Hypothesis Testing for an Exposure–Disease Association in Case–Control Studies Under Nondifferential Exposure Misclassification in the Presence of Validation Data: Bayesian and Frequentist Adjustments

In epidemiologic studies, measurement error in the exposure variable can have a detrimental effect on the power of hypothesis testing for detecting the impact of exposure in the development of a disease. To adjust for misclassification in the hypothesis testing procedure involving a misclassified binary exposure variable, we consider a retrospective case–control scenario under the assumption of nondifferential misclassification. We develop a test under Bayesian approach from a posterior distribution generated by a MCMC algorithm and a normal prior under realistic assumptions. We compared this test with an equivalent likelihood ratio test developed under the frequentist approach, using various simulated settings and in the presence or the absence of validation data. In our simulations, we considered varying degrees of sensitivity, specificity, sample sizes, exposure prevalence, and proportion of unvalidated and validated data. In these scenarios, our simulation study shows that the adjusted model (with-validation data model) is always better than the unadjusted model (without validation data model). However, we showed that exception is possible in the fixed budget scenario where collection of the validation data requires a much higher cost. We also showed that both Bayesian and frequentist hypothesis testing procedures reach the same conclusions for the scenarios under consideration. The Bayesian approach is, however, computationally more stable in rare exposure contexts. A real case–control study was used to show the application of the hypothesis testing procedures under consideration.     

A Comparison of Formulae for Calculating Cost‐Efficient Sample Sizes of Case‐Control Studies with an Internal Validation Scheme

When a case‐control study is planned to include an internal validation study, the sample size of the study and the proportion of validated observations has to be calculated. There are a variety of alternative methods to accomplish this. In this article some possible procedures will be compared in order to clarify whether considerable differences in the suggested optimal designs occur, dependent on the used method.     

Extending McNemar's test: estimation and inference when paired binary outcome data are misclassified

McNemar's test is popular for assessing the difference between proportions when two observations are taken on each experimental unit. It is useful under a variety of epidemiological study designs that produce correlated binary outcomes. In studies involving outcome ascertainment, cost or feasibility concerns often lead researchers to employ error-prone surrogate diagnostic tests. Assuming an available gold standard diagnostic method, we address point and confidence interval estimation of the true difference in proportions and the paired-data odds ratio by incorporating external or internal validation data. We distinguish two special cases, depending on whether it is reasonable to assume that the diagnostic test properties remain the same for both assessments (e.g., at baseline and at follow-up). Likelihood-based analysis yields closed-form estimates when validation data are external and requires numeric optimization when they are internal. The latter approach offers important advantages in terms of robustness and efficient odds ratio estimation. We consider internal validation study designs geared toward optimizing efficiency given a fixed cost allocated for measurements. Two motivating examples are presented, using gold standard and surrogate bivariate binary diagnoses of bacterial vaginosis (BV) on women participating in the HIV Epidemiology Research Study (HERS).     

Survival Analysis with Error‐Prone Time‐Varying Covariates: A Risk Set Calibration Approach

Summary Occupational, environmental, and nutritional epidemiologists are often interested in estimating the prospective effect of time‐varying exposure variables such as cumulative exposure or cumulative updated average exposure, in relation to chronic disease endpoints such as cancer incidence and mortality. From exposure validation studies, it is apparent that many of the variables of interest are measured with moderate to substantial error. Although the ordinary regression calibration (ORC) approach is approximately valid and efficient for measurement error correction of relative risk estimates from the Cox model with time‐independent point exposures when the disease is rare, it is not adaptable for use with time‐varying exposures. By recalibrating the measurement error model within each risk set, a risk set regression calibration (RRC) method is proposed for this setting. An algorithm for a bias‐corrected point estimate of the relative risk using an RRC approach is presented, followed by the derivation of an estimate of its variance, resulting in a sandwich estimator. Emphasis is on methods applicable to the main study/external validation study design, which arises in important applications. Simulation studies under several assumptions about the error model were carried out, which demonstrated the validity and efficiency of the method in finite samples. The method was applied to a study of diet and cancer from Harvard's Health Professionals Follow‐up Study (HPFS).     

