Zero-inflated Poisson models with measurement error in the response

Zero-inflated count data arise frequently from genomics studies. Analysis of such data is often based on a mixture model which facilitates excess zeros in combination with a Poisson distribution, and various inference methods have been proposed under such a model. Those analysis procedures, however, are challenged by the presence of measurement error in count responses. In this article, we propose a new measurement error model to describe error-contaminated count data. We show that ignoring the measurement error effects in the analysis may generally lead to invalid inference results, and meanwhile, we identify situations where ignoring measurement error can still yield consistent estimators. Furthermore, we propose a Bayesian method to address the effects of measurement error under the zero-inflated Poisson model and discuss the identifiability issues. We develop a data-augmentation algorithm that is easy to implement. Simulation studies are conducted to evaluate the performance of the proposed method. We apply our method to analyze the data arising from a prostate adenocarcinoma genomic study.     

A Poisson model of sequence comparison and its application to coronavirus phylogeny

In this paper, we propose two metrics to compare DNA and protein sequences based on a Poisson model of word occurrences. Instead of comparing the frequencies of all fixed-length words in two sequences, we consider (1) the probability of ‘generating’ one sequence under the Poisson model estimated from the other; (2) their different expression levels of words. Phylogenetic trees of 25 viruses including SARS-CoVs are constructed to illustrate our approach.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models

Variance components for five consecutive measurements of body weight in Polish sheep were estimated using random regression and multi-trait animal models. The data included between 7856 and 31694 body weight records at 5 age classes from birth to 150 days of age. The random additive genetic, maternal environmental and individual permanent environmental effects were fitted. All variance components were increasing over time (not at equal rates), which reflects increasing phenotypic mean and variance with age. Direct heritability tended to increase with age, whereas the effect of dam was reduced for older ages, and the proportion of permanent environmental component was relatively stable. Generally, similar tendencies were registered for estimates obtained via multi-trait animal model. The results confirm that there is a scope for genetic improvement in growth pattern in Polish sheep.     

Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease

This paper presents a Bayesian analysis of a time series of counts to assess its dependence on an explanatory variable. The time series represented is the incidence of the infectious disease ESBL-producing Klebsiella pneumoniae in an Australian hospital and the explanatory variable is the number of grams of antibiotic (third generation) cephalosporin used during that time. We demonstrate that there is a statistically significant relationship between disease occurrence and use of the antibiotic, lagged by three months. The model used is a parameter-driven model in the form of a generalized linear mixed model. Comparison of models is made in terms of mean square error.     

不同模型对拟合大兴安岭林火发生与气象因素关系的适用性

选用符合林火发生数据结构的Poisson和零膨胀Poisson(ZIP)模型对大兴安岭林区1980—2005年间林火发生与气象因素关系进行建模分析,并与普通最小二乘回归(ordinary least squares,OLS)方法的结果进行了对比分析.结果表明:OLS模型对研究区域林火发生与气象因素关系的拟合结果较差(R2=0.215);Poisson和ZIP模型的拟合效果较好,具有较好的火灾次数预测能力,且ZIP模型的预测能力高于Poisson模型.运用AIC和Vuong检验方法对Poisson和ZIP模型的拟合水平进行进一步检验,表明ZIP模型的数据拟合度优于Poisson模型.     

Identification of partially linear structure in additive models with an application to gene expression prediction from sequences

The additive model is a semiparametric class of models that has become extremely popular because it is more flexible than the linear model and can be fitted to high-dimensional data when fully nonparametric models become infeasible. We consider the problem of simultaneous variable selection and parametric component identification using spline approximation aided by two smoothly clipped absolute deviation (SCAD) penalties. The advantage of our approach is that one can automatically choose between additive models, partially linear additive models and linear models, in a single estimation step. Simulation studies are used to illustrate our method, and we also present its applications to motif regression.     

