One‐inflation and unobserved heterogeneity in population size estimation by Ryan T. Godwin

In this study, we would like to show that the one‐inflated zero‐truncated negative binomial (OIZTNB) regression model can be easily implemented in R via built‐in functions when we use mean‐parameterization feature of negative binomial distribution to build OIZTNB regression model. From the practitioners' point of view, we believe that this approach presents a computationally convenient way for implementation of the OIZTNB regression model.     

Estimation in the progressive illness‐death model: A nonexhaustive review

Multistate models can be successfully used for describing complex event history data, for example, describing stages in the disease progression of a patient. The so‐called “illness‐death” model plays a central role in the theory and practice of these models. Many time‐to‐event datasets from medical studies with multiple end points can be reduced to this generic structure. In these models one important goal is the modeling of transition rates but biomedical researchers are also interested in reporting interpretable results in a simple and summarized manner. These include estimates of predictive probabilities, such as the transition probabilities, occupation probabilities, cumulative incidence functions, and the sojourn time distributions. We will give a review of some of the available methods for estimating such quantities in the progressive illness‐death model conditionally (or not) on covariate measures. For some of these quantities estimators based on subsampling are employed. Subsampling, also referred to as landmarking, leads to small sample sizes and usually to heavily censored data leading to estimators with higher variability. To overcome this issue estimators based on a preliminary estimation (presmoothing) of the probability of censoring may be used. Among these, the presmoothed estimators for the cumulative incidences are new. We also introduce feasible estimation methods for the cumulative incidence function conditionally on covariate measures. The proposed methods are illustrated using real data. A comparative simulation study of several estimation approaches is performed and existing software in the form of R packages is discussed.     

On Combining Family‐Based and Population‐Based Case–Control Data in Association Studies

Summary Combining data collected from different sources can potentially enhance statistical efficiency in estimating effects of environmental or genetic factors or gene–environment interactions. However, combining data across studies becomes complicated when data are collected under different study designs, such as family‐based and unrelated individual‐based case–control design. In this article, we describe likelihood‐based approaches that permit the joint estimation of covariate effects on disease risk under study designs that include cases, relatives of cases, and unrelated individuals. Our methods accommodate familial residual correlation and a variety of ascertainment schemes. Extensive simulation experiments demonstrate that the proposed methods for estimation and inference perform well in realistic settings. Efficiencies of different designs are contrasted in the simulation. We applied the methods to data from the Colorectal Cancer Family Registry.     

Variable selection for zero‐inflated and overdispersed data with application to health care demand in Germany

In health services and outcome research, count outcomes are frequently encountered and often have a large proportion of zeros. The zero‐inflated negative binomial (ZINB) regression model has important applications for this type of data. With many possible candidate risk factors, this paper proposes new variable selection methods for the ZINB model. We consider maximum likelihood function plus a penalty including the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and minimax concave penalty (MCP). An EM (expectation‐maximization) algorithm is proposed for estimating the model parameters and conducting variable selection simultaneously. This algorithm consists of estimating penalized weighted negative binomial models and penalized logistic models via the coordinated descent algorithm. Furthermore, statistical properties including the standard error formulae are provided. A simulation study shows that the new algorithm not only has more accurate or at least comparable estimation, but also is more robust than the traditional stepwise variable selection. The proposed methods are applied to analyze the health care demand in Germany using the open‐source R package mpath .     

SREBP‐1c,Pdx‐1, and GLP‐1R involved in palmitate–EPA regulated glucose‐stimulated insulin secretion in INS‐1 cells

Impairment of glucose‐stimulated insulin secretion (GSIS) caused by glucolipotoxicity is an essential feature in type 2 diabetes mellitus (T2DM). Palmitate and eicosapentaenoate (EPA), because of their lipotoxicity and protection effect, were found to impair or restore the GSIS in beta cells. Furthermore, palmitate was found to up‐regulate the expression level of sterol regulatory element‐binding protein (SREBP)‐1c and down‐regulate the levels of pancreatic and duodenal homeobox (Pdx)‐1 and glucagon‐like peptide (GLP)‐1 receptor (GLP‐1R) in INS‐1 cells. To investigate the underlying mechanism, the lentiviral system was used to knock‐down or over‐express SREBP‐1c and Pdx‐1, respectively. It was found that palmitate failed to suppress the expression of Pdx‐1 and GLP‐1R in SREBP‐1c‐deficient INS‐1 cells. Moreover, down‐regulation of Pdx‐1 could cause the low expression of GLP‐1R with/without palmitate treatment. Additionally, either SREBP‐1c down‐regulation or Pdx‐1 over‐expression could partially alleviate palmitate‐induced GSIS impairment. These results suggested that sequent SREBP‐1c‐Pdx‐1‐GLP‐1R signal pathway was involved in the palmitate‐caused GSIS impairment in beta cells. J. Cell. Biochem. 111: 634–642, 2010. © 2010 Wiley‐Liss, Inc.     

