A generalized Gompertz-Rayleigh model as a survival distribution

A generalized Gompertz-Rayleigh distribution is proposed as a potential survival distribution for the case of modeling dual components of risk acting on a population. The hazard function is expressed as the sum of two risks. The early risk component allows for either a high initial death rate that can decrease rapidly or an initial death rate that increases to a maximum before decaying. The late risk component is generally relatively constant with the possibility of an increase after a long followup period. An example is provided based on data collected on 569 patients who were operated on for the simultaneous replacement of aortic and mitral heart valves at the University of Alabama in Birmingham Medical Center.     

The generalized Markov-Polya probability model for ascertainment of groups of individuals in social processes

The generalized Markov-Polya distribution is proposed as a probability model in the ascertainment of a group of individuals through its members who have committed criminal acts. This distribution provides excellent alternatives to the familiar binomial distribution in such studies and includes several distributions as special cases, such as the binomial, quasibinomial, and quasinegative hypergeometric models. This new probability model incorporates the intrinsic effect and an artificial effect for the next member in a group to commit a criminal act. Several results are proved to illustrate the use of this model in segregation analysis. A numerical example illustrates the procedure developed in the present paper and proves the superiority of the model over the Markov-Polya and the binomial probability models.     

Robust joint modeling of longitudinal measurements and time to event data using normal/independent distributions: A Bayesian approach

Joint modeling of longitudinal data and survival data has been used widely for analyzing AIDS clinical trials, where a biological marker such as CD4 count measurement can be an important predictor of survival. In most of these studies, a normal distribution is used for modeling longitudinal responses, which leads to vulnerable inference in the presence of outliers in longitudinal measurements. Powerful distributions for robust analysis are normal/independent distributions, which include univariate and multivariate versions of the Student's t, the slash and the contaminated normal distributions in addition to the normal. In this paper, a linear‐mixed effects model with normal/independent distribution for both random effects and residuals and Cox's model for survival time are used. For estimation, a Bayesian approach using Markov Chain Monte Carlo is adopted. Some simulation studies are performed for illustration of the proposed method. Also, the method is illustrated on a real AIDS data set and the best model is selected using some criteria.     

The MIAmaxent R package: Variable transformation and model selection for species distribution models

The widely used “Maxent” software for modeling species distributions from presence‐only data (Phillips et al., Ecological Modelling, 190, 2006, 231) tends to produce models with high‐predictive performance but low‐ecological interpretability, and implications of Maxent's statistical approach to variable transformation, model fitting, and model selection remain underappreciated. In particular, Maxent's approach to model selection through lasso regularization has been shown to give less parsimonious distribution models—that is, models which are more complex but not necessarily predictively better—than subset selection. In this paper, we introduce the MIAmaxent R package, which provides a statistical approach to modeling species distributions similar to Maxent's, but with subset selection instead of lasso regularization. The simpler models typically produced by subset selection are ecologically more interpretable, and making distribution models more grounded in ecological theory is a fundamental motivation for using MIAmaxent. To that end, the package executes variable transformation based on expected occurrence–environment relationships and contains tools for exploring data and interrogating models in light of knowledge of the modeled system. Additionally, MIAmaxent implements two different kinds of model fitting: maximum entropy fitting for presence‐only data and logistic regression (GLM) for presence–absence data. Unlike Maxent, MIAmaxent decouples variable transformation, model fitting, and model selection, which facilitates methodological comparisons and gives the modeler greater flexibility when choosing a statistical approach to a given distribution modeling problem.     

Generalized F accelerated failure time model for mapping survival trait loci

As the two most popular models in survival analysis, the accelerated failure time (AFT) model can more easily fit survival data than the Cox proportional hazards model (PHM). In this study, we develop a general parametric AFT model for identifying survival trait loci, in which the flexible generalized F distribution, including many commonly used distributions as special cases, is specified as the baseline survival distribution. EM algorithm for maximum likelihood estimation of model parameters is given. Simulations are conducted to validate the flexibility and the utility of the proposed mapping procedure. In analyzing survival time following hyperoxic acute lung injury (HALI) of mice in an F(2) mating population, the generalized F distribution performed best among the six competing survival distributions and detected four QTLs controlling differential HALI survival.     

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors

Our present work proposes a new survival model in a Bayesian context to analyze right‐censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region‐specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa.     

