Assessing overdispersion and dose-response in the male dominant lethal assay.

In dominant lethal studies the primary variables of interest are typically expressed as discrete counts or proportions (e.g., live implants, resorptions, percent pregnant). Simple statistical sampling models for discrete data such as binomial or Poisson generally do not fit this type of data because of extra-binomial or extra-Poisson departures from variability predicted under these simple models. Extra-variability in the fetal response may originate from parental contributions. These can lead to over- or under-dispersion seen as, e.g., extra-binomial variability in the proportion response. Utilizing a large control database, we investigated the relative impact of extra-variability from male or female contributions on the endpoints of interest. Male-related effects did not seem to contribute to overdispersion in our database; female-related effects were, however, evidenced. Various statistical methods were considered to test for significant treatment differences under these forms of sampling variability. Computer simulations were used to evaluate these methods and to determine which are most appropriate for practical use in the evaluation of dominant lethal data. Our results suggest that distribution-free statistical methods such as a nonparametric permutation test or rank-based tests for trend can be recommended for use.     

Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.     

Trend Test for Overdispersed Proportions

The Cochran-Armitage test has commonly been used for a trend test in binomial proportions. The quasi-likelihood method provides a simple approach to model extra-binomial proportions. Two versions of the score and Wald tests using different parameterizations for the extra-binomial variance were investigated: one in terms of intercluster correlation, and another in terms of variance. The Monte Carlo simulation was used to evaluate the performance of the each version of the score test and the Wald test, and the Cochran-Armitage test. The simulation shows that the Cochran-Armitage test has the proper size only for the binomial sample data, and the test is no longer valid when applied to the extra-binomial data. The Wald test is more likely to exceed the nominal level than the score test under either intercluster correlation model or variance model. Both score tests performed very well even with the binomial data; the tests control the type I error and in the meantime maintain the power of detecting the dose effects. Based on the design considered in this paper, the two scores test are comparable. The score test based on the intercluster correlations model seems better controlling the Type I error but appears less powerful than that based on the variance model. An example from a developmental toxicity experiment is given.     

On a likelihood-based goodness-of-fit test of the beta-binomial model

When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta-binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-fit test proposed by Brooks et al. (1997, Biometrics 53, 1097-1115) but find that it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.     

A study of deleterious gene structure in plants using Markov chain Monte Carlo

The characteristics of deleterious genes have been of great interest in both theory and practice in genetics. Because of the complex genetic mechanism of these deleterious genes, most current studies try to estimate the overall magnitude of mortality effects on a population, which is characterized classically by the number of lethal equivalents. This number is a combination of several parameters, each of which has a distinct biological effect on genetic mortality. In conservation and breeding programs, it is important to be able to distinguish among different combinations of these parameters that lead to the same number of lethal equivalents, such as a large number of mildly deleterious genes or a few lethal genes, The ability to distinguish such parameter combinations requires more than one generation of mating. We propose a model for survival data from a two-generation mating experiment on the plant species Brassica rapa, and we enable inference with Markov chain Monte Carlo. This computational strategy is effective because a vast amount of missing genotype information must be accounted for. In addition to the lethal equivalents, the two-generation data provide separate information on the average intensity of mortality and the average number of deleterious genes carried by an individual. In our Markov chain Monte Carlo algorithm, we use a vector proposal distribution to overcome inefficiency of a single-site Gibbs sampler. Information about environmental effects is obtained from an outcrossing experiment conducted in parallel with the two-generation mating experiments.     

Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.     

巴岳山-西温泉风景名胜区种子植物区系特征分析

在对重庆市巴岳山-西温泉风景名胜区种子植物详细调查、标本采集及鉴定的基础上,对其科、属的分布区类型进行统计分析,其种子植物区系特征如下：（1）区系成分丰富,有136科,573属,1043种;包括11种科的分布区类型和15种属的分布区类型。（2）优势科、属明显。（3）种子植物区系起源古老,单型科、单型属及原始多心皮古老类群较多。（4）科属分布区类型以热带分布为主,温带分布类型也占相当比例;同时,有许多分布区亚型及间断分布类型,呈现出明显的区系过渡性质。（5）珍稀濒危及重点保护植物、中国特有分布类型丰富,有较高的保护价值。     

A shared response model for clustered binary data in developmental toxicity studies

Existing distributions for modeling fetal response data in developmental toxicology such as the beta-binomial distribution have a tendency of inflating the probability of no malformed fetuses, and hence understating the risk of having at least one malformed fetus within a litter. As opposed to a shared probability extra-binomial model, we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response. An explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses. The EM algorithm can be used to estimate the model parameters. Results of a simulation study show that the EM estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level. Simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form, but not so for the estimates of intralitter correlation and the litter-level probability of having at least one malformed fetus. The proposed model is fitted to a set of data from the U.S. National Toxicology Program. For the same dose-response relationship, the fit based on the shared response distribution is superior to that based on the beta-binomial, and comparable to that based on the recently proposed q-power distribution (Kuk, 2004, Applied Statistics53, 369-386). An advantage of the shared response model over the q-power distribution is that it is more interpretable and can be extended more easily to the multivariate case. To illustrate this, a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation.     