Regression Calibration in Semiparametric Accelerated Failure Time Models

Summary In large cohort studies, it often happens that some covariates are expensive to measure and hence only measured on a validation set. On the other hand, relatively cheap but error‐prone measurements of the covariates are available for all subjects. Regression calibration (RC) estimation method ( Prentice, 1982 , Biometrika 69 , 331–342) is a popular method for analyzing such data and has been applied to the Cox model by Wang et al. (1997, Biometrics 53 , 131–145) under normal measurement error and rare disease assumptions. In this article, we consider the RC estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error. Asymptotic properties of the proposed method are investigated under a two‐phase sampling scheme for validation data that are selected via stratified random sampling, resulting in neither independent nor identically distributed observations. We show that the estimates converge to some well‐defined parameters. In particular, unbiased estimation is feasible under additive normal measurement error models for normal covariates and under Berkson error models. The proposed method performs well in finite‐sample simulation studies. We also apply the proposed method to a depression mortality study.     

A measurement error model for time-series studies of air pollution and mortality

One barrier to interpreting the observational evidence concerning the adverse health effects of air pollution for public policy purposes is the measurement error inherent in estimates of exposure based on ambient pollutant monitors. Exposure assessment studies have shown that data from monitors at central sites may not adequately represent personal exposure. Thus, the exposure error resulting from using centrally measured data as a surrogate for personal exposure can potentially lead to a bias in estimates of the health effects of air pollution. This paper develops a multi-stage Poisson regression model for evaluating the effects of exposure measurement error on estimates of effects of particulate air pollution on mortality in time-series studies. To implement the model, we have used five validation data sets on personal exposure to PM10. Our goal is to combine data on the associations between ambient concentrations of particulate matter and mortality for a specific location, with the validation data on the association between ambient and personal concentrations of particulate matter at the locations where data have been collected. We use these data in a model to estimate the relative risk of mortality associated with estimated personal-exposure concentrations and make a comparison with the risk of mortality estimated with measurements of ambient concentration alone. We apply this method to data comprising daily mortality counts, ambient concentrations of PM10measured at a central site, and temperature for Baltimore, Maryland from 1987 to 1994. We have selected our home city of Baltimore to illustrate the method; the measurement error correction model is general and can be applied to other appropriate locations.Our approach uses a combination of: (1) a generalized additive model with log link and Poisson error for the mortality-personal-exposure association; (2) a multi-stage linear model to estimate the variability across the five validation data sets in the personal-ambient-exposure association; (3) data augmentation methods to address the uncertainty resulting from the missing personal exposure time series in Baltimore. In the Poisson regression model, we account for smooth seasonal and annual trends in mortality using smoothing splines. Taking into account the heterogeneity across locations in the personal-ambient-exposure relationship, we quantify the degree to which the exposure measurement error biases the results toward the null hypothesis of no effect, and estimate the loss of precision in the estimated health effects due to indirectly estimating personal exposures from ambient measurements.     

Simulation‐based evaluation of the linear‐mixed model in the presence of an increasing proportion of singletons

Data in medical sciences often have a hierarchical structure with lower level units (e.g. children) nested in higher level units (e.g. departments). Several specific but frequently studied settings, mainly in longitudinal and family research, involve a large number of units that tend to be quite small, with units containing only one element referred to as singletons. Regardless of sparseness, hierarchical data should be analyzed with appropriate methodology such as, for example linear‐mixed models. Using a simulation study, based on the structure of a data example on Ceftriaxone consumption in hospitalized children, we assess the impact of an increasing proportion of singletons (0–95%), in data with a low, medium, or high intracluster correlation, on the stability of linear‐mixed models parameter estimates, confidence interval coverage and F test performance. Some techniques that are frequently used in the presence of singletons include ignoring clustering, dropping the singletons from the analysis and grouping the singletons into an artificial unit. We show that both the fixed and random effects estimates and their standard errors are stable in the presence of an increasing proportion of singletons. We demonstrate that ignoring clustering and dropping singletons should be avoided as they come with biased standard error estimates. Grouping the singletons into an artificial unit might be considered, although the linear‐mixed model performs better even when the proportion of singletons is high. We conclude that the linear‐mixed model is stable in the presence of singletons when both lower‐ and higher level sample sizes are fixed. In this setting, the use of remedial measures, such as ignoring clustering and grouping or removing singletons, should be dissuaded.     