Gamma generalized linear models for pharmacokinetic data

Summary .   This article considers the modeling of single-dose pharmacokinetic data. Traditionally, so-called compartmental models have been used to analyze such data. Unfortunately, the mean function of such models are sums of exponentials for which inference and computation may not be straightforward. We present an alternative to these models based on generalized linear models, for which desirable statistical properties exist, with a logarithmic link and gamma distribution. The latter has a constant coefficient of variation, which is often appropriate for pharmacokinetic data. Inference is convenient from either a likelihood or a Bayesian perspective. We consider models for both single and multiple individuals, the latter via generalized linear mixed models. For single individuals, Bayesian computation may be carried out with recourse to simulation. We describe a rejection algorithm that, unlike Markov chain Monte Carlo, produces independent samples from the posterior and allows straightforward calculation of Bayes factors for model comparison. We also illustrate how prior distributions may be specified in terms of model-free pharmacokinetic parameters of interest. The methods are applied to data from 12 individuals following administration of the antiasthmatic agent theophylline.     

Physiology in ecological niche modeling: using zebra mussel's upper thermal tolerance to refine model predictions through Bayesian analysis

Climate change and human-mediated dispersal are increasingly influencing species’ geographic distributions. Ecological niche models (ENMs) are widely used in forecasting species’ distributions, but are weak in extrapolation to novel environments because they rely on available distributional data and do not incorporate mechanistic information, such as species’ physiological response to abiotic conditions. To improve accuracy of ENMs, we incorporated physiological knowledge through Bayesian analysis. In a case study of the zebra mussel Dreissena polymorpha, we used native and global occurrences to obtain native and global models representing narrower and broader understanding of zebra mussel’ response to temperature. We also obtained thermal limit and survival information for zebra mussel from peer-reviewed literature and used the two types of information separately and jointly to calibrate native models. We showed that, compared to global models, native models predicted lower relative probability of presence along zebra mussel's upper thermal limit, suggesting the shortcoming of native models in predicting zebra mussel's response to warm temperature. We also found that native models showed improved prediction of relative probability of presence when thermal limit was used alone, and best approximated global models when both thermal limit and survival data were used. Our result suggests that integration of physiological knowledge enhances extrapolation of ENM in novel environments. Our modeling framework can be generalized for other species or other physiological limits and may incorporate evolutionary information (e.g. evolved thermal tolerance), thus has the potential to improve predictions of species’ invasive potential and distributional response to climate change.     

Bagging GLM: Improved generalized linear model for the analysis of zero-inflated data

Species-occurrence data sets tend to contain a large proportion of zero values, i.e., absence values (zero-inflated). Statistical inference using such data sets is likely to be inefficient or lead to incorrect conclusions unless the data are treated carefully. In this study, we propose a new modeling method to overcome the problems caused by zero-inflated data sets that involves a regression model and a machine-learning technique. We combined a generalized liner model (GLM), which is widely used in ecology, and bootstrap aggregation (bagging), a machine-learning technique. We established distribution models of Vincetoxicum pycnostelma (a vascular plant) and Ninox scutulata (an owl), both of which are endangered and have zero-inflated distribution patterns, using our new method and traditional GLM and compared model performances. At the same time we modeled four theoretical data sets that contained different ratios of presence/absence values using new and traditional methods and also compared model performances. For distribution models, our new method showed good performance compared to traditional GLMs. After bagging, area under the curve (AUC) values were almost the same as with traditional methods, but sensitivity values were higher. Additionally, our new method showed high sensitivity values compared to the traditional GLM when modeling a theoretical data set containing a large proportion of zero values. These results indicate that our new method has high predictive ability with presence data when analyzing zero-inflated data sets. Generally, predicting presence data is more difficult than predicting absence data. Our new modeling method has potential for advancing species distribution modeling.     

A novel generalized normal distribution for human longevity and other negatively skewed data

Negatively skewed data arise occasionally in statistical practice; perhaps the most familiar example is the distribution of human longevity. Although other generalizations of the normal distribution exist, we demonstrate a new alternative that apparently fits human longevity data better. We propose an alternative approach of a normal distribution whose scale parameter is conditioned on attained age. This approach is consistent with previous findings that longevity conditioned on survival to the modal age behaves like a normal distribution. We derive such a distribution and demonstrate its accuracy in modeling human longevity data from life tables. The new distribution is characterized by 1. An intuitively straightforward genesis; 2. Closed forms for the pdf, cdf, mode, quantile, and hazard functions; and 3. Accessibility to non-statisticians, based on its close relationship to the normal distribution.     

