A new method for dealing with measurement error in explanatory variables of regression models

We introduce a new method, moment reconstruction, of correcting for measurement error in covariates in regression models. The central idea is similar to regression calibration in that the values of the covariates that are measured with error are replaced by "adjusted" values. In regression calibration the adjusted value is the expectation of the true value conditional on the measured value. In moment reconstruction the adjusted value is the variance-preserving empirical Bayes estimate of the true value conditional on the outcome variable. The adjusted values thereby have the same first two moments and the same covariance with the outcome variable as the unobserved "true" covariate values. We show that moment reconstruction is equivalent to regression calibration in the case of linear regression, but leads to different results for logistic regression. For case-control studies with logistic regression and covariates that are normally distributed within cases and controls, we show that the resulting estimates of the regression coefficients are consistent. In simulations we demonstrate that for logistic regression, moment reconstruction carries less bias than regression calibration, and for case-control studies is superior in mean-square error to the standard regression calibration approach. Finally, we give an example of the use of moment reconstruction in linear discriminant analysis and a nonstandard problem where we wish to adjust a classification tree for measurement error in the explanatory variables.     

Shared uncertainty in measurement error problems, with application to Nevada Test Site fallout data

In radiation epidemiology, it is often necessary to use mathematical models in the absence of direct measurements of individual doses. When complex models are used as surrogates for direct measurements to estimate individual doses that occurred almost 50 years ago, dose estimates will be associated with considerable error, this error being a mixture of (a) classical measurement error due to individual data such as diet histories and (b) Berkson measurement error associated with various aspects of the dosimetry system. In the Nevada Test Site(NTS) Thyroid Disease Study, the Berkson measurement errors are correlated within strata. This article concerns the development of statistical methods for inference about risk of radiation dose on thyroid disease, methods that account for the complex error structure inherence in the problem. Bayesian methods using Markov chain Monte Carlo and Monte-Carlo expectation-maximization methods are described, with both sharing a key Metropolis-Hastings step. Regression calibration is also considered, but we show that regression calibration does not use the correlation structure of the Berkson errors. Our methods are applied to the NTS Study, where we find a strong dose-response relationship between dose and thyroiditis. We conclude that full consideration of mixtures of Berkson and classical uncertainties in reconstructed individual doses are important for quantifying the dose response and its credibility/confidence interval. Using regression calibration and expectation values for individual doses can lead to a substantial underestimation of the excess relative risk per gray and its 95% confidence intervals.     

Use of the individual data of the a-bomb survivors for biologically based cancer models

All recent analyses of the data on solid cancer incidence of the atomic bomb survivors are corrected for migration and random dose errors. In the usual treatment with grouped data and regression calibration, the calibration of doses depends on the used dose response. For solid cancers, it usually is linear. Here, an individual likelihood is presented which works without further adjustment for all dose responses. When the same assumptions are made as in the usual Poisson regression, equivalent results are obtained. But, the individual likelihood has the potential to use more detailed models for dose errors and to estimate non-linear dose responses without recalibration. As an example for the potential of the individual data set for the analysis of risk at low doses, signals for a saturating bystander effect are investigated.     

A multifunctional system for automating physiological experiments

The methodical problems of automatization of physiological investigations on the basis of modern computer complexes "micro-CAMAC-lab" are discussed. The considered conceptions are illustrated by example of CAMEX-program-system ensuring the measurement, storing, visual control, editing and analysis of physiological experimental data.     

Identifying latent clusters of variability in longitudinal data

Means or other central tendency measures are by far the most common focus of statistical analyses. However, as Carroll (2003) noted, "systematic dependence of variability on known factors" may be "fundamental to the proper solution of scientific problems" in certain settings. We develop a latent cluster model that relates underlying "clusters" of variability to baseline or outcome measures of interest. Because estimation of variability is inextricably linked to estimation of trend, assumptions about underlying trends are minimized by using nonparametric regression estimates. The resulting residual errors are then clustered into unobserved clusters of variability that are in turn related to subject-level predictors of interest. An application is made to psychological affect data.     