A dual discrimination mode for improved specificity towards let‐7a detection via a single‐base mutated padlock probe‐based exponential rolling circle amplification

MicroRNA (miRNA) family members are usually highly homologous sequences, and it is a challenging task to selectively detect one miRNA member from other family members in medical diagnosis. Here, we describe the design of a dual discrimination mode for improved specificity towards let‐7a detection over the other members of the let‐7 family, in which an intentional base mutation was introduced into the padlock probe of an exponential rolling circle amplification. The inherent discrimination power of the padlock probe and the introduced base mutation constituted a dual discrimination mode, which provided enhanced specificity for let‐7a, even over single‐base mismatched family sequences. Furthermore, the assay enabled the quantitative detection of let‐7a in a dynamic range from 200 amol to 100 fmol. This technique has also been successfully applied to real small RNA samples extracted from human lung cancers. For the first time, through intentionally mutating one base on the padlock probe of the exponential rolling circle amplification (RCA), we improved the discrimination capability for let‐7 family members, while maintaining adequate sensitivity. Overall, this dual discrimination mode and the high amplification strategy have the potential to be extended to other short, but highly homologous, miRNA sequences.     

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Summary Ye, Lin, and Taylor (2008, Biometrics 64 , 1238–1246) proposed a joint model for longitudinal measurements and time‐to‐event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two‐stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time‐to‐event data. In the second stage, the posterior expectation of an individual's random effects from the mixed‐model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time‐to‐event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008) . In agreement with the methodology proposed by Ye et al. (2008) , an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.     

Analysis of Longitudinal Data of Epileptic Seizure Counts – A Two‐State Hidden Markov Regression Approach

This paper discusses a two‐state hidden Markov Poisson regression (MPR) model for analyzing longitudinal data of epileptic seizure counts, which allows for the rate of the Poisson process to depend on covariates through an exponential link function and to change according to the states of a two‐state Markov chain with its transition probabilities associated with covariates through a logit link function. This paper also considers a two‐state hidden Markov negative binomial regression (MNBR) model, as an alternative, by using the negative binomial instead of Poisson distribution in the proposed MPR model when there exists extra‐Poisson variation conditional on the states of the Markov chain. The two proposed models in this paper relax the stationary requirement of the Markov chain, allow for overdispersion relative to the usual Poisson regression model and for correlation between repeated observations. The proposed methodology provides a plausible analysis for the longitudinal data of epileptic seizure counts, and the MNBR model fits the data much better than the MPR model. Maximum likelihood estimation using the EM and quasi‐Newton algorithms is discussed. A Monte Carlo study for the proposed MPR model investigates the reliability of the estimation method, the choice of probabilities for the initial states of the Markov chain, and some finite sample behaviors of the maximum likelihood estimates, suggesting that (1) the estimation method is accurate and reliable as long as the total number of observations is reasonably large, and (2) the choice of probabilities for the initial states of the Markov process has little impact on the parameter estimates.     

Joint generalized models for multidimensional outcomes: A case study of neuroscience data from multimodalities

This paper is motivated from the analysis of neuroscience data in a study of neural and muscular mechanisms of muscle fatigue. Multidimensional outcomes of different natures were obtained simultaneously from multiple modalities, including handgrip force, electromyography (EMG), and functional magnetic resonance imaging (fMRI). We first study individual modeling of the univariate response depending on its nature. A mixed‐effects beta model and a mixed‐effects simplex model are compared for modeling the force/EMG percentages. A mixed‐effects negative‐binomial model is proposed for modeling the fMRI counts. Then, I present a joint modeling approach to model the multidimensional outcomes together, which allows us to not only estimate the covariate effects but also to evaluate the strength of association among the multiple responses from different modalities. A simulation study is conducted to quantify the possible benefits by the new approaches in finite sample situations. Finally, the analysis of the fatigue data is illustrated with the use of the proposed methods.     

A measure for spatial heterogeneity of a grassland vegetation based on the beta‐binomial distribution

Abstract. A method is proposed to estimate the frequency and the spatial heterogeneity of occurrence of individual plant species composing the community of a grassland or a plant community with a short height. The measure is based on the beta‐binomial distribution. The weighted average heterogeneity of all the species composing a community provides a measure of community‐level heterogeneity determining the spatial intricateness of community composition of existing species. As an example to illustrate the method, a sown grassland with grazing cows was analysed, on 102 quadrats of 50 cm × 50 cm, each of which divided into four small quadrats of 25 cm × 25 cm. The frequency of occurrence for all the species was recorded in each small quadrat. Good fits to the beta‐binomial series for most species of the community were obtained. These results indicate that (1) each species is distributed heterogeneously with respective spatial patterns, (2) the degree of heterogeneity is different from species to species, and (3) the beta‐binomial distribution can be applied for grassland communities. In most of the observed species spatial heterogeneity is often characterized by species‐specific propagating traits: seed‐propagating plant species exhibited a low heterogeneity/random pattern while clonal species exhibited a high heterogeneity/aggregated pattern. This measure can be applied to field surveys and to the estimation of community parameters for grassland diagnosis.     