Development and validation of efficient stable isotope dilution LC-HESI-MS/MS method for the verification of β-lyase metabolites in human urine after sulfur mustard exposure

As a part of the project for screening unequivocal biomarkers after sulfur mustard exposure, a quantitative method for the determination of β-lyase metabolites 1,1'-sulfonylbis-[2-(methylsulfinyl)ethane] (SBMSE) and 1-methylsulfinyl-2-[2-(methylthio)ethylsulfonyl]ethane (MSMTESE) was validated. Full validation was conducted according to the FDA guidelines for method validation using pooled human urine as a sample matrix. The metabolites were extracted from urine with an optimized sample preparation procedure using ENV+ solid phase extraction cartridge with reduced volume of sample and solvents. Metabolites were detected by improved and faster liquid chromatography-heated electrospray ionization-tandem mass spectrometry (LC-HESI-MS/MS) method with two transitions of each chemical using non-buffered eluents, post-column splitter and higher flow-rate. These provided over five times faster analysis than previously published method providing 4.5 min/sample cycle time, to achieve up to 200 samples per day (24 h). Quantification was performed using deuterium labelled internal standard of SBMSE. The method was linear over the concentration range of 5-200 ng/ml (average correlation coefficients were R(2)=0.997 and R(2)=0.989) for both β-lyase metabolites, SBMSE and MSMTESE, respectively. The average retention times for SBMSE and MSMTESE were 1.96±0.01 min and 3.24±0.03 min (n=54). Calculated limits of detection were 4 ng/ml for both SBMSE and MSMTESE, respectively. Lower limits of quantification were 10 ng/ml and 11 ng/ml for SBMSE and MSMTESE, respectively. This validated method was successfully used in the First Confidence Building Exercise on Biomedical Samples Analysis organized by the Organisation for the Prohibition of Chemical Weapons (OPCW). Identification criteria for analysing unequivocal biomarkers of sulfur mustard with LC-MS/MS after alleged use is discussed and proposed based on the validation and exercise results.     

IMU-based ambulatory walking speed estimation in constrained treadmill and overground walking

This study evaluated the performance of a walking speed estimation system based on using an inertial measurement unit (IMU), a combination of accelerometers and gyroscopes. The walking speed estimation algorithm segments the walking sequence into individual stride cycles (two steps) based on the inverted pendulum-like behaviour of the stance leg during walking and it integrates the angular velocity and linear accelerations of the shank to determine the displacement of each stride. The evaluation was performed in both treadmill and overground walking experiments with various constraints on walking speed, step length and step frequency to provide a relatively comprehensive assessment of the system. Promising results were obtained in providing accurate and consistent walking speed/step length estimation in different walking conditions. An overall percentage root mean squared error (%RMSE) of 4.2 and 4.0% was achieved in treadmill and overground walking experiments, respectively. With an increasing interest in understanding human walking biomechanics, the IMU-based ambulatory system could provide a useful walking speed/step length measurement/control tool for constrained walking studies.     

IMU-based ambulatory walking speed estimation in constrained treadmill and overground walking

This study evaluated the performance of a walking speed estimation system based on using an inertial measurement unit (IMU), a combination of accelerometers and gyroscopes. The walking speed estimation algorithm segments the walking sequence into individual stride cycles (two steps) based on the inverted pendulum-like behaviour of the stance leg during walking and it integrates the angular velocity and linear accelerations of the shank to determine the displacement of each stride. The evaluation was performed in both treadmill and overground walking experiments with various constraints on walking speed, step length and step frequency to provide a relatively comprehensive assessment of the system. Promising results were obtained in providing accurate and consistent walking speed/step length estimation in different walking conditions. An overall percentage root mean squared error (%RMSE) of 4.2 and 4.0% was achieved in treadmill and overground walking experiments, respectively. With an increasing interest in understanding human walking biomechanics, the IMU-based ambulatory system could provide a useful walking speed/step length measurement/control tool for constrained walking studies.     

Self-designing two-stage trials to minimize expected costs

In the design of clinical trials, the sample size for the trial is traditionally calculated from estimates of parameters of interest, such as the mean treatment effect, which can often be inaccurate. However, recalculation of the sample size based on an estimate of the parameter of interest that uses accumulating data from the trial can lead to inflation of the overall Type I error rate of the trial. The self-designing method of Fisher, also known as the variance-spending method, allows the use of all accumulating data in a sequential trial (including the estimated treatment effect) in determining the sample size for the next stage of the trial without inflating the Type I error rate. We propose a self-designing group sequential procedure to minimize the expected total cost of a trial. Cost is an important parameter to consider in the statistical design of clinical trials due to limited financial resources. Using Bayesian decision theory on the accumulating data, the design specifies sequentially the optimal sample size and proportion of the test statistic's variance needed for each stage of a trial to minimize the expected cost of the trial. The optimality is with respect to a prior distribution on the parameter of interest. Results are presented for a simple two-stage trial. This method can extend to nonmonetary costs, such as ethical costs or quality-adjusted life years.     