Hemodynamic and electroencephalographic effects of epidural buprenorphine during orthopedic hindlimb surgery in sheep: A comparison with intramuscular buprenorphine and epidural saline

Epidural opioids exert segmentally limited spinal analgesia by acting at dorsal horn neurons. While the spinal cord may be the predominant site of action for hydrophilic opioids such as morphine, initial supraspinal effects have been suggested for lipophilic opioids such as buprenorphine. In view of significant systemic effects, the value of epidural administration of lipophilic opioids in human patients has been questioned. Since epidural buprenorphine may be beneficial for hindlimb surgeries in sheep, intraoperative hemodynamic and central nervous effects were evaluated. In a prospective, randomized, and placebo-controlled study, 15 adult sheep anesthetized for cranial cruciate ligament reconstruction were treated with either epidural buprenorphine (5 μg/kg, n = 5), intramuscular buprenorphine (5 μg/kg, n = 5), or epidural saline (0.15 ml/kg, n = 5) preoperatively. Heart rate, arterial blood pressures and the electroencephalographic variables /δ ratio, α/δ ratio, β/δ ratio, median power frequency (MED), and 80% spectral edge frequency were recorded before and immediately after skin incision and during drilling a tunnel through the tibia bone. Arterial pressures after epidural buprenorphine were significantly lower compared with epidural saline but were quite similar to intramuscular buprenorphine before skin incision. Mean EEG /δ ratios and MED values following epidural and intramuscular buprenorphine were significantly lower compared with epidural saline but quite similar for the two buprenorphine groups during drilling. In conclusion, similar hemodynamic and electroencephalographic effects of epidural and intramuscular buprenorphine suggest systemic effects of epidural buprenorphine in sheep.     

A comparison of absolute performance of different correlative and mechanistic species distribution models in an independent area

To investigate the comparative abilities of six different bioclimatic models in an independent area, utilizing the distribution of eight different species available at a global scale and in Australia. Global scale and Australia. We tested a variety of bioclimatic models for eight different plant species employing five discriminatory correlative species distribution models (SDMs) including Generalized Linear Model (GLM), MaxEnt, Random Forest (RF), Boosted Regression Tree (BRT), Bioclim, together with CLIMEX (CL) as a mechanistic niche model. These models were fitted using a training dataset of available global data, but with the exclusion of Australian locations. The capabilities of these techniques in projecting suitable climate, based on independent records for these species in Australia, were compared. Thus, Australia is not used to calibrate the models and therefore it is as an independent area regarding geographic locations. To assess and compare performance, we utilized the area under the receiver operating characteristic (ROC) curves (AUC), true skill statistic (TSS), and fractional predicted areas for all SDMs. In addition, we assessed satisfactory agreements between the outputs of the six different bioclimatic models, for all eight species in Australia. The modeling method impacted on potential distribution predictions under current climate. However, the utilization of sensitivity and the fractional predicted areas showed that GLM, MaxEnt, Bioclim, and CL had the highest sensitivity for Australian climate conditions. Bioclim calculated the highest fractional predicted area of an independent area, while RF and BRT were poor. For many applications, it is difficult to decide which bioclimatic model to use. This research shows that variable results are obtained using different SDMs in an independent area. This research also shows that the SDMs produce different results for different species; for example, Bioclim may not be good for one species but works better for other species. Also, when projecting a “large” number of species into novel environments or in an independent area, the selection of the “best” model/technique is often less reliable than an ensemble modeling approach. In addition, it is vital to understand the accuracy of SDMs' predictions. Further, while TSS, together with fractional predicted areas, are appropriate tools for the measurement of accuracy between model results, particularly when undertaking projections on an independent area, AUC has been proved not to be. Our study highlights that each one of these models (CL, Bioclim, GLM, MaxEnt, BRT, and RF) provides slightly different results on projections and that it may be safer to use an ensemble of models.     

Model selection and parameter estimation for ion channel recordings with an application to the K + outward-rectifier in barley leaf

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K⁺ outward-rectifier in barley leaf.Acknowledgement The authors thank Sake Vogelzang, Bert van Duijn and Bert de Boer for their helpful advice and useful comments and suggestions.     

A codon-based model of host-specific selection in parasites,with an application to the influenza A virus

Parasites sometimes expand their host range by acquiring a new host species. After a host change event, the selective regime acting on a given parasite gene may change as a result of host-specific adaptive alterations of protein functionality or host-specific immune-mediated selection. We present a codon-based model that attempts to include these effects by allowing the position-specific substitution process to change in conjunction with a host change event. Following maximum-likelihood parameter estimation, we employ an empirical Bayesian procedure to identify candidate sites potentially involved in host-specific adaptation. We discuss the applicability of the model to the more general problem of ascertaining whether the selective regime differs in two groups of related organisms. The utility of the model is illustrated on a data set of nucleoprotein sequences from the influenza A virus obtained from avian and human hosts.     