Inverse‐probability‐of‐treatment weighted estimation of causal parameters in the presence of error‐contaminated and time‐dependent confounders

Inverse‐probability‐of‐treatment weighted (IPTW) estimation has been widely used to consistently estimate the causal parameters in marginal structural models, with time‐dependent confounding effects adjusted for. Just like other causal inference methods, the validity of IPTW estimation typically requires the crucial condition that all variables are precisely measured. However, this condition, is often violated in practice due to various reasons. It has been well documented that ignoring measurement error often leads to biased inference results. In this paper, we consider the IPTW estimation of the causal parameters in marginal structural models in the presence of error‐contaminated and time‐dependent confounders. We explore several methods to correct for the effects of measurement error on the estimation of causal parameters. Numerical studies are reported to assess the finite sample performance of the proposed methods.     

A weighted partial likelihood approach for zero‐truncated models

Zero‐truncated data arises in various disciplines where counts are observed but the zero count category cannot be observed during sampling. Maximum likelihood estimation can be used to model these data; however, due to its nonstandard form it cannot be easily implemented using well‐known software packages, and additional programming is often required. Motivated by the Rao–Blackwell theorem, we develop a weighted partial likelihood approach to estimate model parameters for zero‐truncated binomial and Poisson data. The resulting estimating function is equivalent to a weighted score function for standard count data models, and allows for applying readily available software. We evaluate the efficiency for this new approach and show that it performs almost as well as maximum likelihood estimation. The weighted partial likelihood approach is then extended to regression modelling and variable selection. We examine the performance of the proposed methods through simulation and present two case studies using real data.     

Two‐stage orthogonality based estimation for semiparametric varying‐coefficient models and its applications in analyzing AIDS data

Semiparametric smoothing methods are usually used to model longitudinal data, and the interest is to improve efficiency for regression coefficients. This paper is concerned with the estimation in semiparametric varying‐coefficient models (SVCMs) for longitudinal data. By the orthogonal projection method, local linear technique, quasi‐score estimation, and quasi‐maximum likelihood estimation, we propose a two‐stage orthogonality‐based method to estimate parameter vector, coefficient function vector, and covariance function. The developed procedures can be implemented separately and the resulting estimators do not affect each other. Under some mild conditions, asymptotic properties of the resulting estimators are established explicitly. In particular, the asymptotic behavior of the estimator of coefficient function vector at the boundaries is examined. Further, the finite sample performance of the proposed procedures is assessed by Monte Carlo simulation experiments. Finally, the proposed methodology is illustrated with an analysis of an acquired immune deficiency syndrome (AIDS) dataset.     

One‐Sided Test to Assess Correlation in Linear Logistic Models using Estimating Equations

A score‐type test is proposed for testing the hypothesis of independent binary random variables against positive correlation in linear logistic models with sparse data and cluster specific covariates. The test is developed for univariate and multivariate one‐sided alternatives. The main advantage of using score test is that it requires estimation of the model only under the null hypothesis, that in this case corresponds to the binomial maximum likelihood fit. The score‐type test is developed from a class of estimating equations with block‐diagonal structure in which the coefficients of the linear logistic model are estimated simultaneously with the correlation. The simplicity of the score test is illustrated in two particular examples.     

Robust parameter estimation during logistic modeling of batch and fed‐batch culture kinetics

Methods for robust logistic modeling of batch and fed‐batch mammalian cell cultures are presented in this study. Linearized forms of the logistic growth, logistic decline, and generalized logistic equation were derived to obtain initial estimates of the parameters by linear least squares. These initial estimates facilitated subsequent determination of refined values by nonlinear optimization using three different algorithms. Data from BHK, CHO, and hybridoma cells in batch or fed‐batch cultures at volumes ranging from 100 mL–300 L were tested with the above approach and solution convergence was obtained for all three nonlinear optimization approaches for all data sets. This result, despite the sensitivity of logistic equations to parameter variation because of their exponential nature, demonstrated that robust estimation of logistic parameters was possible by this combination of linearization followed by nonlinear optimization. The approach is relatively simple and can be implemented in a spreadsheet to robustly model mammalian cell culture batch or fed‐batch data. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Time for a rethink: time sub‐sampling methods in disparity‐through‐time analyses

