.     

Finding optimal vaccination strategies for pandemic influenza using genetic algorithms

In the event of pandemic influenza, only limited supplies of vaccine may be available. We use stochastic epidemic simulations, genetic algorithms (GA), and random mutation hill climbing (RMHC) to find optimal vaccine distributions to minimize the number of illnesses or deaths in the population, given limited quantities of vaccine. Due to the non-linearity, complexity and stochasticity of the epidemic process, it is not possible to solve for optimal vaccine distributions mathematically. However, we use GA and RMHC to find near optimal vaccine distributions. We model an influenza pandemic that has age-specific illness attack rates similar to the Asian pandemic in 1957-1958 caused by influenza A(H2N2), as well as a distribution similar to the Hong Kong pandemic in 1968-1969 caused by influenza A(H3N2). We find the optimal vaccine distributions given that the number of doses is limited over the range of 10-90% of the population. While GA and RMHC work well in finding optimal vaccine distributions, GA is significantly more efficient than RMHC. We show that the optimal vaccine distribution found by GA and RMHC is up to 84% more effective than random mass vaccination in the mid range of vaccine availability. GA is generalizable to the optimization of stochastic model parameters for other infectious diseases and population structures.     

Chain binomial models and binomial autoregressive processes

Summary We establish a connection between a class of chain‐binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag‐ conditional distribution and related quantities. We focus on two types of chain‐binomial model, extinction–colonization and colonization–extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite‐sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation.     

广义模型及分类回归树在物种分布模拟中的应用与比较

比较3个应用较广的模拟物种地理分布模型:广义线性模型(GLM)、广义加法模型(GAM)与分类回归树(CART)对中国树种地理分布模拟的优劣,以提出更为合适的模拟物种地理分布模型,并用于预测气候变化对物种地理分布的影响。3个模型对中国15种树种地理分布的模拟研究表明:除对油松、辽东栎分布的模拟精度稍差外,对其余树种分布的模拟精度均较高,其中以GAM模型最好。结合地理信息系统(GIS),比较分析了这3个模型对青冈、木荷、红松和油松4种树种的地理分布模拟效果,结果亦表明:这3个模型均能很好模拟青冈和木荷的地理分布,而GLM模型对红松分布的模拟结果不太理想,3个模型对油松分布的模拟结果均不甚理想,其中以GLM模型最差。基于3个模型对未来气候变化下青冈与蒙古栎地理分布的预测表明:GLM模型与GAM模型对青冈分布的预测结果较为接近,青冈在未来气候变化情景下向西和向北扩展,而CART模型预测青冈在未来气候变化情景下除有向西、向北扩展趋势外,广东和广西南部的青冈分布区将消失;3个模型均预测蒙古栎在未来气候变化情景下向西扩展,扩展面积的大小为:模型的模拟面积>模型>模型。     

A general approach for two-stage analysis of multilevel clustered non-Gaussian data

In this article, we propose a two-stage approach to modeling multilevel clustered non-Gaussian data with sufficiently large numbers of continuous measures per cluster. Such data are common in biological and medical studies utilizing monitoring or image-processing equipment. We consider a general class of hierarchical models that generalizes the model in the global two-stage (GTS) method for nonlinear mixed effects models by using any square-root-n-consistent and asymptotically normal estimators from stage 1 as pseudodata in the stage 2 model, and by extending the stage 2 model to accommodate random effects from multiple levels of clustering. The second-stage model is a standard linear mixed effects model with normal random effects, but the cluster-specific distributions, conditional on random effects, can be non-Gaussian. This methodology provides a flexible framework for modeling not only a location parameter but also other characteristics of conditional distributions that may be of specific interest. For estimation of the population parameters, we propose a conditional restricted maximum likelihood (CREML) approach and establish the asymptotic properties of the CREML estimators. The proposed general approach is illustrated using quartiles as cluster-specific parameters estimated in the first stage, and applied to the data example from a collagen fibril development study. We demonstrate using simulations that in samples with small numbers of independent clusters, the CREML estimators may perform better than conditional maximum likelihood estimators, which are a direct extension of the estimators from the GTS method.     