A generalized spatial niche model for aquatic macrophytes

The spatial niches of submerged macrophytes and some relevant statistics for niche extensions and boundaries are described. An interpretation of the potential niche as a probability measure of survival over an n-dimensional gradient space is given. To this end a set of probability measure of is introduced. It is shown that these measures closely relate to statistical concepts found in survival and failure time analysis. By this approach, potential niches are wholly defined as a statistical concept. Realized niches then arise as samples from the specified statistical model: hence appropriate niche location and size measures can be derived.The conceptualized model of the survival niche extends to a general model which describes the shape of realized spatial niches for aquatic macrophytes. This general model was derived from actual vegetation data sampled by diving in many Norwegian lakes. Spatial performance on the vertical gradient can be described by a product of doubly exponential functions. Each of these corresponds to a Gumbel EV1 distribution and expresses the probability distribution of the species' up- and downslope niche boundaries, respectively. Theoretically, both potential and realized niches separate into a persistent and a transient region, each related to ddifferent time scales. The deep-water patchiness, commonly observed for submerged macrophytes, might indicate the transient domain of a realized niche. Published data indicate that the proposed model had widespread applicability, and also relevance to, for example, periphyton.     

New Better than Used and Other Concepts for a Class of Life Distributions

It is well-known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed. As a simple application of the result proved in the paper, the life expectancy of an organism at age γ₀ involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.     

Parametric proportional hazards model for mapping genomic imprinting of survival traits

A number of imprinted genes have been observed in plants, animals and humans. They not only control growth and developmental traits, but may also be responsible for survival traits. Based on the Cox proportional hazards (PH) model, we constructed a general parametric model for dissecting genomic imprinting, in which a baseline hazard function is selectable for fitting the effects of imprinted quantitative trait loci (iQTL) genotypes on the survival curve. The expectation–maximisation (EM) algorithm is derived for solving the maximum likelihood estimates of iQTL parameters. The imprinting patterns of the detected iQTL are statistically tested under a series of null hypotheses. The Bayesian information criterion (BIC) model selection criterion is employed to choose an optimal baseline hazard function with maximum likelihood and parsimonious parameterisation. We applied the proposed approach to analyse the published data in an F₂ population of mice and concluded that, among five commonly used survival distributions, the log-logistic distribution is the optimal baseline hazard function for the survival time of hyperoxic acute lung injury (HALI). Under this optimal model, five QTL were detected, among which four are imprinted in different imprinting patterns.     

Turning the analysis of obesity–mortality associations upside down: Modeling years of life lost through conditional distributions

Objective:

We demonstrate the utility of parametric survival analysis. The analysis of longevity as a function of risk factors such as body mass index (BMI; kg/m²), activity levels, and dietary factors is a mainstay of obesity research. Modeling survival through hazard functions, relative risks, or odds of dying with methods such as Cox proportional hazards or logistic regression are the most common approaches and have many advantages. However, they also have disadvantages in terms of the ease of interpretability, especially for non‐statisticians; the need for additional data to convert parameter estimates to estimates of years of life lost (YLL); debates about the appropriate time scale in the model; and an inability to estimate median survival time when the censoring rate is too high.

Design and Methods:

We will conduct parametric survival analyses with multiple distributions, including distributions that are known to be poor fits (Gaussian), as well as a newly discovered “Compressed Gaussian”'' distribution.

Results:

Parametric survival analysis models were able to accurately estimate median survival times in a population‐based data set of 15,703 individuals, even for distributions that were not good fits and the censoring rate was high, due to the central limit theorem.

Conclusions:

Parametric survival models are able to provide more direct answers, and in our analysis of an obesity‐related data set, gave consistent YLL estimates regardless of the distribution used. We recommend increased consideration of parametric survival models in chronic disease and risk factor epidemiology.     

Conditionally in Bivariate Generalized Poisson Distributions

Three types of bivariate generalized Poisson distributions are defined and the structure of their conditional distributions is examined by using the Faa Di Bruno's formula. The resulting expressions involve Bell polynomials and can be interpreted in terms of convoluted random variables with one of the convolutes having the form of the marginal distribution. The three types of bivariate Neyman A distributions are used to illustrate the procedure.     