Disparity‐through‐time analyses can be used to determine how morphological diversity changes in response to mass extinctions, or to investigate the drivers of morphological change. These analyses are routinely applied to palaeobiological datasets, yet, although there is much discussion about how to best calculate disparity, there has been little consideration of how taxa should be sub‐sampled through time. Standard practice is to group taxa into discrete time bins, often based on stratigraphic periods. However, this can introduce biases when bins are of unequal size, and implicitly assumes a punctuated model of evolution. In addition, many time bins may have few or no taxa, meaning that disparity cannot be calculated for the bin and making it harder to complete downstream analyses. Here we describe a different method to complement the disparity‐through‐time tool‐kit: time‐slicing. This method uses a time‐calibrated phylogenetic tree to sample disparity‐through‐time at any fixed point in time rather than binning taxa. It uses all available data (tips, nodes and branches) to increase the power of the analyses, specifies the implied model of evolution (punctuated or gradual), and is implemented in R. We test the time‐slicing method on four example datasets and compare its performance in common disparity‐through‐time analyses. We find that the way we time sub‐sample taxa can change our interpretations of the results of disparity‐through‐time analyses. We advise using multiple methods for time sub‐sampling taxa, rather than just time binning, to gain a better understanding disparity‐through‐time.     

Confidence Interval of a Proportion with Over‐dispersion

A new approach that extends the classical Clopper‐Pearson procedure is proposed for the estimation of the (1–α)% confidence interval of a proportion with over‐dispersion. Over‐dispersion occurs when a proportion of interest shows more variation (variance inflation) than predicted by the binomial distribution. There are two steps in the approach. The first step consists of the estimation of the variance inflation factor. In the second step, an extended Clopper‐Pearson procedure is applied to calculate the confidence interval after the effective sample size is obtained by adjusting with the estimated variance inflation factor. The performance of the extended Clopper‐Pearson procedure is evaluated via a Monte Carlo study under the setup motivated from head lice studies. It is demonstrated that the 95% confidence intervals constructed from the new approach generally have the closest coverage rate to target (95%) when compared with those constructed from competing procedures.     

Predicting events in clinical trials using two time‐to‐event outcomes

In clinical trials with time‐to‐event outcomes, it is of interest to predict when a prespecified number of events can be reached. Interim analysis is conducted to estimate the underlying survival function. When another correlated time‐to‐event endpoint is available, both outcome variables can be used to improve estimation efficiency. In this paper, we propose to use the convolution of two time‐to‐event variables to estimate the survival function of interest. Propositions and examples are provided based on exponential models that accommodate possible change points. We further propose a new estimation equation about the expected time that exploits the relationship of two endpoints. Simulations and the analysis of real data show that the proposed methods with bivariate information yield significant improvement in prediction over that of the univariate method.     

Cornification in reptilian epidermis occurs through the deposition of keratin‐associated beta‐proteins (beta‐keratins) onto a scaffold of intermediate filament keratins

The isolation of genes for alpha‐keratins and keratin‐associated beta‐proteins (formerly beta‐keratins) has allowed the production of epitope‐specific antibodies for localizing these proteins during the process of cornification epidermis of reptilian sauropsids. The antibodies are directed toward proteins in the alpha‐keratin range (40–70 kDa) or beta‐protein range (10–30 kDa) of most reptilian sauropsids. The ultrastructural immunogold study shows the localization of acidic alpha‐proteins in suprabasal and precorneous epidermal layers in lizard, snake, tuatara, crocodile, and turtle while keratin‐associated beta‐proteins are localized in precorneous and corneous layers. This late activation of the synthesis of keratin‐associated beta‐proteins is typical for keratin‐associated and corneous proteins in mammalian epidermis (involucrin, filaggrin, loricrin) or hair (tyrosine‐rich or sulfur‐rich proteins). In turtles and crocodilians epidermis, keratin‐associated beta‐proteins are synthesized in upper spinosus and precorneous layers and accumulate in the corneous layer. The complex stratification of lepidosaurian epidermis derives from the deposition of specific glycine‐rich versus cysteine‐glycine‐rich keratin‐associated beta‐proteins in cells sequentially produced from the basal layer and not from the alternation of beta‐ with alpha‐keratins. The process gives rise to Oberhäutchen, beta‐, mesos‐, and alpha‐layers during the shedding cycle of lizards and snakes. Differently from fish, amphibian, and mammalian keratin‐associated proteins (KAPs) of the epidermis, the keratin‐associated beta‐proteins of sauropsids are capable to form filaments of 3–4 nm which give rise to an X‐ray beta‐pattern as a consequence of the presence of a beta‐pleated central region of high homology, which seems to be absent in KAPs of the other vertebrates. J. Morphol., 2013. © 2012 Wiley Periodicals, Inc.     

Partial‐Likelihood Analysis of Spatio‐Temporal Point‐Process Data

Summary We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio‐temporal point‐process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum‐likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial‐likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain.