Point and Interval Estimation of the Population Size Using a Zero‐Truncated Negative Binomial Regression Model

This paper presents the zero‐truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero‐truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero‐truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

One‐inflation and unobserved heterogeneity in population size estimation

We present the one‐inflated zero‐truncated negative binomial (OIZTNB) model, and propose its use as the truncated count distribution in Horvitz–Thompson estimation of an unknown population size. In the presence of unobserved heterogeneity, the zero‐truncated negative binomial (ZTNB) model is a natural choice over the positive Poisson (PP) model; however, when one‐inflation is present the ZTNB model either suffers from a boundary problem, or provides extremely biased population size estimates. Monte Carlo evidence suggests that in the presence of one‐inflation, the Horvitz–Thompson estimator under the ZTNB model can converge in probability to infinity. The OIZTNB model gives markedly different population size estimates compared to some existing truncated count distributions, when applied to several capture–recapture data that exhibit both one‐inflation and unobserved heterogeneity.     

锌剂联合叶酸佐治小儿腹泻随机对照试验的Meta分析

目的 采用Meta分析方法评价锌剂联合叶酸佐治小儿腹泻的有效性和安全性。方法 检索中国期刊全文数据库、万方数据库、维普数据库及PubMed、The Cochrane Library中锌剂联合叶酸佐治小儿腹泻的随机对照试验（RCT）。采用Stata 11.0软件进行统计分析,采用Q值统计量检验法和I2统计量对纳入的研究进行异质性检验,若各研究结果间无异质性,研究选择固定效应模型计算合并量,否则使用随机效应模型,并采用倒漏斗图分析和 Egger's检验评估发表偏倚。P<0.1为差异有统计学意义。结果 共纳入22个RCT、2 238例小儿腹泻患者。锌剂联合叶酸佐治小儿腹泻的总有效率高于对照组,止泻时间和脱水纠正时间均短于对照组。结论 在常规治疗的基础上配合锌剂和叶酸辅佐治疗小儿腹泻的临床疗效更佳,值得临床推广,但仍需要多中心、大样本、双盲的高质量RCT支持。     

Theoretical effects of radioligand diffusional gradients and microscopic neuroreceptor distribution inin vivo kinetic studies

A simplified one-dimensional model system was used to test the possibility that physically realistic parameters would lead to the prediction of microscopic heterogeneity of radioligand distribution in the brain and that microscopic heterogeneity of radioligand and neuroreceptor distribution could influence the macroscopically observedin vivo kinetics. The model was represented mathematically by a partial differential equation which is similar to the heat diffusion equation, but with special boundary conditions. The equation was solved analytically under the condition of negligible receptor occupancy by inversion of the Laplace transform and in the more general case of arbitrary receptor occupancy by cubic spline approximation. In simulations with physically reasonable values for rate constants and parameters, we find that significant radioligand gradients can occur. Thus, the level of radioligand in the immediate vicinity of the receptor may be substantially different from the average level in a macroscopically measured region of interest. In order to analyze the simulated data, we derived a rigorous steady-state solution, including both a statement of necessary and sufficient conditions for the validity of the steady-state approximation as well as a demonstration of the proper technique for assessing the consistency of the derived parameter with the requirements of the approximation. The radioligand heterogeneity leads to significant errors in the parameters estimated in the steady-state kinetic analysis. In particular, the pseudo first-order rate constant for radioligand-neuroreceptor association, which is often used as a measure of the total amount of neuroreceptor, is underestimated. The first-order rate constant for radioligand-neuroreceptor dissociation is also underestimated. These effects can partially account for the experimentally-observed discrepancy betweenin vivo andin vitro estimates of these kinetic parameters.     

Overdispersed logistic regression for SAGE: Modelling multiple groups and covariates

Background  

Two major identifiable sources of variation in data derived from the Serial Analysis of Gene Expression (SAGE) are within-library sampling variability and between-library heterogeneity within a group. Most published methods for identifying differential expression focus on just the sampling variability. In recent work, the problem of assessing differential expression between two groups of SAGE libraries has been addressed by introducing a beta-binomial hierarchical model that explicitly deals with both of the above sources of variation. This model leads to a test statistic analogous to a weighted two-sample t-test. When the number of groups involved is more than two, however, a more general approach is needed.     

