Use of the beta-binomial distribution in dominant-lethal testing for “weak mutagenic activity”: Part 2

Experiments in Dominant-Lethal Testing have been simulated on the computer to estimate the type I error rates and the power of the Beta-Binomial test under various models. (1) The mating ratio is one; and p, the probability that an implant will die, is distributed over the couples. (2) The mating ratio is larger than one; and p is distributed over the males, the females mated to the same male being binomial observations of the value p supplied by the male. (3) The mating ratio is larger than one; and p is distributed over the females.The average rates of dead implants have been set at 0.08 and 0.10 for the control and treatment groups, respectively, and a nominal level of significance equal to 0.05 has been chosen. The type I error rate of the traditional chi-square test has also been estimated.A by-product of these simulations is the behaviour of the estimates α̌ and β̌ of the beta-distribution parameters, which discloses that, in the actual experiments with mice, p is distributed over the females.Our results lead to the recommendations that, for a given number of animals per group, a mating ratio larger than one should be adopted and that the males should be considered as the experimental units for the calculations. With 300 and 450 animals per group, average powers of 0.72 and 0.85 are reached, respectively, for the chosen increment of 2% in the rate of dead implants.Under these models, the type I error rate of the traditional chi-square test may grow to 0.30 for the nominal level of 0.05.     

COMPARISON OF METHODS FOR ANALYZING REPLICATED PREFERENCE TESTS

Preference testing is commonly used in consumer sensory evaluation. Traditionally, it is done without replication, effectively leading to a single 0/1 (binary) measurement on each panelist. However, to understand the nature of the preference, replicated preference tests are a better approach, resulting in binomial counts of preferences on each panelist. Variability among panelists then leads to overdispersion of the counts when the binomial model is used and to an inflated Type I error rate for statistical tests of preference. Overdispersion can be adjusted by Pearson correction or by other models such as correlated binomial or beta‐binomial. Several methods are suggested or reviewed in this study for analyzing replicated preference tests and their Type I error rates and power are compared. Simulation studies show that all methods have reasonable Type I error rates and similar power. Among them, the binomial model with Pearson adjustment is probably the safest way to analyze replicated preference tests, while a normal model in which the binomial distribution is not assumed is the easiest.     

Use of compound-probability distributions in the study of induced post-implantation dominant lethals

The nature of the probability distribution of post-implantation dominant lethality was investigated in terms of the distribution of dead implants per female. It has been postulated that this distribution would be poisson in a control series of females but may follow a compound or a contagious distribution such as the beta binomial, negative binomial or Neyman type A in the treated series of females. The nature of these compound distributions for fitting mammalian mutagenicity has been examined. The implications of the results on the estimation of induced mutation rates are discussed.     

CANOES: detecting rare copy number variants from whole exome sequencing data

We present CANOES, an algorithm for the detection of rare copy number variants from exome sequencing data. CANOES models read counts using a negative binomial distribution and estimates variance of the read counts using a regression-based approach based on selected reference samples in a given dataset. We test CANOES on a family-based exome sequencing dataset, and show that its sensitivity and specificity is comparable to that of XHMM. Moreover, the method is complementary to Gaussian approximation-based methods (e.g. XHMM or CoNIFER). When CANOES is used in combination with these methods, it will be possible to produce high accuracy calls, as demonstrated by a much reduced and more realistic de novo rate in results from trio data.     

A Multinomial Model for the Quality Control of Colony Counting Procedures

The so‐called good‐laboratory‐practice (GLP) test provides an experimental design and appropriate statistical analysis for the problem of analyst performance assessment in microbiological laboratories. For a given sample material multiple dilution series are generated yielding colony counts from several dilution levels. Statistical evaluation is based on the assumption of Poisson‐distributed colony forming units. In this paper a new model based on conditional binomial and multinomial distributions is presented and it is shown how it is related to the standard model which assumes Poisson‐distributed colony counts. The effects of common working errors on the statistical evaluation of the GLP‐test are investigated.     

