Control for confounding in the presence of measurement error in hierarchical models

Hierarchical modeling is becoming increasingly popular in epidemiology, particularly in air pollution studies. When potential confounding exists, a multilevel model yields better power to assess the independent effects of each predictor by gathering evidence across many sub-studies. If the predictors are measured with unknown error, bias can be expected in the individual substudies, and in the combined estimates of the second-stage model. We consider two alternative methods for estimating the independent effects of two predictors in a hierarchical model. We show both analytically and via simulation that one of these gives essentially unbiased estimates even in the presence of measurement error, at the price of a moderate reduction in power. The second avoids the potential for upward bias, at the price of a smaller reduction in power. Since measurement error is endemic in epidemiology, these approaches hold considerable potential. We illustrate the two methods by applying them to two air pollution studies. In the first, we re-analyze published data to show that the estimated effect of fine particles on daily deaths, independent of coarse particles, was downwardly biased by measurement error in the original analysis. The estimated effect of coarse particles becomes more protective using the new estimates. In the second example, we use published data on the association between airborne particles and daily deaths in 10 US cities to estimate the effect of gaseous air pollutants on daily deaths. The resulting effect size estimates were very small and the confidence intervals included zero.     

A retrospective assessment of the accuracy of the paternity inference program CERVUS

CERVUS is a Windows-based software package written to infer paternity in natural populations. It offers advantages over exclusionary-based methods of paternity inference in that multiple nonexcluded males can be statistically distinguished, laboratory typing error is considered and statistical confidence is determined for assigned paternities through simulation. In this study we use a panel of 84 microsatellite markers to retrospectively determine the accuracy of statistical confidence when CERVUS was used to infer paternity in a population of red deer (Cervus elaphus). The actual confidence of CERVUS-assigned paternities was not significantly different from that predicted by simulation.     

Modeling markers of disease progression by a hidden Markov process: application to characterizing CD4 cell decline

Multistate models have been increasingly used to model natural history of many diseases as well as to characterize the follow-up of patients under varied clinical protocols. This modeling allows describing disease evolution, estimating the transition rates, and evaluating the therapy effects on progression. In many cases, the staging is defined on the basis of a discretization of the values of continuous markers (CD4 cell count for HIV application) that are subject to great variability due mainly to short time-scale noise (intraindividual variability) and measurement errors. This led us to formulate a Bayesian hierarchical model where, at a first level, a disease process (Markov model on the true states, which are unobserved) is introduced and, at a second level, the measurement process making the link between the true states and the observed marker values is modeled. This hierarchical formulation allows joint estimation of the parameters of both processes. Estimation of the quantities of interest is performed via stochastic algorithms of the family of Markov chain Monte Carlo methods. The flexibility of this approach is illustrated by analyzing the CD4 data on HIV patients of the Concorde clinical trial.     

Measuring tolerance to herbivory: accuracy and precision of estimates made using natural versus imposed damage

Abstract.— Tolerance to herbivory (the ability of a plant to incur herbivore damage without a corresponding reduction in fitness) can be measured using either naturally occurring or imposed herbivore damage. After briefly reviewing some of the advantages and disadvantages of these approaches, we present calculations describing the degree to which estimates of tolerance will be biased by environmental variables that affect both herbivory and fitness. With naturally occurring herbivory the presence of environmental variables that are correlated with herbivory and fitness will result in biased estimates of tolerance. In contrast, estimates obtained from experiments in which herbivory is artificially imposed will be unbiased; however, under a wide range of parameter values these estimates will be less precise than estimates obtained from experiments in which herbivory is not manipulated.     

参数仪器变量估计近似分布方差的一种算法

本文对更一般的结构模型给出了参数的一种常用的仪器变量估计近似分布方差的一种算法．并且给出了未知真值x服从指数分布的例子．此算法对生物科学中统计规律的探讨有一定的应用价值．     

Indices of reproductive skew depend on average reproductive success

Several indices of reproductive skew, which quantify the degree of unequal partitioning of reproductive output among members in an animal society, have been proposed. Here we point out the drawbacks of these indices. The most serious problem is the dependence of the indices on mean reproductive success: skew values tend to be larger, as average numbers of offspring decrease, due to random sampling error in numbers of offspring. Thus it is difficult to compare societies with different average lifetime reproductive success using these indices, even though we have presented methods to calculate the expected reproductive skew caused by random sampling error, especially when average numbers of offspring are small, as is often the case with cooperatively breeding vertebrates. As an alternative, we propose using the spatial dispersion indices of population ecology (Morisita's index or its standardized version) for the measurement of reproductive skew. These indices are almost independent of average fecundity and have their own method of testing for random variation in offspring numbers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of species and habitat positional errors on the performance and interpretation of species distribution models

Aim A key assumption in species distribution modelling is that both species and environmental data layers contain no positional errors, yet this will rarely be true. This study assesses the effect of introduced positional errors on the performance and interpretation of species distribution models. Location Baixo Alentejo region of Portugal. Methods Data on steppe bird occurrence were collected using a random stratified sampling design on a 1‐km² pixel grid. Environmental data were sourced from satellite imagery and digital maps. Error was deliberately introduced into the species data as shifts in a random direction of 0–1, 2–3, 4–5 and 0–5 pixels. Whole habitat layers were shifted by 1 pixel to cause mis‐registration, and the cumulative effect of one to three shifted layers investigated. Distribution models were built for three species using three algorithms with three replicates. Test models were compared with controls without errors. Results Positional errors in the species data led to a drop in model performance (larger errors having larger effects – typically up to 10% drop in area under the curve on average), although not enough for models to be rejected. Model interpretation was more severely affected with inconsistencies in the contributing variables. Errors in the habitat layers had similar although lesser effects. Main conclusions Models with species positional errors are hard to detect, often statistically good, ecologically plausible and useful for prediction, but interpreting them is dangerous. Mis‐registered habitat layers produce smaller effects probably because shifting entire layers does not break down the correlation structure to the same extent as random shifts in individual species observations. Spatial autocorrelation in the habitat layers may protect against species positional errors to some extent but the relationship is complex and requires further work. The key recommendation must be that positional errors should be minimised through careful field design and data processing.     

High error rates for avian molecular sex identification primer sets applied to molted feathers

ABSTRACT Molted feathers are becoming increasingly important as a source of DNA for identifying the sex of individuals, and accurate methods for molecular sex identification are needed. Three molecular sex identification primer sets have been developed for use in nearly all nonratite birds, but performance of these primer sets has not been evaluated for molted feathers. For two species of birds, the Ring‐necked Pheasant (Phasianus colchicus) and the Scarlet Macaw (Ara macao), we evaluated success and error rates among primer sets using DNA from molted feathers and assessed the percentage of times an incorrect sex would be assigned when analyses are completed in duplicate. Amplification success rates differed among the primer sets for both species, ranging from 67.5% to 89.2% (P= 0.0002 and 0.009), and error rates were high, ranging from 1.9% to 24.2%. Success rates and error rates were not consistent between species and among primer sets. To improve the accuracy of molecular sex identification tests when using molted feathers, we suggest determining acceptable confidence levels in the accuracy of sex assignment, conducting pilot tests to evaluate the performance of different primer sets, and using high‐resolution electrophoresis systems to increase detection of errors.