An Extended ANOVA F‐Test with Applications to the Heterogeneity Problem in Meta‐Analysis

The classical F‐test in the one‐way random effects ANOVA model is extended to solve the long outstanding problem of testing the between‐group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly for balanced homoscedastic models. By simulation, the tests are shown to attain acceptable significance levels and high power even in data that do not follow the usual ANOVA model. An important application of the tests is given by the heterogeneity questions concerning the treatment effects across studies in meta‐analysis.     

A goodness-of-fit test for capture-recapture model Mt under closure

A new, fully efficient goodness-of-fit test for the time-specific closed-population capture-recapture model Mt is presented. This test is based on the residual distribution of the capture history data given the maximum likelihood parameter estimates under model Mt, is partitioned into informative components, and is based on chi-square statistics. Comparison of this test with Leslie's test (Leslie, 1958, Journal of Animal Ecology 27, 84-86) for model Mt, using Monte Carlo simulations, shows the new test generally outperforms Leslie's test. The new test is frequently computable when Leslie's test is not, has Type I error rates that are closer to nominal error rates than Leslie's test, and is sensitive to behavioral variation and heterogeneity in capture probabilities. Leslie's test is not sensitive to behavioral variation in capture probabilities but, when computable, has greater power to detect heterogeneity than the new test.     

GlobalANCOVA: exploration and assessment of gene group effects

MOTIVATION: Several authors have studied expression in gene sets with specific goals: overrepresentation of interesting genes in functional groups, predictive power for class membership and searches for groups where the constituent genes show coordinated changes in expression under the experimental conditions. The purpose of this article is to follow the third direction. One important aspect is that the gene sets under analysis are known a priori and are not determined from the experimental data at hand. Our goal is to provide a methodology that helps to identify the relevant structural constituents (phenotypical, experimental design, biological component) that determine gene expression in a group. RESULTS: Gene-wise linear models are used to formalize the structural aspects of a study. The full model is contrasted with a reduced model that lacks the relevant design component. A comparison with respect to goodness of fit is made and quantified. An asymptotic test and a permutation test are derived to test the null hypothesis that the reduced model sufficiently explains the observed expression within the gene group of interest. Graphical tools are available to illustrate and interpret the results of the analysis. Examples demonstrate the wide range of application. AVAILABILITY: The R-package GlobalAncova (http://www.bioconductor.org) offers data and functions as well as a vignette to guide the user through specific analysis steps.     

Logistic regression in capture-recapture models

The effect of population heterogeneity in capture-recapture, or dual registration, models is discussed. An estimator of the unknown population size based on a logistic regression model is introduced. The model allows different capture probabilities across individuals and across capture times. The probabilities are estimated from the observed data using conditional maximum likelihood. The resulting population estimator is shown to be consistent and asymptotically normal. A variance estimator under population heterogeneity is derived. The finite-sample properties of the estimators are studied via simulation. An application to Finnish occupational disease registration data is presented.     

A new statistical test for linkage heterogeneity.

A new, statistical test for linkage heterogeneity is described. It is a likelihood-ratio test based on a beta distribution for the prior distribution of the recombination fraction among families (or individuals). The null distribution for this statistic (called the B-test) is derived under a broad range of circumstances. Two other heterogeneity test statistics--the admixture test or A-test first described by Smith and Morton's test (here referred to as the K-test)--are also examined. The probability distribution for the K-test statistic is very sensitive to family size, whereas the other two statistics are not. All three statistics are somewhat sensitive to the magnitude of the recombination fraction theta. Critical values for each of the test statistics are given. A conservative approximation for both the A-test and B-test is given by a chi 2 distribution when P/2 instead of P is used for the observed significance level. In terms of power, the B-test performs best among the three tests over a broad range of alternate heterogeneity hypotheses--except for the specific case of admixture with loose linkage, in which the A-test performs best. Overall, the difference in power among the three tests is not large. An application to some recently published data on the fragile-X syndrome and X-chromosome markers is given.     