Allowance for random dose estimation errors in atomic bomb survivor studies: a revision

Allowing for imprecision of radiation dose estimates for A-bomb survivors followed up by the Radiation Effects Research Foundation can be improved through recent statistical methodology. Since the entire RERF dosimetry system has recently been revised, it is timely to reconsider this. We have found that the dosimetry revision itself does not warrant changes in these methods but that the new methodology does. In addition to assumptions regarding the form and magnitude of dose estimation errors, previous and current methods involve the apparent distribution of true doses in the cohort. New formulas give results conveniently and explicitly in terms of these inputs. Further, it is now possible to use assumptions about two components of the dose errors, referred to in the statistical literature as "classical" and "Berkson-type". There are indirect statistical indications, involving non-cancer biological effects, that errors may be somewhat larger than assumed before, in line with recommendations made here. Inevitably, methods must rely on uncertain assumptions about the magnitude of dose errors, and it is comforting to find that, within the range of plausibility, eventual cancer risk estimates are not very sensitive to these.     

A review of the calibration methods for measuring the carbon and oxygen isotopes in CO2 based on isotope ratio infrared spectroscopy北大核心CSCD

With the development of isotope ratio infrared spectroscopy (IRIS) technology, it is now possible for the in situ high temporal resolution and high precision measurement of carbon isotopic composition (d13C) and oxygen isotopic composition (d18O) of atmospheric CO2, which overcomes the low temporal resolution and labor intensive shortcoming of traditional isotope ratio mass spectrometry (IRMS). The dependence of d13C and d18O on CO2 concentration (termed as concentration dependence) and the drift due to sensitivity to changing environmental conditions (termed as instrumental drift) are the two main sources of error affecting the IRIS measurements. Therefore, it is important to obtain precise measurements by constructing a proper calibration strategy to solve the concentration dependence and instrumental drift. In this study, we briefly discussed the definition and related theoretical principle of concentration dependence, and elaborated the theoretical and empirical calibration methods of concentration dependence. Moreover, we introduced the calibration methods of instrumental drift, and reviewed the state of the art of calibration methods and its application of IRIS technology. Additionally, we briefly discussed the definition and method of data traceability to the international standard, and reviewed its application of IRIS technology. Finally, we recommend that concentration dependence is corrected by using three standards or above with known CO2 concentration and its d13C and d18O, bracketing the CO2 concentration of samples. The instrumental drift is corrected by setting appropriate calibration frequency and all dataset are traceable to the international standard. In the future, the comparative study of different IRIS instruments and calibration methods should be enhanced, and the similar methods should be used for measuring CH4, N2O and H2O isotopes by IRIS technique. The IRIS technology combined with other technology will provide a new opportunity for ecological research. © 2018 Editorial Office of Chinese Journal of Plant Ecology. All rights reserved.     

A review of the calibration methods for measuring the carbon and oxygen isotopes in CO2 based on isotope ratio infrared spectroscopy

稳定同位素红外光谱(IRIS)技术克服了传统的大气CO₂气瓶采样-同位素质谱(IRMS)技术时间分辨率低且耗时费力的缺点, 可以实现高时间分辨率和高精度的大气CO₂碳同位素组成(δ ¹³C)和氧同位素组成(δ ¹⁸O)的原位连续测定。基于IRIS技术测量CO₂ δ ¹³C和δ ¹⁸O的误差来源主要包括δ ¹³C和δ ¹⁸O测量值对CO₂浓度变化的非线性响应(浓度依赖性)以及对环境条件变化的敏感性导致的漂移(时间漂移)。如何有效地校正浓度依赖性和时间漂移导致的误差是IRIS仪器应用的前提。该综述阐述了δ ¹³C和δ ¹⁸O测量值的浓度依赖性产生的理论基础, 回顾了浓度依赖性的理论校正和经验方程校正方法和应用; 回顾了时间漂移的校正原理、方法和应用; 概述了数据溯源至国际标准的原理、方法与应用现状。结合实际情况推荐利用3个或3个以上已知CO₂浓度和δ ¹³C、δ ¹⁸O真值的CO₂标准气体涵盖待测气体CO₂浓度的浓度依赖性校正, 设置适当的校正频率校正时间漂移并进行数据溯源。指出应该加强不同仪器和校正方法的比对研究; 采用IRIS技术测定CH₄、N₂O和H₂O同位素组成也可以采取类似的校正方法。     