Testing transition rates in generalized binomial models

In toxicological experiments the type II error is of important interest, but it is seldom discussed. For certain experiments like those in reproduction toxicology this paper gives some ideas to calculate it analytically. The basis is a generalized binomial model describing transition processes in experimental units. Each experimental unit contains a set of × members which develop from one to another specified state with some probability P. This transition probability P is allowed to vary from one experimental unit to the other; there is no restriction on the distribution of P and X, nor is P assumed to be independent of the total number × in contrast to the commonly used models. The model is extended to describe the treatment of an experimental unit, which permits to separate the treatment effect from the spontaneous development. This allows to investigate the power of some statistical tests for calculating sample sizes and for comparing different experimental designs.     

An estimator of the mutant frequency in assays using transgenic animals

The Poisson distribution is a fundamental probability model for count data, and is a natural model for the observed plaque counts in mutation assays using animals with lambda or PhiX174 transgenes. The Poisson likelihood for observed counts is a function of the mutant fraction, and it is straightforward to derive the associated maximum likelihood estimate of the mutant fraction and its variance. The estimate is easy to calculate, and if not the same, very similar to ad hoc estimates in current use. The model indicates the proper way to combine data from a number of plates, possibly prepared with different sample dilutions. The estimator of the mutant fraction is biased as a consequence of dividing by a random variable, the plaque count used to calculate the total recovered plaque-forming units. Fortunately, the bias becomes negligible as this count becomes large. On the other hand, increasing this count can increase the variance by decreasing the amount of sample assayed for mutant phages. Concurrent heed to the bias and the variance provides some guidance as to the optimum allocation of a sample into portions assayed for mutant phages and total recovered phages. The distribution of the estimate of the mutant fraction is related to the binomial distribution. This relationship implies a binomial distribution for the mutant count conditional on an overall count (either the sum of mutant and counted total plaques or the sum of counted mutant and non-mutant plaques). A special but important case occurs when each plate can be evaluated for mutant plaques and non-mutant plaques. Then, the observed proportion of mutants estimates the mutant fraction. More generally, the relationship to a binomial distribution provides a procedure for calculating a confidence interval.     

Nonbinomial distributions of relative neurite outgrowth in PC-12 cells

Previously we reported the results of a series of experimental tests using PC-12 cells to examine the biological effects of prescribed combinations of both nerve growth factor and magnetic fields. Because our assay of the PC-12 cells is based on a binary classification of the cells following treatment, our data might be expected to have a binomial distribution. However, our data consistently show a smaller variability than that predicted by the binomial distribution model. In this paper, we examine some possible reasons for this reduction in variability in our results. © 1996 Wiley-Liss, Inc.     

Estimating forest habitat complexity in relation to time since fire

Forest structure does not form an even distribution over forested landscapes; rather, it produces a mosaic or patchwork pattern. ‘Habitat complexity scores’ provide a method of describing changes in vegetation biomass and, when assessed at randomly located plots, a frequency distribution of habitat can be developed. The frequency distribution can be used to describe characteristics of the pattern of habitat complexity, such as the mean and heterogeneity of habitat over the whole forest. In the present paper, an historical sequence of habitat complexity scores collected from 99 sites over an 18‐year period was used. The frequency distribution of the habitat complexity scores was fitted using a binomial distribution and the parameters of the binomial distribution were modelled to provide a relationship between the frequency of different habitat environments across the landscape and the time since wildfire. In most cases, the binomial distributions fitted the observed data significantly. The relationship between the binomial parameters and the time since fire was found to be highly significant (P < 0.01). Habitat complexity scores were predicted from the model solely as a function of time since fire, allowing both retrospective and future predictions of the distribution of habitats to be undertaken.     