Development of a micro-turbulent flow chromatography focus mode method for drug quantitation in discovery bioanalysis

An online turbulent flow chromatography method coupled to tandem mass spectrometry (TFC-MS/MS) has been developed within our bioanalytical group, suited to the analysis of mid to late stage discovery compounds. A dual column configuration utilising isocratic focusing of the analyte upon the analytical column maintained an excellent peak shape for a large proportion of compounds encountered and enabled consistent quantitation to sub-nanogram concentrations (<15 pg on column). Furthermore, the low sample injection volume coupled with rapid column washing using basic and acidic mobile phases, has proved advantageous in removing sample carryover and also the overall exposure to biological material; favourable for good system robustness. All the data discussed were generated with a method cycle time of 5 min providing accurate quantitation (acceptance criteria based upon FDA method validation guidelines) with multiple analytes and biological matrices.     

Isocratic high-performance liquid chromatographic method for the separation of testosterone metabolites

An isocratic reversed-phase high-performance liquid chromatographic (HPLC) method using an Ultrasphere IP column has been developed for the determination of testosterone and its metabolites after incubation of 4-¹⁴C-labelled or unlabelled testosterone with rat liver microsomes. Compounds were eluted with methanol-water-tetrahydrofuran (35:55:10, v/v, pH 4.0) and detected by ultraviolet (UV) absorption at 245 nm. UV or on-line radioactivity detection can be used although, due to differences in detector cell volumes, peak resolution is slightly better with UV detection. Selectivity was validated by collecting HPLC peaks and verifying their identity by gas chromatography-mass spectrometry after derivatization by N,O-bis(trimethylsily)trifluoroacetamide-trimethylchlorosilane. A three-day validation was performed to determine the linearity, repeatability, reproducibility and accuracy of the method, using corticosterone as internal standard. The method is applicable to the measurement of cytochrome P-450 isoenzyme activities in rat liver.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Correcting for measurement error in individual ancestry estimates in structured association tests

We present theoretical explanations and show through simulation that the individual admixture proportion estimates obtained by using ancestry informative markers should be seen as an error-contaminated measurement of the underlying individual ancestry proportion. These estimates can be used in structured association tests as a control variable to limit type I error inflation or reduce loss of power due to population stratification observed in studies of admixed populations. However, the inclusion of such error-containing variables as covariates in regression models can bias parameter estimates and reduce ability to control for the confounding effect of admixture in genetic association tests. Measurement error correction methods offer a way to overcome this problem but require an a priori estimate of the measurement error variance. We show how an upper bound of this variance can be obtained, present four measurement error correction methods that are applicable to this problem, and conduct a simulation study to compare their utility in the case where the admixed population results from the intermating between two ancestral populations. Our results show that the quadratic measurement error correction (QMEC) method performs better than the other methods and maintains the type I error to its nominal level.     

Allowing for never and episodic consumers when correcting for error in food record measurements of dietary intake

Food records, including 24-hour recalls and diet diaries, are considered to provide generally superior measures of long-term dietary intake relative to questionnaire-based methods. Despite the expense of processing food records, they are increasingly used as the main dietary measurement in nutritional epidemiology, in particular in sub-studies nested within prospective cohorts. Food records are, however, subject to excess reports of zero intake. Measurement error is a serious problem in nutritional epidemiology because of the lack of gold standard measurements and results in biased estimated diet-disease associations. In this paper, a 3-part measurement error model, which we call the never and episodic consumers (NEC) model, is outlined for food records. It allows for both real zeros, due to never consumers, and excess zeros, due to episodic consumers (EC). Repeated measurements are required for some study participants to fit the model. Simulation studies are used to compare the results from using the proposed model to correct for measurement error with the results from 3 alternative approaches: a crude approach using the mean of repeated food record measurements as the exposure, a linear regression calibration (RC) approach, and an EC model which does not allow real zeros. The crude approach results in badly attenuated odds ratio estimates, except in the unlikely situation in which a large number of repeat measurements is available for all participants. Where repeat measurements are available for all participants, the 3 correction methods perform equally well. However, when only a subset of the study population has repeat measurements, the NEC model appears to provide the best method for correcting for measurement error, with the 2 alternative correction methods, in particular the linear RC approach, resulting in greater bias and loss of coverage. The NEC model is extended to include adjustment for measurements from food frequency questionnaires, enabling better estimation of the proportion of never consumers when the number of repeat measurements is small. The methods are applied to 7-day diary measurements of alcohol intake in the EPIC-Norfolk study.     

