Optimizing occupational exposure measurement strategies when estimating the log-scale arithmetic mean value--an example from the reinforced plastics industry

When assessing occupational exposures, repeated measurements are in most cases required. Repeated measurements are more resource intensive than a single measurement, so careful planning of the measurement strategy is necessary to assure that resources are spent wisely. The optimal strategy depends on the objectives of the measurements. Here, two different models of random effects analysis of variance (ANOVA) are proposed for the optimization of measurement strategies by the minimization of the variance of the estimated log-transformed arithmetic mean value of a worker group, i.e. the strategies are optimized for precise estimation of that value. The first model is a one-way random effects ANOVA model. For that model it is shown that the best precision in the estimated mean value is always obtained by including as many workers as possible in the sample while restricting the number of replicates to two or at most three regardless of the size of the variance components. The second model introduces the 'shared temporal variation' which accounts for those random temporal fluctuations of the exposure that the workers have in common. It is shown for that model that the optimal sample allocation depends on the relative sizes of the between-worker component and the shared temporal component, so that if the between-worker component is larger than the shared temporal component more workers should be included in the sample and vice versa. The results are illustrated graphically with an example from the reinforced plastics industry. If there exists a shared temporal variation at a workplace, that variability needs to be accounted for in the sampling design and the more complex model is recommended.     

STATISTICAL ANALYSIS OF INTRACLASS CORRELATIONS FROM MULTIPLE SAMPLES WITH APPLICATIONS TO ARTERIAL BLOOD PRESSURE DATA

We consider inference procedures on intraclass correlations for unbalanced data from several multivariate normal populations. We derive several tests, including ones based on Fisher's variance stabilizing transformation and Neyman's score functions, to test the homogeneity of intraclass correlations. We illustrate the methodology with an example that uses arterial blood pressure data collected by Miall and Oldham and we compare the procedures in terms of their empirical levels and powers with a Monte Carlo simulation study. We recommend the use of Neyman's C(α) test and a test based on the ANOVA estimators of the intraclass correlations as they hold their significance levels and give consistently higher powers. © 1997 John Wiley & Sons, Ltd.     

On the estimation of total variability in assay validation

In the pharmaceutical industry, an assay method is considered validated if the accuracy and precision for an assay meet some acceptable limits. This paper discusses the assessment of assay precision in terms of the estimation of total variability of an assay from a one-way random effects model which is often considered in assay validation. We propose a general class of estimators that includes the analysis of variance estimator and the maximum likelihood estimator. We derive the optimal estimator, in terms of smallest mean squared error, within this class and consider an approximate version of this optimal estimator. We report on a Monte Carlo simulation to study its finite sample performance. We also present two examples to illustrate the use of the proposed methodology.     

Confidence intervals for the risk ratio under cluster sampling based on the beta-binomial model

In cohort studies, the risk ratio (RR) is one of the most commonly used epidemiologic indices to quantify the effect of a suspected risk factor on the probability of developing a disease. When we employ cluster sampling to collect data, an interval estimator that does not account for the intraclass correlation between subjects within clusters is likely inappropriate. In application of the beta-binomial model to account for the intraclass correlation, we develop four asymptotic interval estimators of the RR, which are direct extensions of some recently developed estimators for independent binomial sampling. We then use Monte Carlo simulation to evaluate the finite-sample performance of these four interval estimators in a variety of situations. We find that the estimator using the logarithmic transformation generally performs well and is preferable to the other three estimators in most of the situations considered here. Finally, we include an example from a study of an educational intervention with emphasis on behaviour change to illustrate the use of the estimators developed in this paper.     

Profile likelihood‐based confidence interval of the intraclass correlation for binary outcome data sampled from clusters