Binomial sampling to estimate rust mite (Acari: Eriophyidae) densities on orange fruit

Binomial sampling based on the proportion of samples infested was investigated for estimating mean densities of citrus rust mite, Phyllocoptruta oleivora (Ashmead), and Aculops pelekassi (Keifer) (Acari: Eriophyidae), on oranges, Citrus sinensis (L.) Osbeck. Data for the investigation were obtained by counting the number of motile mites within 600 sample units (each unit a 1-cm2 surface area per fruit) across a 4-ha block of trees (32 blocks total): five areas per 4 ha, five trees per area, 12 fruit per tree, and two samples per fruit. A significant (r2 = 0.89), linear relationship was found between ln(-ln(1 -Po)) and ln(mean), where P0 is the proportion of samples with more than zero mites. The fitted binomial parameters adequately described a validation data set from a sampling plan consisting of 192 samples. Projections indicated the fitted parameters would apply to sampling plans with as few as 48 samples, but reducing sample size resulted in an increase of bootstrap estimates falling outside expected confidence limits. Although mite count data fit the binomial model, confidence limits for mean arithmetic predictions increased dramatically as proportion of samples infested increased. Binomial sampling using a tally threshold of 0 therefore has less value when proportions of samples infested are large. Increasing the tally threshold to two mites marginally improved estimates at larger densities. Overall, binomial sampling for a general estimate of mite densities seemed to be a viable alternative to absolute counts of mites per sample for a grower using a low management threshold such as two or three mites per sample.     

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model

On the basis of experimental observations, this paper develops two well-defined mathematical models for the level of activity of Pharaoh’s ants within their nesting area, with the aim of providing a more general understanding of animal activity. Under specific conditions, we observe that the activity of ants within their nesting area appears to show no dependence on their density. Making the assumption that all ants move independently of one another, this behaviour can be mathematically modelled as a random process based on the binomial distribution. Developing the model on this basis allows an exponential distribution to be exposed that underlies the time-intervals between ants leaving the nesting area. Such a distribution is present, irrespective of whether the ant population in the nesting area remains constant or steadily depletes, and suggests that ant-ant interactions do not play any significant role in determining ant activity under the experimental conditions adopted.The mathematical framework presented plays the role of a null model that will have a wide range of applications for detecting other determinants of activity-level (not addressed in this study) including environmental and social factors such as food availability, temperature, humidity, presence of pheromone trails, along with intraspecific and interspecific interactions outside the nest and, indeed, more generally. The null model should have applications to a range of organisms.Lastly, we discuss our data in relation to a recent study of ants leaving their nest (Richardson et al., 2010) in which the null model was rejected in favour of record dynamics, where ant-ant interactions were conjectured to play a role.     

Electrochemical disinfection of dental implants--a proof of concept

Background

Peri-implantitis has gained significant clinical attention in recent years. This disease is an inflammatory reaction to microorganisms around dental implants. Due to the limited accessibility, non-invasive antimicrobial strategies are of high interest. An unexpected approach to implant disinfection may evolve from electrolysis. Given the electrical conductivity of titanium implants, alkalinity or active oxidants can be generated in body fluids. We investigated the use of dental titanium implants as electrodes for the local generation of disinfectants. Our hypothesis was that electrolysis can reduce viable counts of adhering bacteria, and that this reduction should be greater if active oxidative species are generated.

Methodology/Principal Findings

As model systems, dental implants, covered with a mono-species biofilm of Escherichia coli C43, were placed in photographic gelatin prepared with physiological saline. Implants were treated by a continuous current of 0 - 10 mA for 15 minutes. The reduction of viable counts was investigated on cathodes and anodes. In separate experiments, the local change in pH was visualized using color indicators embedded in the gelatin. Oxidative species were qualitatively detected by potassium iodide-starch paper. The in situ generated alkaline environment around cathodic implants caused a reduction of up to 2 orders of magnitude in viable E. coli counts. On anodic implants, in contrast to cathodic counterparts, oxidative species were detected. Here, a current of merely 7.5 mA caused complete kill of the bacteria.