Predicting fundamental and realized distributions based on thermal niche: A case study of a freshwater turtle

Species distribution models (SDM) have been broadly used in ecology to address theoretical and practical problems. Currently, there are two main approaches to generate SDMs: (i) correlative, which is based on species occurrences and environmental predictor layers and (ii) process-based models, which are constructed based on species' functional traits and physiological tolerances. The distributions estimated by each approach are based on different components of species niche. Predictions of correlative models approach species realized niches, while predictions of process-based are more akin to species fundamental niche. Here, we integrated the predictions of fundamental and realized distributions of the freshwater turtle Trachemys dorbigni. Fundamental distribution was estimated using data of T. dorbigni's egg incubation temperature, and realized distribution was estimated using species occurrence records. Both types of distributions were estimated using the same regression approaches (logistic regression and support vector machines), both considering macroclimatic and microclimatic temperatures. The realized distribution of T. dorbigni was generally nested in its fundamental distribution reinforcing theoretical assumptions that the species' realized niche is a subset of its fundamental niche. Both modelling algorithms produced similar results but microtemperature generated better results than macrotemperature for the incubation model. Finally, our results reinforce the conclusion that species realized distributions are constrained by other factors other than just thermal tolerances.     

Orthogonal Components of the Kruskal-Wallis and Related K-sample Linear Rank Statistics

It is shown that the KRUSKAL -WALLIS statistic may be decomposed into components designed to detect trends in the underlying distributions. Extensions to other K sample linear rank statistics and to nonparametric regression statistics are noted.     

A Generalized Intrinsic Rank Test for k Independent Samples

The original intrinsic rank test is generalized in that the sizes of the k samples may now be arbitrary, and the number of intrinsic rank intervals need not equal the number of samples. Furthermore, the size of these intervals can be made variable, subject only to relatively mild constraints. These generalizations permit the formulation and testing of more specific hypotheses concerning the commonality of the sample distributions. A generalized intrinsic rank function is used to transform the usual ordinal ranks, obtained from the combined samples, into intrinsic ranks. Original sample identity and intrinsic ranks are then cross-tabulated and evaluated as 2-way contingency table.     

Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems

Summary The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject‐specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed‐effects state‐space models based on the longitudinal feature of dynamic systems. State‐space models with mixed‐effects components are very flexible in modeling the serial correlation of within‐subject observations and between‐subject variations. The Bayesian approach and the maximum likelihood method for standard mixed‐effects models and state‐space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E‐step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed‐effects state‐space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.     

A new Class of Drugs for BNCT? Borylated derivatives of ferrocenium compounds in animal experiments

A new class of drugs, borylated derivatives of ferrocenium compounds, which show a comparatively facile synthesis is investigated on their boron neutron capture accumulation. Investigations focused on the fast and effective testing of 12 ferrocene derivatives with tetracoordinated boron atoms, which should accumulate in rodent tumors. The macroscopic studies on time-dependent boron distributions and boron concentrations in mice were carried out by inductively coupled plasma-atomic emission spectrometry, inductively coupled plasma-mass spectrometry, and quantitative neutron capture radiography. The determination of boron concentrations after injection of 2b showed high boron contents in spleen, liver, kidneys, less in lung and muscle, and poor in integral blood, blood plasma, tumor, and brain. It is interesting to note that 2b penetrates the blood-brain barrier which may be advantageous in the treatment of astrocytomas and glioblastomas.     

Dominant climate influences on North American bird distributions

Aim Geographic distributions of species are constrained by several factors acting at different scales, with climate assumed to be a major determinant at broad extents. Recent studies, however, have challenged this statement and indicated that climate may not dominate among the factors governing geographic distributions of species. Here, we argue that these results are misleading due to the lack of consideration of the geographic area that has been accessible to the species. Location North America. Methods We generated null distributions for 75 North American endemic and 19 non‐endemic bird species. For each species, climatic envelopes of observed and null distributions were modelled using neural networks and generalized linear models, and seven climatic predictors. Values of the area under the receiver–operating characteristic curve (AUC) based on models of observed distributions were compared with corresponding AUC values for the null distributions. Results More than 82% of the endemic species showed AUC higher for the observed than for the null distributions, while 63% of the non‐endemic species showed such a pattern. Main conclusions We demonstrate a dominant climatic signal in shaping North American bird distributions. Our results attest to the importance of climate in determining species distributions and support the use of climate‐envelope models for estimating potential distributional areas at the appropriate spatial scales.     