A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies

We study a system of partial differential equations which models the disease transmission dynamics of schistosomiasis. The model incorporates both the definitive human hosts and the intermediate snail hosts. The human hosts have an age-dependent infection rate and the snail hosts have an infection-age-dependent cercaria releasing rate. The parasite reproduction number R is computed and is shown to determine the disease dynamics. Stability results are obtained via both analytic and numerical studies. Results of the model are used to discuss age-targeted drug treatment strategies for humans. Sensitivity and uncertainty analysis is conducted to determine the role of various parameters on the variation of R. The effects of various drug treatment programs on disease control are compared in terms of both R and the mean parasite load within the human hosts.     

Maternal and paternal genetic diversity of ancient sheep in Estonia from the Late Bronze Age to the post‐medieval period and comparison with other regions in Eurasia

Sheep were among the first domesticated animals to appear in Estonia in the late Neolithic and became one of the most widespread livestock species in the region from the Late Bronze Age onwards. However, the origin and historical expansion of local sheep populations in Estonia remain poorly understood. Here, we analysed fragments of the hypervariable D‐loop of mitochondrial DNA (mtDNA; 213 bp) and the Y‐chromosome SRY gene (130 bp) extracted from 31 archaeological sheep bones dated from approximately 800 BC to 1700 AD. The ancient DNA data of sheep from Estonia were compared with ancient sheep from Finland as well as a set of contemporary sheep breeds from across Eurasia in order to place them in a wider phylogeographical context. The analysis shows that: (i) 24 successfully amplified and analysed mtDNA sequences of ancient sheep cluster into two haplogroups, A and B, of which B is predominant; (ii) four of the ancient mtDNA haplotypes are novel; (iii) higher mtDNA haplotype diversity occurred during the Middle Ages as compared to other periods, a fact concordant with the historical context of expanding international trade during the Middle Ages; (iv) the proportion of rarer haplotypes declined during the expansion of sheep from the Near Eastern domestication centre to the northern European region; (v) three male samples showed the presence of the characteristic northern European haplotype, SNP G‐oY1 of the Y‐chromosome, and represent the earliest occurrence of this haplotype. Our results provide the first insight into the genetic diversity and phylogeographical background of ancient sheep in Estonia and provide basis for further studies on the temporal fluctuations of ancient sheep populations.     

A model to predict the presence of longfin eels in some New Zealand streams, with particular reference to riparian vegetation and elevation

Two logistic regression models were developed from a database of 27 biotic and physicochemical variables for 99 sites in the Taieri River, New Zealand, to predict the probability of occurrence of longfin eels. Average depth was associated positively with eels while woody debris and oxygen concentration were negatively associated. At a macro-scale probability of eel occurrence declined with increasing elevation and, for a given elevation, was higher in tussock and pasture catchments and lower in pine and native forest settings. Using a separate fish database for the Taieri River this macro-scale model predicted eel presence 95·4% in agreement with observation. A map was generated from the model showing areas of predicted high, moderate and low probabilities of eel occurrence. The model also estimated the minimum total number of eels present in the Taieri River catchment (excluding lakes, and streams below 100 m and above 1000 m) as 20 865 (95% CL: 10 560-36 350).     

Modelling stomatal conductanceof field-grown sunflower under varying soil water content and leafenvironment: comparison of three models of stomatal response toleaf environment and coupling with an abscisic acid-based modelof stomatal response to soil drying

Stomatal conductance, g_s, responds both tothe immediate or local environment of the leaf, such as CO₂ partialpressure and irradiance, and to root‐sourced signals of water stress,particularly abscisic acid (ABA). Two models for the combined controlof g_s were formulated and tested in sunflower(Helianthus annuus). First, several empirical models weretested for the local control, demonstrating that the Ball–Berrymodel [Ball, Woodrow & Berry (in Progress in PhotosynthesisResearch Vol. 4, pp. 5.221–5.224: M. Nijhoff,Dordrecht, The Netherlands) 1987] is consistently amongthe most accurate. A problem of statistical non‐independence inthis model is shown to be minor. The model offers regularity ofparameter values among most species and, despite an oversimplicationin representing known humidity‐response mechanisms, it incorporates othersignalling loops from CO₂ and assimilation. In the firstcombined model, ABA as its concentration in xylem sap, [ABA]_xy,down‐regulates the slope, m, in the Ball–Berry modelby the factor g_fac = exp(– β[ABA]_xy).The ABA‐induced reduction in g_s decreases CO₂ assimilation andsurface humidity, thus appearing to induce the local‐control mechanismto amplify the ABA‐induced stomatal closure. In the second combinedmodel, g_s is estimated as the minimum of the local(Ball–Berry) response and the product g_fac g_s,max,with g_s,max as a maximal unstressed conductance.Both models can predict g_s from the external environmentalvariables with good accuracy (r² near 0·8 over20‐fold variations in g_s). Further analyses showthat g_s responds to humidity almost quadraticallyrather than linearly. It also responds to assimilation as a powerlaw with an exponent that is significantly less than 1. These limitations,shared by other models, suggest more research into biochemical signalling.     

