Estimating Treatment Effects of Longitudinal Designs using Regression Models on Propensity Scores

Summary We derive regression estimators that can compare longitudinal treatments using only the longitudinal propensity scores as regressors. These estimators, which assume knowledge of the variables used in the treatment assignment, are important for reducing the large dimension of covariates for two reasons. First, if the regression models on the longitudinal propensity scores are correct, then our estimators share advantages of correctly specified model‐based estimators, a benefit not shared by estimators based on weights alone. Second, if the models are incorrect, the misspecification can be more easily limited through model checking than with models based on the full covariates. Thus, our estimators can also be better when used in place of the regression on the full covariates. We use our methods to compare longitudinal treatments for type II diabetes mellitus.     

Correction for Covariate Measurement Error in Nonparametric Longitudinal Regression

Summary We introduce a correction for covariate measurement error in nonparametric regression applied to longitudinal binary data arising from a study on human sleep. The data have been surveyed to investigate the association of some hormonal levels and the probability of being asleep. The hormonal effect is modeled flexibly while we account for the error‐prone measurement of its concentration in the blood and the longitudinal character of the data. We present a fully Bayesian treatment utilizing Markov chain Monte Carlo inference techniques, and also introduce block updating to improve sampling and computational performance in the binary case. Our model is partly inspired by the relevance vector machine with radial basis functions, where usually very few basis functions are automatically selected for fitting the data. In the proposed approach, we implement such data‐driven complexity regulation by adopting the idea of Bayesian model averaging. Besides the general theory and the detailed sampling scheme, we also provide a simulation study for the Gaussian and the binary cases by comparing our method to the naive analysis ignoring measurement error. The results demonstrate a clear gain when using the proposed correction method, particularly for the Gaussian case with medium and large measurement error variances, even if the covariate model is misspecified.     

Influence of castration-induced testosterone and estradiol deficiency on obesity and glucose metabolism in male Göttingen minipigs

Low testosterone and estradiol concentrations are predictive for the development of the metabolic syndrome in men and women, respectively. The aim of this study was to investigate the influence of sex hormone deficiency on food intake, body weight, body composition and glucose metabolism in male Göttingen minipigs.Five adult male Göttingen minipigs were studied before castration (pre-cast), 10-18 days (post-cast 1) and 10-11 weeks (post-cast 2) after castration. Parameters of interest were food intake, body weight, body fat percentage and sex hormone concentrations. Furthermore glucose tolerance, glucagon suppression, insulin resistance, beta cell function and disposition index were evaluated by oral and intravenous glucose tolerance tests.Castration led to almost complete disappearance of circulating testosterone and estradiol and secondarily to increased food intake, body weight and body fat percentage. Ten-eighteen days sex hormone deficiency (post-cast 1) did not significantly change any of the investigated metabolic parameters compared to pre-cast levels. Ten weeks after castration (post-cast 2) significant insulin resistance, glucose intolerance and hyperglucagonemia was found, and the beta cell function and the disposition index both were decreased.In conclusion, castration-induced sex hormone deficiency in male Göttingen minipigs results in hyperphagia, obesity and disturbed glucose metabolism, which are some of the features typical for the human metabolic syndrome.     

Uncertainty in allometric exponent estimation: a case study in scaling metabolic rate with body mass

Many factors could influence the allometric scaling exponent β estimation, but have not been explored systematically. We investigated the influences of three factors on the estimate of β based on a data set of 626 species of basal metabolic rate and mass in mammals. The influence of sampling error was tested by re-sampling with different sample sizes using a Monte Carlo method. Small random errors were introduced to measured data to examine their influence on parameter estimations. The influence of analysis method was also evaluated by applying nonlinear and linear regressions to the original data. Results showed that a relative large sample size was required to lower statistical inference errors. When sample size n was 10% of the base population size (n=63), 35% of the samples supported β=2/3, 39% supported β=3/4, and 15% rejected β=0.711, even though the base population had a β=0.711. The controversy surrounding the estimation of β in the literature could be partially attributable to such small sample sizes in many studies. Measurement errors in body mass and base metabolic rate, especially in body mass, could largely increase alpha and beta errors. Analysis methods also affected parameter estimations. Nonlinear regressions provided better estimates of the scaling exponent that were significantly higher than these commonly estimated by linear regressions. This study demonstrated the importance of the quantity and quality of data as well as analysis method in power law analysis, raising caution in interpreting power law results. Meta-data synthesis using data from independent studies seems to be a proper approach in the future, but caution should be taken to make sure that such measurements are made using similar protocols.     

Noninvasive Estimation of Black Bear Abundance Incorporating Genotyping Errors and Harvested Bear

ABSTRACT Estimating black bear (Ursus americanus) population size is a difficult but important requirement when justifying harvest quotas and managing populations. Advancements in genetic techniques provide a means to identify individual bears using DNA contained in tissue and hair samples, thereby permitting estimates of population abundance based on established mark-capture-recapture methodology. We expand on previous noninvasive population-estimation work by geographically extending sampling areas (36,848 km²) to include the entire Northern Lower Peninsula (NLP) of Michigan, USA. We selected sampling locations randomly within biologically relevant bear habitat and used barbed wire hair snares to collect hair samples. Unlike previous noninvasive studies, we used tissue samples from harvested bears as an additional sampling occasion to increase recapture probabilities. We developed subsampling protocols to account for both spatial and temporal variance in sample distribution and variation in sample quality using recently published quality control protocols using 5 microsatellite loci. We quantified genotyping errors using samples from harvested bears and estimated abundance using statistical models that accounted for genotyping error. We estimated the population of yearling and adult black bears in the NLP to be 1,882 bears (95% CI = 1,389-2,551 bears). The derived population estimate with a 15% coefficient of variation was used by wildlife managers to examine the sustainability of harvest over a large geographic area.     