Size-dependent species richness: trends within plant communities and across latitude

We examine how species richness and species‐specific plant density (number of species and number of individuals per species, respectively) vary within community size frequency distributions and across latitude. Communities from Asia, Africa, Europe, and North, Central and South America were studied (60°4′N–41°4′S latitude) using the Gentry data base. Log–log linear stem size (diameter) frequency distributions were constructed for each community and the species richness and species‐specific plant density within each size class were determined for each frequency distribution. Species richness in the smallest stem size class correlated with the Y‐intercepts (β‐values) of the regression curves describing each log–log linear size distributions. Two extreme community types were identified (designated as type A and type B). Type A communities had steep size distributions (i.e. large β‐values), log–log linear species‐richness size distributions, low species‐specific plant density distributions, and a small size class (2–4 cm) containing the majority of all species but rarely conspecifics of the dominant tree species. Type B communities had shallow size distributions (i.e. small β‐values), more or less uniform (and low) size class species‐ richness and species‐specific density distributions and size‐dominant species resident in the smallest size class. Type A communities were absent in the higher latitudes but increased in number towards the equator, i.e. in the smallest size class, species richness increased (and species‐specific density decreased) towards the tropics. Based on our survey of type A and type B communities (and their intermediates), species richness evinces size‐dependent and latitudinal trends, i.e. species richness increased with decreasing body size and most species increasingly reside in the smallest plant size class towards the tropics. Across all latitudes, a trade‐off exists between the number of species and the number of individuals per species residing in the smaller size classes.     

An evaluation of methods for modelling species distributions

Aim Various statistical techniques have been used to model species probabilities of occurrence in response to environmental conditions. This paper provides a comprehensive assessment of methods and investigates whether errors in model predictions are associated to specific kinds of geographical and environmental distributions of species. Location Portugal, Western Europe. Methods Probabilities of occurrence for 44 species of amphibians and reptiles in Portugal were modelled using seven modelling techniques: Gower metric, Ecological Niche Factor Analysis, classification trees, neural networks, generalized linear models, generalized additive models and spatial interpolators. Generalized linear and additive models were constructed with and without a term accounting for spatial autocorrelation. Model performance was measured using two methods: sensitivity and Kappa index. Species were grouped according to their spatial (area of occupancy and extent of occurrence) and environmental (marginality and tolerance) distributions. Two‐way comparison tests were performed to detect significant interactions between models and species groups. Results Interaction between model and species groups was significant for both sensitivity and Kappa index. This indicates that model performance varied for species with different geographical and environmental distributions. Artificial neural networks performed generally better, immediately followed by generalized additive models including a covariate term for spatial autocorrelation. Non‐parametric methods were preferred to parametric approaches, especially when modelling distributions of species with a greater area of occupancy, a larger extent of occurrence, lower marginality and higher tolerance. Main conclusions This is a first attempt to relate performance of modelling techniques with species spatial and environmental distributions. Results indicate a strong relationship between model performance and the kinds of species distributions being modelled. Some methods performed generally better, but no method was superior in all circumstances. A suggestion is made that choice of the appropriate method should be contingent on the goals and kinds of distributions being modelled.     

Compound Regression Models for Ordered Categorical Data

A general class of sequential models for the analysis of ordered categorical variables is developed and discussed. The models apply if the ordinal response may be subdivided into two or more meaningful sets of response categories. The parametrization explicitly makes use of this subdivision. The models furnish a linear alternative to non-linear models which incorporate a scale parameter. They are shown to be special cases of multivariate generalized linear models. Applications are discussed with the use of several examples.