Applications and extensions of Chao's moment estimator for the size of a closed population

This article revisits Chao's (1989, Biometrics45, 427-438) lower bound estimator for the size of a closed population in a mark-recapture experiment where the capture probabilities vary between animals (model M(h)). First, an extension of the lower bound to models featuring a time effect and heterogeneity in capture probabilities (M(th)) is proposed. The biases of these lower bounds are shown to be a function of the heterogeneity parameter for several loglinear models for M(th). Small-sample bias reduction techniques for Chao's lower bound estimator are also derived. The application of the loglinear model underlying Chao's estimator when heterogeneity has been detected in the primary periods of a robust design is then investigated. A test for the null hypothesis that Chao's loglinear model provides unbiased abundance estimators is provided. The strategy of systematically using Chao's loglinear model in the primary periods of a robust design where heterogeneity has been detected is investigated in a Monte Carlo experiment. Its impact on the estimation of the population sizes and of the survival rates is evaluated in a Monte Carlo experiment.     

Consequences of heterogeneity in survival probability in a population of Florida scrub-jays

1. Using data on breeding birds from a 35-year study of Florida scrub-jays Aphelocoma coerulescens (Bosc 1795), we show that survival probabilities are structured by age, birth cohort, and maternal family, but not by sex. Using both accelerated failure time (AFT) and Cox proportional hazard models, the data are best described by models incorporating variation among birth cohorts and greater mortality hazard with increasing age. AFT models using Weibull distributions with the shape parameter > 1 were always the best-fitting models. 2. Shared frailty models allowing for family structure greatly reduce model deviance. The best-fitting models included a term for frailty shared by maternal families. 3. To ask how long a data set must be to reach qualitatively the same conclusions, we repeated the analyses for all possible truncated data sets of 2 years in length or greater. Length of the data set affects the parameter estimates, but not the qualitative conclusions. In all but three of 337 truncated data sets the best-fitting models pointed to same conclusions as the full data set. Shared frailty models appear to be quite robust. 4. The data are not adequate for testing hypotheses as to whether variation in frailty is heritable. 5. Substantial structured heterogeneity for survival exists in this population. Such structured heterogeneity has been shown to have substantial effects in reducing demographic stochasticity.     

Two-part permutation tests for DNA methylation and microarray data

Background  

One important application of microarray experiments is to identify differentially expressed genes. Often, small and negative expression levels were clipped-off to be equal to an arbitrarily chosen cutoff value before a statistical test is carried out. Then, there are two types of data: truncated values and original observations. The truncated values are not just another point on the continuum of possible values and, therefore, it is appropriate to combine two statistical tests in a two-part model rather than using standard statistical methods. A similar situation occurs when DNA methylation data are investigated. In that case, there are null values (undetectable methylation) and observed positive values. For these data, we propose a two-part permutation test.     

<Emphasis Type="Italic">TDT-HET</Emphasis>: A new transmission disequilibrium test that incorporates locus heterogeneity into the analysis of family-based association data

Background  

Locus heterogeneity is one of the most documented phenomena in genetics. To date, relatively little work had been done on the development of methods to address locus heterogeneity in genetic association analysis. Motivated by Zhou and Pan's work, we present a mixture model of linked and unlinked trios and develop a statistical method to estimate the probability that a heterozygous parent transmits the disease allele at a di-allelic locus, and the probability that any trio is in the linked group. The purpose here is the development of a test that extends the classic transmission disequilibrium test (TDT) to one that accounts for locus heterogeneity.     

Posttranslational processing of recombinant human interferon-gamma in animal expression systems.