Response ofNabis roseipennis [Heteroptera: Nabidae] to Larvae of Mexican bean beetle,Epilachna varivestis [Col.: Coccinellidae]

Laboratory studies were done to measure predation by adult damsel bugs,Nabis roseipennis Reuter [Heteroptera: Nabidae], on 3^rd instar larvae of Mexican bean beetle (MBB),Epilachna varivestis Mulsant [Coleoptera: Coccinellidae], and to measure longevity and body weight of the nabids. In the 1^st experiment, field-collected nabids were isolated for 24h in 9 cm Petri dishes with lima bean foliage (Phaseolus lunatus L.) and were assigned to one of 3 prey treatments: either 4 3^rd-instar MBB larvae, 4 3^rd-instar larvae of boll weevil (BW),Anthonomus grandis Boheman [Coleoptera: Curculionidae], or 2 larvae of each species. No MBB larvae were attacked in either the MBB treatment or 2-species treatment. In contrast, BW larvae were attacked in both BW and 2-species treatments. Significantly more BW larvae were attacked in the BW treatment than in the 2-species treatment, and both were greater than the number of MBB larvae attacked. Nabids that did not attack prey lost weight during the 24 h, whereas those that attacked prey gained weight. In the 2^nd experiment, nabids that had attacked prey were isolated with lima foliage, and nabids that had not attacked prey were kept with MBB and lima foliage until an attack or death. In no instances were MBB attacked. Longevity and the pattern of weight loss did not differ between nabids that did or did not attack prey. We discuss possible reasons for the failure ofN. roseipennis to attack MBB larvae, as well as the implications for using nabids to influence pest populations in the field.      

Computer-assisted analysis of mixtures (C.A.MAM): statistical algorithms.

This paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one-parameter family of densities and provides a unifying computer-oriented concept for the statistical analysis of unobserved heterogeneity (i.e., observations stemming from different subpopulations) in a univariate sample. The case with unknown number of population subgroups as well as the case with known number of population subgroups, with emphasis on the first, is considered in the computer package C.A.MAN (Computer Assisted Mixture Analysis). It includes an algorithmic menu with choices of the EM algorithm, the vertex exchange algorithm, a combination of both, as well as the vertex direction method. To ensure reliable convergence, a step-length menu is provided for the three latter methods, each achieving monotonicity for the direction of choice. C.A.MAN has the option to work with restricted support size-that is, the case when the number of components is known a priori. In the latter case, the EM algorithm is used. Applications of mixture modelling in medical problems are discussed.     

Estimation of the Proportion of Differentially Expressed Genes Using Hellinger Distance

We consider the problem of estimating the proportion of differentially expressed genes from the distribution of P-values arising from statistical tests in a microarray experiment. A two-component mixture model is studied in which one component is uniform on [0,1] and corresponds to equally expressed genes and the other component corresponds to differentially expressed genes. Two different parametric families are explicitly investigated for modeling the nonuniform component—the Beta family and a mixture of uniform densities whose supports form a partition of [0,1]. The Minimum Hellinger discrepancy is used to estimate the mixture proportions which are then used to estimate the proportion of differentially expressed genes in the microarray study. The performance of the proposed methods are investigated using simulation studies in which they are also compared with selected other published procedures. The methods are illustrated through a case study involving data from a published microarray experiment.     

Radiation-induced dominant lethal mutations in oocytes of Musca domestica

Dominant lethal mutations induced by γ-radiation were measured in stage-7 and stage-14 oocytes of Musca domestica. At both stages the data are consistent with the multi-hit theory on radiation induction of dominant lethals. This conclusion is supported by fractionation experiments which indicate that both] S7 and S14 oocytes are capable of repairing, in defferent periods of time, a similar amount of dominant lethal damage.     

Correct and logical inference on efficacy in subgroups and their mixture for binary outcomes

Targeted therapies are becoming more common. In targeted therapy development, suppose its companion diagnostic test divides patients into a marker‐positive subgroup and its complementary marker‐negative subgroup. To find the right patient population for the therapy to target, inference on efficacy in the marker‐positive and marker‐negative subgroups as well as efficacy in the overall mixture population are all of interest. Depending on the type of clinical endpoints, inference on mixture population can be nontrivial and commonly used efficacy measures may not be suitable for a mixture population. Correlations among estimates of efficacy in the marker‐positive, marker‐negative, and overall mixture population play a crucial role in using an earlier phase study to inform on the design of a confirmatory study (e.g., determination of sample size). This article first shows that when the clinical endpoint is binary (such as respond or not), odds ratio is inappropriate as an efficacy measure in this setting, but relative response (RR) is appropriate. We show a safe way of calculating estimated correlations is to consider mixing subgroup response probabilities within each treatment arm first, and then derive the joint distribution of RR estimates. We also show, if one calculates RR within each subgroup first, how wrong the correlations can be if the Delta method derivation fails to take randomness of estimating the mixing coefficient into account.     