Analysis and reduction of thermal dose errors in MRgFUS treatment

ExAblate 2000 MRgFUS system (InSightec) installed in Ospedale Maggiore Niguarda Ca' Granda (Milano, Italy) is currently used to treat uterine fibroids. Through the magnetic resonance thermometry (PRF method), it is possible to monitor the temperature in the target in real-time and compute the treated region calculating the thermal dose. The purpose of this work is to investigate the errors in the temperature measurements and their effect on thermal dose. A low pass filtering of temperature maps is proposed to reduce the errors and therefore to improve the reliability of the treated regions calculated.The PRF method was studied through a calibration experiment on ex vivo pig muscle. The outcome resulted to be a very good linearity (p value 0.03) between phase and temperature in the range of interest, and an α value of −0.0109 ± 0.0002 ppm/°C. Temperature statistical uncertainty was evaluated by analyzing the temperature readout variability in specific gel provided by InSightec for daily quality assurance control. It resulted to be 1.89 ± 0.32 °C.A Monte Carlo simulation of the MRI temperature measurement and thermal dose calculations in our specific conditions of geometry and statistical uncertainty revealed that a low-pass filtering process on each temperature map can strongly reduce systematic errors in thermal dose evaluations (1.11 overestimation factor instead of 2.62 without filter); consequently the systematic errors on the size of the predicted ablated area are reduced as well.     

Weighted scores method for regression models with dependent data

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a "weighted scores method", which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our method is robust and nearly as efficient as maximum likelihood for fully specified copula models. An illustrative example is given to show the use of our weighted scores method to analyze utilization of health care based on family characteristics.     

An augmented probit model for missing predictable covariates in quantal bioassay with small sample size

Summary Quantal bioassay experiments relate the amount or potency of some compound; for example, poison, antibody, or drug to a binary outcome such as death or infection in animals. For infectious diseases, probit regression is commonly used for inference and a key measure of potency is given by the ID_P , the amount that results in P% of the animals being infected. In some experiments, a validation set may be used where both direct and proxy measures of the dose are available on a subset of animals with the proxy being available on all. The proxy variable can be viewed as a messy reflection of the direct variable, leading to an errors‐in‐variables problem. We develop a model for the validation set and use a constrained seemingly unrelated regression (SUR) model to obtain the distribution of the direct measure conditional on the proxy. We use the conditional distribution to derive a pseudo‐likelihood based on probit regression and use the parametric bootstrap for statistical inference. We re‐evaluate an old experiment in 21 monkeys where neutralizing antibodies (nABs) to HIV were measured using an old (proxy) assay in all monkeys and with a new (direct) assay in a validation set of 11 who had sufficient stored plasma. Using our methods, we obtain an estimate of the ID₁ for the new assay, an important target for HIV vaccine candidates. In simulations, we compare the pseudo‐likelihood estimates with regression calibration and a full joint likelihood approach.     

An ab initio algorithm for low-resolution 3-D reconstructions from cryoelectron microscopy images

A statistical method for determining low-resolution 3-D reconstructions of virus particles from cryoelectron microscope images by an ab initio algorithm is described. The method begins with a novel linear reconstruction method that generates a spherically symmetric reconstruction, which is followed by a nonlinear reconstruction method implementing an expectation-maximization procedure using the spherically symmetric reconstruction as an initial condition and resulting in a reconstruction with icosahedral symmetry. An important characteristic of the complete method is that very little need be known about the particle before the reconstruction is computed, in particular, only the type of symmetry and inner and outer radii. The method is demonstrated on synthetic cowpea mosaic virus data, and its robustness to 5% errors in the contrast transfer function, 5% errors in the location of the center of the particles in the images, and 5% distortion in the 3-D structure from which the images are derived is demonstrated numerically.     