We have characterized the heterogeneity of recombinant human interferon-gamma (IFN-gamma) produced by three expression systems: Chinese hamster ovary cells, the mammary gland of transgenic mice, and baculovirus-infected Spodopera frugiperda (Sf9) insect cells. Analyses of whole IFN-gamma proteins by electrospray ionization-mass spectrometry (ESI-MS) from each recombinant source revealed heterogeneous populations of IFN-gamma molecules resulting from variations in N-glycosylation and C-terminal polypeptide cleavages. A series of more specific analyses assisted interpretation of maximum entropy deconvoluted ESI-mass spectra of whole IFN-gamma proteins; MALDI-MS analyses of released, desialylated N-glycans and of deglycosylated IFN-gamma polypeptides were combined with analyses of 2-aminobenzamide labeled sialylated N-glycans by cation-exchange high-performance liquid chromatography. These analyses enabled identification of specific polypeptide cleavage sites and characterization of associated N-glycans. Production of recombinant IFN-gamma in the mammalian expression systems yielded polypeptides C-terminally truncated at dibasic amino acid sites. Mammalian cell derived IFN-gamma molecules displayed oligosaccharides with monosaccharide compositions equivalent to complex, sialylated, or high-mannose type N-glycans. In contrast, IFN-gamma derived from baculovirus-infected Sf9 insect cells was truncated further toward the C-terminus and was associated with neutral (nonsialylated) N-glycans. These data demonstrate the profound influence of host cell type on posttranslational processing of recombinant proteins produced in eukaryotic systems.     

Testing homogeneity in Weibull-regression models

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.     

Anisotropic constitutive equations and experimental tensile behavior of brain tissue

The present study deals with the experimental analysis and mechanical modeling of tensile behavior of brain soft tissue. A transversely isotropic hyperelastic model recently proposed by Meaney (2003) is adopted and mathematically studied under uniaxial loading conditions. Material parameter estimates are obtained through tensile tests on porcine brain materials accounting for regional and directional differences. Attention is focused on the short-term response. An extrapolation of tensile test data to the compression range is performed theoretically, to study the effect of the heterogeneity in the tensile/compressive response on the material parameters. Experimental and numerical results highlight the sensitivity of the adopted model to the test direction.     

A combined test of linkage heterogeneity.

This paper focuses on the problem of testing for heterogeneity once linkage is established. In an investigation of genetic linkage, Morton first proposed a general purpose test to detect heterogeneity in the recombination fraction. Two more commonly used tests of linkage heterogeneity are the admixture test (A-test) of Smith, Ott, and Risch and Baron, and the B-test of Risch. All are likelihood-ratio tests, but they differ in the models specifying the heterogeneity. A new test of heterogeneity in the presence of linkage is presented here. I propose a mixture model of heterogeneity, which allows the recombination fraction to vary among families, as does the B-model, yet also allows some families to be unlinked, as the A-model does. This model contains the A and B models as special cases and thus allows a direct test (D-test), which can provide justification for choosing one of these extremes.     

Adaptive treatment allocation for comparative clinical studies with recurrent events data

In long-term clinical studies, recurrent event data are sometimes collected and used to contrast the efficacies of two different treatments. The event reoccurrence rates can be compared using the popular negative binomial model, which incorporates information related to patient heterogeneity into a data analysis. For treatment allocation, a balanced approach in which equal sample sizes are obtained for both treatments is predominately adopted. However, if one treatment is superior, then it may be desirable to allocate fewer subjects to the less-effective treatment. To accommodate this objective, a sequential response-adaptive treatment allocation procedure is derived based on the doubly adaptive biased coin design. Our proposed treatment allocation schemes have been shown to be capable of reducing the number of subjects receiving the inferior treatment while simultaneously retaining a test power level that is comparable to that of a balanced design. The redesign of a clinical study illustrates the advantages of using our procedure.     

Use of a generalized linear mixed model to reduce excessive heterogeneity in petroleum spray oil bioassay data

High heterogeneity (variance) is a consistent and significant problem in petroleum spray oil derived bioassay data. It can mask small statistical differences sought by researchers in relative toxicity or potency analysis. To compensate for excessive heterogeneity, researchers often use very large sample sizes to improve statistical accuracy. We present a statistical method of modeling heterogeneity extending the conventional probit model by adding random effects to it. We illustrate this by reanalyzing 26 of our own published experiments. Twelve of these had excessive heterogeneity that was significantly reduced in ten cases by including random replicate effects with or without random slopes. Five were further improved by allowing a nonlinear (spline) response. The result was tighter confidence intervals for the estimates of lethal dose.