Structure model of core proteins in photosystem I inferred from the comparison with those in photosystem II and bacteria; an application of principal component analysis to detect the similar regions between distantly related families of proteins.

A principal component analysis based on the physico-chemical properties of amino acid residues is developed to assign similar regions between distantly related families of proteins, taking account of the species diversities in respective families. The most important advantage of this analysis should be that it reflects different physico-chemical properties and thus can predict more detailed structural properties, including the transmembrane helices, than the hydropathy analysis. Its first application reconfirms the similarity between the core proteins of photosynthetic reaction center in purple bacteria and those of photosystem II, indicating that the low percentage of identical amino acid residues estimated previously between them is due to much allowance for amino acid substitutions in purple bacteria. The application of this analysis to the core proteins of photosystem I reveals that any of these proteins includes two domains, each showing high similarity to the amino acid sequences of core proteins in photosystem II and purple bacteria. A core structure model of A1 and A2 proteins folded into four layers of sheets of transmembrane helices is proposed to provide a molecular basis for the electron pathway suggested by spectroscopic experiments as well as for the interaction sites with plastocyanin, 9 kDa protein and LHC proteins.     

A comparison between aerobic growth of Bacillus licheniformis in continuous culture and partial-recycling fermentor,with contributions to the discussion on maintenance energy demand

Energy costs of biomass synthesis are relatively higher at low than at high specific growth rates () because of an increased protein content of the cell and increased costs of protein synthesis as such at low values. A comparison of aerobic, glucose limited cultures of Bacillus licheniformis in a chemostat and in a partial-recycling fermentor indicated that pulse-wise nutrient addition increased the maintenance energy demand (m). In the chemostat experiments, we also found a striking deviation from linearity between substrate consumption and , with large implications for the maintenance coefficient. The deviation is mainly due to a large shift in metabolic carbon flows at specific growth rates between 50 and 100% of _max. At those growth rates, uncoupled growth occurs, presumably as a necessary condition for faster growth, since uncoupling results in a faster energysupply for biosynthetic purposes.The maintenance coefficient as determined by chemostat studies should be regarded as a compounds parameter, constituted of maintenance energy demands like ppGpp accumulation, variable costs of mRNA and protein accumulation, kinetic proofreading etc. and influenced by fermentor operation parameters like the substrate addition rate; moreover, both constancy of m and a linear relation between m and appear quite unlikely.     

Patch-clamp studies on the anomalous mole fraction effect of the K+ channel in cytoplasmic droplets ofNitella: An attempt to distinguish between a multi-ion single-file pore and an enzyme kinetic model with lazy state

Summary Patch-clamp studies have been employed in order to check whether the assumption of a multi-ion single-file pore is necessary for the explanation of the anomalous mole fraction effect or whether this effect can also be explained by a single-barrier enzyme kinetic model. Experiments in the cell-attached configuration were done on the tonoplast membrane of cytoplasmic droplets ofNitella in solutions containing 150 mol m^–3 of K⁺ plus Tl⁺ with seven different K⁺/Tl⁺ ratios. At first sight, the results seem to support the multi-ion single-file pore, because apparent open channel conductivity displays the anomalous mole fraction effect, whereas open-probability has not been found to be dependent on the K⁺/Tl⁺ ratio. Changes in open probability would be expected for a single-barrier enzyme kinetic model with a lazy state. On the other hand, the lazy-state model is more successful in explaining the measuredI-V curves. The entire slope of the apparent open channel current-voltage curves rotates with changing K⁺/Tl⁺ ratios in the whole voltage range between –100 and + 80 mV. Numerical calculations on the basis of multi-ion single-file pores could create the anomalous mole fraction effect only in a limited voltage range with intersectingI-V curves. The apparent absence of an effect on open probability which is postulated by the lazy-state model can be explained if switching into and out of the lazy state is faster than can be resolved by the temporal resolution of 1 msec.