Transitory increase in chromosomal DNA (Fleulgen) during floral differentiation in Rhoeo discolor.

Scanning cytophotometric measurements on 3200 telophase and 1700 interphase nuclei (Feulgen-stained) in vegetative and reproductive buds of Rhoeo discolor revealed a transitory increase in staining intensity in more than half of the cells in early differentiating floral buds. The differences between the vegetative and floral nuclei are significant at the 0.001 level of probability and highly reproducible, independent of the type of hydrolysis used. We suggest that the different Feulgen extinction values reflect different nuclear DNA amounts, because methodical errors can fairly be excluded. The occurrence of an extra DNA (control DNA) of the kind of the floral DNA' detected by Wardell and Skoog (1973) and Wardell (1976) in tobacco is discussed.     

A new approach for calibrating dental caries frequency of skeletal remains

It is a fact that researchers make use of various calibration methods for calculating and correcting dental caries frequency. The lack of standardization and accuracy of such methods has made it difficult for the researchers to draw reliable and differentiated conclusions from caries frequencies. Besides, the number of studies on how far the calculation methods reflect the "real" caries frequency is very limited. In this study, various methods for calculating caries frequency in skeletal samples are discussed and a new calculation method is proposed for estimating "real" caries frequency. The Hardwick's correction, which is one of the methods discussed in this study, is not successful in estimating "real" caries frequency as it proposes standard values for different life styles and dietary habits. The decayed and missing index is also considered inefficient as it assumes that all antemortem tooth loss is due to caries. The caries correction factor, proposed by Lukacs, achieves more successful results by considering factors other than caries in antemortem tooth loss, but because it does not differentiate between the anterior and posterior tooth groups during calculation, the results to be obtained therefrom may deviate from actual figures. In order to correct any such deviation, the caries correction factor must be applied separately for the anterior and posterior teeth groups since the resistance of each group to cariogenic factors is different. All the methods outlined above do not consider the effects of postmortem tooth loss on caries frequency. As a result, these methods are still far from reflecting a reliable caries frequency. The application of a proportional correction factor--as a technique newly introduced here--corrects the deviation caused by postmortem tooth loss and achieves more realistic results.     

Allowing for random errors in radiation dose estimates for the atomic bomb survivor data

The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.     

Modeling random effects for censored data by a multivariate normal regression model

A normal distribution regression model with a frailty-like factor to account for statistical dependence between the observed survival times is introduced. This model, as opposed to standard hazard-based frailty models, has survival times that, conditional on the shared random effect, have an accelerated failure time representation. The dependence properties of this model are discussed and maximum likelihood estimation of the model's parameters is considered. A number of examples are considered to illustrate the approach. The estimated degree of dependence is comparable to other models, but the present approach has the advantage that the interpretation of the random effect is simpler than in the frailty model.     

Genetic Effects of Low-Dose Chronic Irradiation of Developing Seeds of <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis> (L.) Heynh.

A six-year study, starting in 1987, was focused on the frequency of embryonic lethals and chlorophyll mutations that arose in developing seeds of Arabidopsis thaliana growing at sites varying in the level of radioactive contamination in the 30-km control region of the Chernobyl Atomic Power Plant. The dose rate of chronic irradiation varied from 200 μR/h to 2.4 R/h. To study the genetic effects of various levels of radioactive contamination, the frequency of mutations arising in a particular generation was determined and the irradiation dose was estimated for the given generation. The dose dependence of the mutation frequency proved to follow a power function with a power less than unity, suggesting a relatively high effect for low-dose irradiation. Possible explanations of this phenomenon are discussed.     

Quantitative receptor autoradiography in the human brain

Summary Quantitative receptor autoradiography on sections of the human brain raises methodical problems of which some are relevant also for studies in animal tissue, but others are unique in studies of human brain tissue. Procedures for the following methodical aspects are discussed image analysis for quantitation of the regional distribution of receptor densities, saturation analysis on autoradiographs, influence of age and post-mortem delay and quenching of -radiation in brain tissue. The solutions proposed to these problems make receptor autoradiography in the human brain to a reliable method for studies of chemical neuroanatomy.