作物模型区域应用两种参数校准方法的比较

区域模拟的目的是利用有限的空间数据模拟出产量等作物性状的时空变异规律.然而站点作物模型应用到区域范围时涉及到数据归一化、参数简化、模型的校准和验证等问题.利用CERES-Rice模型对作物模型在我国的区域应用进行了尝试并对部分参数进行了校准.首先利用田间观测数据在各实验点上对模型进行了详细的站点校准,以验证模型在我国的模拟能力;其次,以我国水稻种植区(精确到亚区)为单位,运用平均值和标准差(RMSE)两种方法进行了区域校准和验证,即找出能反映出品种空间差异的代表性品种参数集;然后分别运用两种方法的校准结果,模拟水稻产量和成熟期,并将模拟结果与实测值进行了比较.结果表明:区域校准能反映出水稻生育期和产量的时空变化规律,其中RMSE法较平均值法效果好.目前作物模型区域应用过程中还存在大量的误差来源,有待进一步研究.     

The cost-effectiveness of reclassification sampling for prevalence estimation

Background

Typically, a two-phase (double) sampling strategy is employed when classifications are subject to error and there is a gold standard (perfect) classifier available. Two-phase sampling involves classifying the entire sample with an imperfect classifier, and a subset of the sample with the gold-standard.

Methodology/Principal Findings

In this paper we consider an alternative strategy termed reclassification sampling, which involves classifying individuals using the imperfect classifier more than one time. Estimates of sensitivity, specificity and prevalence are provided for reclassification sampling, when either one or two binary classifications of each individual using the imperfect classifier are available. Robustness of estimates and design decisions to model assumptions are considered. Software is provided to compute estimates and provide advice on the optimal sampling strategy.

Conclusions/Significance

Reclassification sampling is shown to be cost-effective (lower standard error of estimates for the same cost) for estimating prevalence as compared to two-phase sampling in many practical situations.     

基于树木起源、立地分级和龄组的单木生物量模型

以马尾松(Pinus massoniana)和落叶松(Larix)的大样本实测资料为建模样本,以独立抽取的样本为验证样本,把样本按起源、立地和龄组进行分级,采用与材积相容的两种相对生长方程,分普通最小二乘和两种加权最小二乘,对地上部分总生物量、地上各部分生物量和地下生物量进行模型拟合和验证,使用决定系数、均方根误差、总相对误差和估计精度等8项统计量对结果进行分析。结果表明:两个树种地上部分总生物量,立地分类方法,模型的拟合结果和适用性都最优;马尾松VAR模型较优,而落叶松CAR模型较好;两种加权最小二乘方法,在建模样本和验证样本中表现得不一致。在建模样本中,加权回归2(权重函数1/f^0.5)略优于加权回归1(权重函数1/y^0.5),但在验证样本中,加权回归1却明显优于加权回归2。而同时满足建模样本拟合结果最优和验证样本检验结果最优的组合中,只有加权回归1。两个树种地上部分各分量生物量,模型拟合结果和适用性,均为干材最优,树叶最差、树枝和树皮居中,样本分类、模型类型和加权最小二乘方法对干材生物量的影响,规律和地上部分总生物量相同;样本分类、模型类型和加权最小二乘方法的最优组合,用验证样本检验的结果,总相对误差树枝不超过±10.0%,树皮不超过±5.0%,树叶马尾松不超过±30.0%,落叶松不超过±20.0%。两个树种地下部分(根)生物量,样本按龄组分类方法,模型拟合结果最优,与材积相容的模型总体上优于与地上部分总生物量相容模型。     

Evidence against the use of fecal pellet size for age determination in European wild rabbits

Techniques for estimating the age of wild animals are crucial to many aspects of the study of population biology. Accurate estimates of the proportion of different age classes in wild rabbit populations would be very useful, and the possibility that it could be obtained from the pellet size holds great appeal. However, this suggestion has created controversy in the literature as this technique has not been validated. This study involved assessment of whether threshold fecal pellet diameters could be used to differentiate adult and juvenile rabbits. The proportion of adults in four wild rabbit populations living in semi-natural conditions was compared with the proportion of animal pellets greater than threshold diameters of 6 mm and 4 mm. Our results suggest that inferring a relationship between the proportion of pellets >6 mm diameter and the proportion of adults in a population is not applicable to European wild rabbits, and that the use of this method could produce erroneous interpretations. The use of a 4 mm pellet diameter threshold appeared to produce even more inaccurate results. Studies that use this technique should include validation, as the results can vary greatly among individuals and populations.