Conclusions/Significance

This laboratory study shows that electrochemical treatment may provide access to a new way to decontaminate dental implants in situ.     

Parameter estimation and goodness-of-fit in log binomial regression

An estimate of the risk, adjusted for confounders, can be obtained from a fitted logistic regression model, but it substantially over-estimates when the outcome is not rare. The log binomial model, binomial errors and log link, is increasingly being used for this purpose. However this model's performance, goodness of fit tests and case-wise diagnostics have not been studied. Extensive simulations are used to compare the performance of the log binomial, a logistic regression based method proposed by Schouten et al. (1993) and a Poisson regression approach proposed by Zou (2004) and Carter, Lipsitz, and Tilley (2005). Log binomial regression resulted in "failure" rates (non-convergence, out-of-bounds predicted probabilities) as high as 59%. Estimates by the method of Schouten et al. (1993) produced fitted log binomial probabilities greater than unity in up to 19% of samples to which a log binomial model had been successfully fit and in up to 78% of samples when the log binomial model fit failed. Similar percentages were observed for the Poisson regression approach. Coefficient and standard error estimates from the three models were similar. Rejection rates for goodness of fit tests for log binomial fit were around 5%. Power of goodness of fit tests was modest when an incorrect logistic regression model was fit. Examples demonstrate the use of the methods. Uncritical use of the log binomial regression model is not recommended.     

过盈植入对种植体-骨界面应力分布影响的三维有限元分析（英文）

目的：应用三维有限元分析法研究牙种植体过盈植入对种植体-骨界面接触压力的影响。方法：选择直径为3.3 mm的ITI种植体和成人离体下颌骨,模拟种植体植入下颌骨内,过盈量为0.5 mm,建立三维有限元模型,应用ANSYS软件分析种植体-骨界面的应力分布情况。结果：种植体周围骨最大应力为48.796 MPa,应力分布均匀。种植体所受应力主要集中于颈部,最大应力值为87.832 MPa。结论：过盈量为0.5 mm时,种植体-骨界面所产生的应力值在骨组织所能承受的最大应力值范围内,种植体所受到的应力值远远小于钛的屈服强度,从生物力学角度,周围骨所受应力在骨组织能够承受范围,种植体也不会断裂,过盈联结在临床种植时有其可行性。     

Cellular spin resonance: Theory and experiment

Living and dead cells, as well as certain inanimate particles, can be made to spin in a rotating electric field, such as that produced by a four-pole electrode system. The theory for the effects and the experimental results for a number of cells are given. Yeast cells (Saccharomyces cerevisiae, dead, and as protoplasts;Schizosaccharomyces octospora); an alga (Chlorella pyrenoidosa); mouse myeloma cells; human Hela cells; and several model particles were studied. Their spectra of spin response are shown to agree with the theory presented. Interestingly, live cells spin in a contrafield direction, while dead ones spin co-field in the low-frequency range. The result indicate that this new technique of cellular spin resonance (CSR) will be useful in determining the effective dielectric constant of individual cells, for the direction and magnitude of the CSR is directly proportional to the effective dielectric constant, and the spin rate can readily and directly be determined over a wide frequency range.     

Extended moment analysis for binomial parameters of transmitter release.

The quantum hypothesis proposes that a binomial distribution should fit the amplitude distribution for synaptic potentials. Since importance is now being attached to significant changes in the n and p parameters of the binomial model during various treatments of synaptic preparations, this paper describes an important extension of the method of moments which can be used to extract binomial parameters in difficult experimental circumstances. Essentially, the skewness (third moment) of the observed amplitude distribution of synaptic responses is used to provide the additional information needed in cases where spontaneous miniature responses are absent. Computer simulations are used to assess the reliability of the proposed new estimators. The estimator bias due to non-uniform unit responses is also evaluated. Other applications of the extended method of moments, including a new test of the binomial hypothesis, are also described.     

