Quantifying intraclass correlations for count and time‐to‐event data

The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter‐rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non‐Gaussian outcomes. The focus here is on count and time‐to‐event outcomes where so‐called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed‐form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies.     

The Multiple Poisson Distribution,Its Characteristics and a Variety of Forms

The multiple Poisson distribution, known under different names, such as generalized Poisson, compound Poisson, composed Poisson, stuttering Poisson, Poisson power series, Poisson-stopped sum distribution, etc., plays an important role in discrete distribution theory. Here we want to show its basic characteristics, the variety of its forms and specify the generalizing distributions.     

Modeling the dependence between the number of trials and the success probability in binary trials

A model for binary trials based on a bivariate generalization of the Poisson process for both the number of successes and number of trials with the transition rates dependent on the accumulating numbers of successes and trials is used to reanalyze some recently published data of Zhu, Eickhoff, and Kaiser (2003, Biometrics59, 955-961). This modeling admits alternative distributions for the numbers of trials and the numbers of successes conditional on the number of trials which generalize the Poisson and binomial distributions, without some of the restrictions apparent in the beta-binomial-Poisson mixed modeling of Zhu et al. (2003). Some quite marked differences between the results of this analysis and those described in Zhu et al. (2003) are apparent.     

混合位置尺度分布中分量参数的统计推断

本文讨论混合位置尺度分布当混合比已知时分量参数的假设检验和区间估计．本文所提出的方法基于广义枢轴模型．当只有感兴趣的参数未知时,检验的实际水平等于名义水平,且各置信域的实际覆盖率等于名义覆盖率．在更一般的场合,检验是相合的,并且各置信域的实际覆盖率趋于名义覆盖率．模拟显示我们的方法是令人满意的．     

On the HIV Incubation Distribution Under AZT Treatment

Assuming some general models for the HIV epidemic, in this paper I derive the HIV incubation distributions under AZT treatment. It is shown that under some conditions, these probability distributions are mixtures of some generalized Gamma distributions and products of generalized Gamma distributions.     

A stochastic model of tumor response to fractionated radiation: limit theorems and rate of convergence

The iterated birth and death Markov process is defined as an n-fold iteration of a birth and death Markov process describing kinetics of certain population combined with random killing of individuals in the population at moments tau 1,...,tau n with given survival probabilities s1,...,sn. A long-standing problem of computing the distribution of the number of clonogenic tumor cells surviving an arbitrary fractionated radiation schedule is solved within the framework of iterated birth and death Markov process. It is shown that, for any initial population size iota, the distribution of the size N of the population at moment t > or = tau n is generalized negative binomial, and an explicit computationally feasible formula for the latter is found. It is shown that if i --> infinity and sn --> 0 so that the product iota s1...sn tends to a finite positive limit, the distribution of random variable N converges to a probability distribution, which for t = tau n turns out to be Poisson. In the latter case, an estimate of the rate of convergence in the total variation metric similar to the classical Law of Rare Events is obtained.     

Response surfaces for overdispersion in the study of the conditions for fish eggs hatching

Response surface methodology, originally developed for determining optimal conditions in industrial experiments, was early adapted to experiments in marine ecology. However, these involved studying the shape of the complete response surface, not only detecting the optimum, and often had counts or durations as the response variable. Thus, nonlinear, nonnormal response models were required. For counts, binomial and beta-binomial models have been used, the latter because of substantial overdispersion. In closely controlled experiments, overdispersion among units held under the same conditions might indicate that some mishap has occurred in conducting the study. One possible check is to model the dispersion as a second response surface. This procedure is used to show that overdispersion in fish egg hatching experiments has a biological explanation in that it occurs only under suboptimal hatching conditions.     

Assessing New Zealand fern diversity from spatial predictions of species assemblages

The utility of explicit spatial predictions for biodiversity assessment is investigated with New Zealand fern flora. Distributions of 43 species were modelled from climatic and landform variables and predicted across New Zealand using generalised additive models (GAM). An original package of functions called generalised regression analysis and spatial prediction (GRASP) was developed to perform the analyses. On average, for the 43 models, the contributions of environmental variables indicate that mean annual temperature is the most important factor at this broad regional scale. Both annual solar radiation and its seasonality had higher correlations than temperature seasonality. Measures of water availability such as ratio of rainfall to potential evapotranspiration, air saturation deficit and soil water deficit presented significant contributions. Lithology was a better predictor than slope and drainage. These results are similar to those obtained from analyses of the distributions of New Zealand tree species and are consistent with the hypothesis that both tree and fern diversity are highest on sites conducive to high productivity. In order to identify hotspots of fern diversity, spatial predictions of individual species were summed up. The resulting map gave a very similar result to the direct prediction of their corresponding richness (number of species by plot out of 43 spp.). As a consequence, and where individual species models were not all available, the number of species within different species assemblages was directly modelled. Predicted richness hotspots of total species (out of 122 spp.), selected species (out of 43 and 21 spp.) and common species (out of 23 spp.) present very similar spatial patterns and are highly correlated. Richness of uncommon species (out of 39 spp.) was also accurately predicted, but presented a different spatial pattern. The number of rare species (out of 60 spp.) was not correctly modelled. Even though the lack of data for rare species clearly limits the application of this approach, fern community composition of more common species can be partially reconstructed from individual species predictions. This case study offers therefore a consistent approach not only for biodiversity hotspots identification, but also for setting targets to biodiversity assessment and restoration programs.     

Marginal models for longitudinal continuous proportional data

Summary. Continuous proportional data arise when the response of interest is a percentage between zero and one, e.g., the percentage of decrease in renal function at different follow‐up times from the baseline. In this paper, we propose methods to directly model the marginal means of the longitudinal proportional responses using the simplex distribution of Barndorff‐Nielsen and Jørgensen that takes into account the fact that such responses are percentages restricted between zero and one and may as well have large dispersion. Parameters in such a marginal model are estimated using an extended version of the generalized estimating equations where the score vector is a nonlinear function of the observed response. The method is illustrated with an ophthalmology study on the use of intraocular gas in retinal repair surgeries.     

Loglinear models for the robust design in mark-recapture experiments

The robust design is a method for implementing a mark-recapture experiment featuring a nested sampling structure. The first level consists of primary sampling sessions; the population experiences mortality and immigration between primary sessions so that open population models apply at this level. The second level of sampling has a short mark-recapture study within each primary session. Closed population models are used at this stage to estimate the animal abundance at each primary session. This article suggests a loglinear technique to fit the robust design. Loglinear models for the analysis of mark-recapture data from closed and open populations are first reviewed. These two types of models are then combined to analyze the data from a robust design. The proposed loglinear approach to the robust design allows incorporating parameters for a heterogeneity in the capture probabilities of the units within each primary session. Temporary emigration out of the study area can also be accounted for in the loglinear framework. The analysis is relatively simple; it relies on a large Poisson regression with the vector of frequencies of the capture histories as dependent variable. An example concerned with the estimation of abundance and survival of the red-back vole in an area of southeastern Québec is presented.