A class of Bayesian shared gamma frailty models with multivariate failure time data

For multivariate failure time data, we propose a new class of shared gamma frailty models by imposing the Box-Cox transformation on the hazard function, and the product of the baseline hazard and the frailty. This novel class of models allows for a very broad range of shapes and relationships between the hazard and baseline hazard functions. It includes the well-known Cox gamma frailty model and a new additive gamma frailty model as two special cases. Due to the nonnegative hazard constraint, this shared gamma frailty model is computationally challenging in the Bayesian paradigm. The joint priors are constructed through a conditional-marginal specification, in which the conditional distribution is univariate, and it absorbs the nonlinear parameter constraints. The marginal part of the prior specification is free of constraints. The prior distributions allow us to easily compute the full conditionals needed for Gibbs sampling, while incorporating the constraints. This class of shared gamma frailty models is illustrated with a real dataset.     

塔里木荒漠河岸林灰胡杨群落最小面积确定与研究方法比较

荒漠河岸林是塔里木极端干旱区唯一的森林群落类型,群落结构组成简单。我们采用种-面积曲线、群落系数-面积曲线与重要值-面积曲线3种方法对塔里木河上游荒漠河岸林灰胡杨（Populus pruinosa Schrenk）群落最小面积进行研究。结果显示,4种饱和种-面积曲线的拟合效果差异明显,S=aA/（1+bA）和S=a（1-e^-bA）模型拟合的相关系数较高（P < 0.01）,拟合效果优于其它2种模型。当取样面积为100 m²时,可包括群落60%~80%的物种数,取样面积为200 m²时,则可包括群落90%的物种数。群落系数-面积曲线与重要值-面积曲线2种方法确定的群落最小面积均为400 m²,二者克服了种-面积曲线仅关注物种出现与否和饱和种的估算问题,拟合结果更符合实际情况,更适用于塔里木荒漠河岸林最小取样面积的确定。本研究结果表明荒漠河岸林包括60%、80%、90%群落物种的临界抽样面积分别为100 m²、200 m²和400 m ²,可以满足不同研究精度的要求;塔里木河上游荒漠河岸林灰胡杨群落学调查的最适取样面积是400 m²。     

Empirical evaluation of a prior for Bayesian phylogenetic inference

The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the large-sample properties of Bayesian model selection and its sensitivity to the prior when several of the models under comparison are nearly equally correct (or nearly equally wrong) and are of the same dimension. A previous suggestion to alleviate the problem is to let the internal branch lengths in the tree become increasingly small in the prior with the increase in the data size so that the bifurcating trees are increasingly star-like. In particular, if the internal branch lengths are assigned the exponential prior, the prior mean mu0 should approach zero faster than 1/square root n but more slowly than 1/n, where n is the sequence length. This paper examines the usefulness of this data size-dependent prior using a dataset of the mitochondrial protein-coding genes from the baleen whales, with the prior mean fixed at mu0=0.1n(-2/3). In this dataset, phylogeny reconstruction is sensitive to the assumed evolutionary model, species sampling and the type of data (DNA or protein sequences), but Bayesian inference using the default prior attaches high PPs for conflicting phylogenetic relationships. The data size-dependent prior alleviates the problem to some extent, giving weaker support for unstable relationships. This prior may be useful in reducing apparent conflicts in the results of Bayesian analysis or in making the method less sensitive to model violations.     

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

In many cell types, the inositol trisphosphate receptor (IPR) is one of the important components that control intracellular calcium dynamics, and an understanding of this receptor (which is also a calcium channel) is necessary for an understanding of calcium oscillations and waves. Recent advances in experimental techniques now allow for the measurement of single-channel activity of the IPR in conditions similar to its native environment, and these data can be used to determine the rate constants in Markov models of the IPR. We illustrate a parameter estimation method based on Markov chain Monte Carlo, which can be used to fit directly to single-channel data, and determining, as an intrinsic part of the fit, the times at which the IPR is opening and closing. We show, using simulated data, the most complex Markov model that can be unambiguously determined from steady-state data and show that non-steady-state data is required to determine more complex models.     

Quantifying and comparing the predictive accuracy of continuous prognostic factors for binary outcomes

The positive and negative predictive values are standard ways of quantifying predictive accuracy when both the outcome and the prognostic factor are binary. Methods for comparing the predictive values of two or more binary factors have been discussed previously (Leisenring et al., 2000, Biometrics 56, 345-351). We propose extending the standard definitions of the predictive values to accommodate prognostic factors that are measured on a continuous scale and suggest a corresponding graphical method to summarize predictive accuracy. Drawing on the work of Leisenring et al. we make use of a marginal regression framework and discuss methods for estimating these predictive value functions and their differences within this framework. The methods presented in this paper have the potential to be useful in a number of areas including the design of clinical trials and health policy analysis.     

Ancestral inference on gene trees under selection

The extent to which natural selection shapes diversity within populations is a key question for population genetics. Thus, there is considerable interest in quantifying the strength of selection. A full likelihood approach for inference about selection at a single site within an otherwise neutral fully linked sequence of sites is described here. A coalescent model of evolution is used to model the ancestry of a sample of DNA sequences which have the selected site segregating. The mutation model, for the selected and neutral sites, is the infinitely many-sites model where there is no back or parallel mutation at sites. A unique perfect phylogeny, a gene tree, can be constructed from the configuration of mutations on the sample sequences under this model of mutation. The approach is general and can be used for any bi-allelic selection scheme. Selection is incorporated through modelling the frequency of the selected and neutral allelic classes stochastically back in time, then using a subdivided population model considering the population frequencies through time as variable population sizes. An importance sampling algorithm is then used to explore over coalescent tree space consistent with the data. The method is applied to a simulated data set and the gene tree presented in Verrelli et al. (2002).     

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics.     

Parameter inference for an individual based model of chytridiomycosis in frogs

Individual based models (IBMs) and Agent based models (ABMs) have become widely used tools to understand complex biological systems. However, general methods of parameter inference for IBMs are not available. In this paper we show that it is possible to address this problem with a traditional likelihood-based approach, using an example of an IBM developed to describe the spread of chytridiomycosis in a population of frogs as a case study. We show that if the IBM satisfies certain criteria we can find the likelihood (or posterior) analytically, and use standard computational techniques, such as MCMC, for parameter inference.     

Novel bis-, tris-, and tetrakis-tertiary amino analogs as antagonists at neuronal nicotinic receptors that mediate nicotine-evoked dopamine release

A series of tertiary amine analogs derived from lead azaaromatic quaternary ammonium salts has been designed and synthesized. The preliminary structure-activity relationships of these new analogs suggest that such tertiary amine analogs, which potently inhibit nicotine-evoked dopamine release from rat striatum, represent drug-like inhibitors of α6-containing nicotinic acetylcholine receptors. The bis-tertiary amine analog 7 exhibited an IC₅₀ of 0.95 nM, while the tris-tertiary amine analog 19 had an IC₅₀ of 0.35 nM at nAChRs mediating nicotine-evoked dopamine release.