Observations on the distribution of leather jackets in Northern Ireland

A map of the geographic distribution of leather jackets across five counties of Northern Ireland was produced from annual survey data. Climatic data were used to develop a multiple regression model explaining variation in the mean annual survey population for the years 1970–1984. Predicted populations for 1985–1988 compared favourably with observed counts. Both negative binomial and Adès distributions were successfully fitted to the frequency distribution of leatherjacket field populations from 1969–1986. It is concluded that the distribution of populations in the Province is not random and factors influencing mean leatherjacket numbers differ from those reported for other regions. The multiple regression model is proposed as a substitute for an annual survey of leatherjacket populations in Northern Ireland and it is suggested that the Adès family of distributions may enable it to be extended to predict leatherjacket frequency distributions each year.     

A Genetic Analysis of Mortality in Pigs

An analysis of mortality is undertaken in two breeds of pigs: Danish Landrace and Yorkshire. Zero-inflated and standard versions of hierarchical Poisson, binomial, and negative binomial Bayesian models were fitted using Markov chain Monte Carlo (MCMC). The objectives of the study were to investigate whether there is support for genetic variation for mortality and to study the quality of fit and predictive properties of the various models. In both breeds, the model that provided the best fit to the data was the standard binomial hierarchical model. The model that performed best in terms of the ability to predict the distribution of stillbirths was the hierarchical zero-inflated negative binomial model. The best fit of the binomial hierarchical model and of the zero-inflated hierarchical negative binomial model was obtained when genetic variation was included as a parameter. For the hierarchical binomial model, the estimate of the posterior mean of the additive genetic variance (posterior standard deviation in brackets) at the level of the logit of the probability of a stillbirth was 0.173(0.039) in Landrace and 0.202(0.048) in Yorkshire. The implications of these results from a breeding perspective are briefly discussed.LITTER size has been under selection in the Danish pig breeding program since the early 1990s and this resulted in considerable increase in total number born and also in the proportion of stillborn piglets (Sorensen et al. 2000; Su et al. 2007). A number of studies have reported genetic variation for mortality with heritabilities ranging from 0.03 to 0.12. These studies have either assumed normality of the sampling model for mortality (e.g., van Arendonk et al. 1996) or based inferences on a variety of threshold models (e.g., Roehe and Kalm 2000; Arango et al. 2006), and critical investigations of the quality of fit of the models used were not reported.Mortality data, regarded as a trait of the mother, show typically a large proportion of zeros (many litters do not have stillborn piglets). Formal genetic analyses of mortality in pigs accounting for this feature of the data are not available in the literature and this article attempts to fill this gap. The focus here is to study the quality of fit and predictive ability of a number of models and to investigate whether they provide statistical evidence for genetic variation for mortality. The statistical genetic analysis involves fitting various hierarchical models involving three discrete distributions: the Poisson, the binomial, and the negative binomial.The statistical analysis of counts based on discrete parametric distributions has a long and rich history (Johnson and Kotz 1969). In the case of unbounded counts, Poisson regression models are standard, whereas for bounded counts, when the response can be viewed as the number of successes out of a fixed number of trials, regression models based on the binomial distribution are often used (Hall 2000). A restriction of the Poisson model is that it imposes equality of mean and variance. Typically the distribution of counts is overdispersed. In the case of the binomial model the only free parameter is the probability of success, which results in a functional relationship between the mean and the variance. Several possible alternatives have been suggested to obtain more flexible models. For example, the negative binomial distribution has two parameters and allows the mean and variance to be fitted separately (Lawless 1987). An application of the negative binomial model in animal breeding can be found in Tempelman and Gianola (1996, 1999). In the same spirit, a robust alternative to the binomial model is the beta-binomial, which is a mixture of binomials where the unequal probabilities of success vary according to a beta-distribution. In general, hierarchical specifications are needed to explain extra variation that is not accounted for by the sampling model of the data. These involve assigning a distribution to the parameters of the sampling model, directly, as in the case of the negative binomial or beta-binomial models, or indirectly, by embedding these parameters in a linear structure that includes random effects as explanatory variables.There are situations where overdispersion is partly associated with an incidence of zero counts that is greater than expected under the sampling model, as in the present study. Hurdle models (Mullahy 1986; Winkelmann 2000) and zero-inflated models are two instances of finite mixture models commonly used to account for this characteristic of the data. In the present work the excess of zeros is studied using zero-inflated models that are described in Johnson and Kotz (1969) and extended by Lambert (1992). Ridout et al. (1998) provide a review of various zero-inflated models; recent applications of zero-inflated Poisson models in animal breeding are in Rodriguez-Motta et al. (2007) and in Naya et al. (2008). Zero-inflated models assume that the population consists of two sets of observations. In the first set, which may include zeros, observations are realizations from a discrete sampling process indexed by unknown parameters (this set is often referred to as the imperfect state); observations from the second set consist only of zeros and the parameter of interest is the proportion of these individuals. This set is often referred to as the perfect state. Either or both sets of parameters may depend on covariates.This article is organized as follows. material and methods describes the data, details of the models, and their Markov chain Monte Carlo (MCMC) implementation. This is followed by a presentation of the results of the analyses and of MCMC-driven explorative tools for model comparison. The article concludes with a discussion.     