Variations in the radiosensitivity of oocyte chromosomes during meiosis in Drosophila melanogaster

The synaptic stages of meiosis in Drosophila melanogaster females are very resistant to the induction of dominant lethal mutations by ionizing radiation. It is assumed that dominant lethals result from interstitial chromatid deletions, and that almost all potential chromatid breaks are repaired in synaptic cells. The type of dose response curve shown by oocytes at later developmental stages is a function of the degree of chromatid coiling and the presence or absence of an investing nuclear envelope.     

A Bayesian two-level model for fluctuation assay

The fluctuation experiment is an essential tool for measuring microbial mutation rates in the laboratory. When inferring the mutation rate from an experiment, one assumes that the number of mutants in each test tube follows a common distribution. This assumption conceptually restricts the scope of applicability of fluctuation assay. We relax this assumption by proposing a Bayesian two-level model, under which an experiment-wide average mutation rate can be defined. The new model suggests a gamma mixture of the Luria-Delbrück distribution, which coincides with a recently discovered discrete distribution. While the mixture model is of considerable independent interest in fluctuation assay, it also offers a practical Markov chain Monte Carlo method for estimating mutation rates. We illustrate the Bayesian approach with a detailed analysis of an actual fluctuation experiment.     

The role of miRNA in the direct and indirect effects of ionizing radiation

This review focuses on a number of recent studies that have examined changes in microRNA (miRNA) expression profiles in response to ionizing radiation and other forms of oxidative stress. In both murine and human cells and tissues, a number of miRNAs display significant alterations in expression levels in response to both direct and indirect radiation exposure. In terms of direct irradiation, or exposure to agents that induce oxidative stress, miRNA array analyses indicate that a number of miRNAs are up- and down-regulated and, in particular, the let-7 family of miRNAs may well be critical in the cellular response to oxidative stress. In bystander cells that are not directly irradiated, but close to, or share media with directly irradiated cells or tissues, the miRNA expression profiles are also altered, but are somewhat distinct from the directly irradiated cells. Based on the results of these numerous studies, as well as our own data presented here, we conclude that miRNA regulation is a critical step in the cellular response to radiation and oxidative stress and that future studies should elucidate the mechanisms through which this altered regulation affects cell metabolism.     

Fitting host-parasitoid models with CV2 > 1 using hierarchical generalized linear models.

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density-dependent heterogeneity (HDD) to be distinguished from between-patch, host density-independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well-known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.     

Mass loss and nutrient dynamics during litter decomposition under three mixing treatments in a typical steppe in Inner Mongolia

Background and aims

Mixing effects during litter decomposition could occur between two or more different litter species because of the potential nutrient transfer. However, evidence of mixing effects is variable and the underlying mechanisms remain unclear. Using a three-year decomposition experiment, we aim to examine for the effects of litter mixing and position on decomposition rates and nitrogen (N) and phosphorus (P) dynamics.

Methods

We studied litter decomposition of Stipa krylovii (Sk) and Astragalus galactites (Ag), two dominant species with contrasting litter quality, in a typical steppe of northern China in both single decomposition and three mixing treatments. The three mixing treatments included thorough mixing (Sk-Ag), Ag over Sk (Ag/Sk), and Sk over Ag (Sk/Ag).

Results

Both the Sk-Ag and the Sk/Ag mixture had negative mixing effects on the mass loss of the litter mixture, while the Ag/Sk mixture had a neutral mixing effect. The percent mass loss was higher when the litter species was placed at the top (25.0 and 51.9 % of mass remaining for Ag and Sk, respectively) than at the bottom (38.3 and 61.8 % of mass remaining for Ag and Sk, respectively). The Sk/Ag mixture had negative effects on the release of N while all three mixing treatments had positive effects on the release of P.

Conclusions

Our results indicate that: (1) mixing treatments can induce different mixing effects; (2) environmental factors likely play an important role in controlling the mixing effect; and (3) litter-mixtures have different non-additive effects on N and P, which may further increase the heterogeneity of N and P availability as the two litter species may fall differentially in terms of space and time.     

Bleomycin: female-specific dominant lethal effects in mice.

Limited comparative data in mice indicate that chemical mutagens that induce dominant lethal mutations in males are not necessarily effective in females, but those which are effective in females are generally equally or more effective in males. Recently, however, a few chemicals have been identified that are female-specific with respect to induction of dominant lethal mutations. The antitumor antibiotic adriamycin is among them. Another antitumor antibiotic, bleomycin was examined for its ability to induce dominant lethal mutations in the reproductive cells of male and female mice. No dominant lethal or cytotoxic effects were observed in males treated with bleomycin, even at a maximum tolerated dose. In females, on the other hand, a dose nearly 1/4 of that used in males induced not only a high level of dominant lethal mutations but also killed oocytes in certain stages of follicular development. The effectiveness of bleomycin in inducing dominant lethal mutations in mouse oocytes makes it a valuable tool for investigating whether gonadal transport, inherent differences in the configuration of chromatin in the germ cells of the two sexes or other factors are responsible for the differential susceptibility to bleomycin, which implies potential gender-specific genetic risk in cancer chemotherapy.