A Variation of the Method of Translation to Generate Bivariate and Multivariate Survival Distributions with Competing Risk or Reliability Applications

In the present paper, a variation of the methode of translation is discussed to generate bivariate or multivariate survival distributions starting a given bivariate or multivariate distribution which is not necessarily a life distribution. The new distribution has been called the dual of the given distribution. The duals of several bivariate and multivariate famílies of distributions are obtained, such as FRECHET'S , FARLIE -GUMBEL -MORGENSTERN'S , MARDIA'S and PLACKETT'S , among others. A necessary and sufficient condition is given for a bivariate distribution to be its own dual. Thus the present paper generates several survival distributions in addition to what are already available in the literature. These have important applications in competing risk theory or reliability of engineering systems.     

Characterization of genomic imprinting effects and patterns with parametric accelerated failure time model

Genomic imprinting, a genetic phenomenon of non-equivalent allele expression that depends on parental origins, has been ubiquitously observed in nature. It does not only control the traits of growth and development but also may be responsible for survival traits. Based on the accelerated failure time model, we construct a general parametric model for mapping the imprinted QTL (iQTL). Within the framework of interval mapping, maximum likelihood estimation of iQTL parameters is implemented via EM algorithm. The imprinting patterns of the detected iQTL are statistically tested according to a series of null hypotheses. BIC model selection criterion is employed to choose an optimal baseline hazard function with maximum likelihood and parsimonious parameters. Simulations are used to validate the proposed mapping procedure. A published dataset from a mouse model system was used to illustrate the proposed framework. Results show that among the five commonly used survival distributions, Log-logistic distribution is the optimal baseline hazard function for mapping QTL of hyperoxic acute lung injury (HALI) survival; under the log-logistic distribution, four QTLs were identified, in which only one QTL was inherited in Mendelian fashion, whereas others were imprinted in different imprinting patterns.     

采用广义加法模型整合数字高程模型和遥感数据进行植被分布预测

为了采用广义加法模型整合数字高程模型和遥感数据进行植被分布的预测, 并探索耦合环境变量和遥感数据作为预测变量是否能够有效地提高植被分布预测的精度, 选择海拔、坡度、至黄河最近距离、至海岸线最近距离, 以及从SPOT5遥感影像中提取的光谱变量作为预测变量, 采用广义加法模型整合环境变量和光谱变量, 建立植被分布预测模型。研究设置3种建模情景(以环境变量作为预测变量, 以光谱变量作为预测变量, 综合使用环境变量与光谱变量作为预测变量)对黄河三角洲的优势植被类型的分布进行了预测, 并对预测结果采用偏差分析、受试者工作特征曲线和野外采样点对比等3种方法进行了验证。结果表明: (1)基于广义加法模型的植被分布预测方法具有一定的实用性, 可以较为准确地预测植被的分布; 盖度较高的植被类型预测精度较高, 盖度较低的植被类型预测精度较低, 植物群落结构的特点是出现这些差异的主要原因; 综合使用环境变量和光谱变量作为预测变量的模型, 预测精度高于单独以环境变量或者光谱变量作为预测变量的模型。(2)环境变量、光谱变量大多被选入模型, 二者均对植被分布预测有重要的作用; 同一预测变量在不同植被类型的预测模型中的贡献不同, 这与植被的光谱、环境特征差异有关; 同一预测变量在不同的建模情景下对模型的贡献不同, 环境变量与光谱变量的耦合效应可能是导致预测变量对模型的贡献出现变化的原因。     

An alternative approach to generalized complementarity

An interaction viewpoint is defined for looking at natural systems. This viewpoint is seen to be connected with quantum mechanical uncertainty and measurement theory. A connection is then shown between quantum mechanical uncertainty and the workability of Grunbaüm's “infinity machines”. Finally the workability of infinity machines is related to Elsasser's “generalized complementarity”. The net result is to show that generalized complementarity is not distinct from complementarity in atomic physics but has its roots in the same place, i.e. quantum mechanical measurement theory. A model system which permits some quantification of these notions is presented.     

A statistical model for red blood cell survival

A statistical model for the survival time of red blood cells (RBCs) with a continuous distribution of cell lifespans is presented. The underlying distribution of RBC lifespans is derived from a probability density function with a bathtub-shaped hazard curve, and accounts for death of RBCs due to senescence (age-dependent increasing hazard rate) and random destruction (constant hazard), as well as for death due to initial or delayed failures and neocytolysis (equivalent to early red cell mortality). The model yields survival times similar to those of previously published studies of RBC survival and is easily amenable to inclusion of drug effects and haemolytic disorders.