Development of sequential multiple comparison procedure for dose response test

We propose a multiple comparison procedure to identify the minimum effective dose level by sequentially comparing each dose level with the zero dose level in the dose finding test. If we can find the minimum effective dose level at an early stage in the sequential test, it is possible to terminate the procedure in the dose finding test after a few group observations up to the dose level. Thus, the procedure is viable from an economical point of view when high costs are involved in obtaining the observations. In the procedure, we present an integral formula to determine the critical values for satisfying a predefined type I familywise error rate. Furthermore, we show how to determine the required sample size in order to guarantee the power of the test in the procedure. In practice, we compare the power of the test and the required sample size for various configurations of the population means in simulation studies and adopt our sequential procedure to the dose response test in a case study.     

非线性拟双曲方程的交替方向变网格有限元方法

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,提出了一种三维交替方向变网格有限元格式,应用微分方程先验估计的理论和技巧,得到了最佳阶的L^2模误差估计结果。并作了数值实验。指明方法是高效可行的．     

A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in Soay sheep (Ovis aries)

Studies of the quantitative genetics of natural populations have contributed greatly to evolutionary biology in recent years. However, while pedigree data required are often uncertain (i.e. incomplete and partly erroneous) and limited, means to evaluate the effects of such uncertainties have not been developed. We have therefore developed a general framework for power and sensitivity analyses of such studies. We propose that researchers first generate a set of pedigree data that they wish to use in a quantitative genetic study, as well as data regarding errors that occur in that pedigree. This pedigree is then permuted using the data regarding errors to generate hypothetical 'true' and 'assumed' pedigrees that differ so as to mimic pedigree errors that might occur in the study system under consideration. Phenotypic data are then simulated across the true pedigree (according to user-defined genetic and environmental covariance structures), before being analysed with standard quantitative genetic techniques in conjunction with the 'assumed' pedigree data. To illustrate this approach, we conducted power and sensitivity analyses in a well-known study of Soay sheep (Ovis aries). We found that, although the estimation of simple genetic (co)variance structures is fairly robust to pedigree errors, some potentially serious biases were detected under more complex scenarios involving maternal effects. Power analyses also showed that this study system provides high power to detect heritabilities as low as about 0.09. Given this range of results, we suggest that such power and sensitivity analyses could greatly complement empirical studies, and we provide the computer program PEDANTICS to aid in their application.     

Reconstructing community relationships: the impact of sampling error, ordination approach, and gradient length

Effectively summarizing complex community relationships is an important feature in studies such as biodiversity, global change, and invasion ecology. The reliability of such community summaries depends on the degree of sampling variability that is present in the data, the structure of the data, and the choice of ordination method, but the relative importance of these factors is not understood. We compared the validity of results from different ordination methods by applying five levels of sampling error to a simulated coenoplane model at two gradient lengths using two types of data (abundance and presence–absence). The multivariate methods we compared were correspondence analysis (CA), detrended correspondence analysis (DCA), non-metric multidimensional scaling (NMDS), principal component analysis (PCA) and principal coordinates analysis (PCoA). Our results showed CA and PCA using presence–absence data were the most successful methods regardless of sampling error and gradient length, closely followed by the other methods using presence–absence data. With abundance data, PCA and CA were the most successful approaches with the short and long gradients, respectively. Approaches based on PCoA and NMDS using abundance data did not perform well regardless of the choice of distance measure used in the analysis. Both of these methods, along with the PCA using abundance data, were strongly affected by the longer gradient, leading to more distorted results.     

Sample size and sampling error in geometric morphometric studies of size and shape

Geometric morphometric studies are increasingly becoming common in systematics and palaeontology. The samples in such studies are often small, due to the paucity of material available for analysis. However, very few studies have tried to assess the impact of sampling error on analytical results. Here, this issue is addressed empirically using repeated randomized selection experiments to build progressively smaller samples from an original dataset of ∼400 vervet monkey (Cercopithecus aethiops) skulls. Size and shape parameters (including mean size and shape, size and shape variances, angles of allometric trajectories) that are commonly used in geometric morphometric studies, are estimated first in the original sample and then in the random subsamples. Estimates are then compared to give an indication of what is the minimum desirable sample size for each parameter. Mean size, standard deviation of size and variance of shape are found to be fairly accurate even in relatively small samples. In contrast, mean shapes and angles between static allometric trajectories are strongly affected by sampling error. If confirmed in other groups, our findings may have substantial implications for studies of morphological variation in present and fossil species. By performing rarefaction analyses like those presented in our study, morphometricians can be easily provided with important clues on how a simple but crucial factor like sample size can alter results of their studies.