Plant-parasitic Nematode Distributions in an Alfalfa Field

A 7-ha alfalfa field (Medicago saliva L. cv Mesa Sirsa) was sampled systematically on a 6 x 6-m grid by removing individual cores (2.54 cm diam) to a depth of 45 cm from each of the 1,936 grid intersections. The soil was mainly coarse-textured with a fine-textured streak running centrally, north to south. Nematodes were extracted by a semiautomatic elutriator and sugar flotation-sieving technique. Five plant-parasitic species were consistently present: Meloidogyne arenaria, Pratylenchus minyus, Merlinius brevidens, Helicotylenchus digonicus, and Paratrichodorus minor. All species had a highly skewed nonnormal frequency distribution that departed significantly from randontness. Goodness-of-fit tests on the distribution of five populations in the entire field showed that three (Meloidogyne, Merlinius, and Helicotylenchus) were described by a negative binomial. When the samples were categorized by soil texture (coarse vs. fine-textured), all populations in the fine-textured areas, and three populations (Meloidogyne, Pratylenchus, and Merlinius) in the coarse areas, fitted a negative binomial distribution. Nearly all populations titted a negative binomial when the frequency distributions from randomly located one-meter-square areas were examined for each species.     

A Modified Chronic Infection Model for Testing Treatment of Staphylococcus aureus Biofilms on Implants

Bacterial biofilms causing implant-associated osteomyelitis is a severe complication with limited antimicrobial therapy options. We designed an animal model, in which implant associated osteomyelitis arise from a Staphylococcus aureus biofilm on a tibia implant. Two bioluminescently engineered (luxA-E transformed), strains of S. aureus were utilized, Xen29 and Xen31. Biofilm formation was assessed with epifluorescence microscopy. Quantitative measurements were performed day 4, 6, 8, 11 and 15 post-surgery. Bacteria were extracted from the biofilm by sonication and the bacterial load quantified by culturing. Biofilm formation was evident from day 6 post-implantation. Mean bacterial load from implants was ∼1×10⁴ CFU/implant, while mean bacterial load from infected tibias were 1×10⁶ CFU/bone. Bioluminesence imaging revealed decreasing activity throughout the 15-day observation period, with signal intensity for both strains reaching that of the negative control by day 15 while there was no significant reduction in bacterial load. The model is suitable for testing antimicrobial treatment options for implant associated OM, as treatment efficacy on both biofilm and viable counts can be assessed.