The intraclass correlation in binary outcome data sampled from clusters is an important and versatile measure in many biological and biomedical investigations. Properties of the different estimators of the intraclass correlation based on the parametric, semi‐parametric, and nonparametric approaches have been studied extensively, mainly in terms of bias and efficiency [see, for example, Ridout et al., Biometrics 1999, 55:137–148; Paul et al., Journal of Statistical Computation and Simulation 2003, 73:507–523; and Lee, Statistical Modelling 2004, 4: 113–126], but little attention has been paid to extending these results to the problem of the confidence intervals. In this article, we generalize the results of the four point estimators by constructing asymptotic confidence intervals obtaining closed‐form asymptotic and sandwich variance expressions of those four point estimators. It appears from simulation results that the asymptotic confidence intervals based on these four estimators have serious under‐coverage. To remedy this, we introduce the Fisher's z‐transformation approach on the intraclass correlation coefficient, the profile likelihood approach based on the beta‐binomial model, and the hybrid profile variance approach based on the quadratic estimating equation for constructing the confidence intervals of the intraclass correlation for binary outcome data. As assessed by Monte Carlo simulations, these confidence interval approaches show significant improvement in the coverage probabilities. Moreover, the profile likelihood approach performs quite well by providing coverage levels close to nominal over a wide range of parameter combinations. We provide applications to biological data to illustrate the methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Intraclass correlation coefficients from three cluster randomised controlled trials in primary and residential health care

OBJECTIVE: This paper provides intraclass correlation coefficients (ICCs) for estimation of sample size inflation required in future cluster randomised trials in primary or residential care. METHODS: Three cluster randomised trials were conducted among middle-aged and older adults in primary care and residential care in Australia and New Zealand between 1995 and 2002. Baseline means or proportions, mean change, and ICCs with their standard errors and 95% confidence intervals are reported for outcome variables used in the three studies. The ICCs were estimated from a one-way random effects model using the analysis of variance method. RESULTS: ICCs for quality of life and psychological variables in the primary care studies were low (below 0.018). ICCs for clinical and physical activity variables ranged from 0 to 0.08. ICCs for health and functional status in residential care for the elderly were high, ranging from 0.025 to 0.514. CONCLUSIONS: The magnitude of the intraclass correlation varies with the venue of the trial, the outcome variables used, and the expected effect of the intervention. However, the intraclass correlations provided will be useful for more appropriate planning of residential and primary care-based trials in the future.     

Effective number of subjects and number of raters for inter-rater reliability studies

A reliability study in which multiple raters evaluate multiple subjects was assumed in order to confirm the inter-rater reliability of rating scales. The two-way ANOVA model defining subjects and raters as random effects was applied, and the combination of the number of subjects and the number of raters that minimizes variance of the intraclass correlation coefficient (ICC) with a fixed total number of ratings (number of subjects x number of raters) was studied. The results revealed that the optimal combination depends on the relative ratio (between-rater variance/error variance), and that large number of raters brings the high precision of estimation of the ICC when the relative ratio was greater. It was concluded that when information concerning the relative ratio is unreliable, the use of identical numbers of raters and subjects minimizes variance when the relative ratio is substantially large and variance is maximized, providing a good study design from the viewpoint of 'maximin'.     

DESIGN AND ANALYSIS OF INTRA-SUBJECT VARIABILITY IN CROSS-OVER EXPERIMENTS

Recently, interest has grown in the development of inferential techniques to compare treatment variabilities in the setting of a cross-over experiment. In particular, comparison of treatments with respect to intra-subject variability has greater interest than has inter-subject variability. We begin with a presentation of a general approach for statistical inference within a cross-over design. We discuss three different statistical models where model choice depends on the design and assumptions about carry-over effects. Each model incorporates t-variate random subject effects, where t is the number of treatments. We develop maximum likelihood (ML) and restricted maximum likelihood (REML) approaches to derive parameter estimators and we consider a special case in which closed-form expressions for the variance component estimators are available. Finally, we illustrate the methodologies with the analysis of data from three examples.     

交叉设计资料的混合效应模型分析

目的 放宽交叉设计方差分析对残留效应假定和探讨交叉设计混合效应分析模型。方法 建立三个模型以适应残留效应的不同假定，即残留效应为零、相等或不等，通过构造对数似然函数以及利用Fisher记分迭代算法可求得卢和口的极大似然估计与限制极大似然估计。结果 用SAS程序实现了交叉设计混合效应模型分析，得到了有关参数的估计值和直接处理效应的比较结果，实例分析表明，混合效应模型能够提供更多的有效信息。结论 混合效应模型较一般方差分析有更强的适应性，可完善和丰富交叉设计资料的分析方法。     

Detecting SNP‐expression associations: A comparison of mutual information and median test with standard statistical approaches

Single nucleotide polymorphism‐gene expression associations have received increasing interest. The aim of these studies is discovering a difference in the location parameters of gene expressions given genotype. Because gene expressions often are highly skewed, heavy‐tailed or data of different genotypes vary in dispersion, the median is the most appropriate measure of location. In this case, model assumptions of standard statistical methods for comparing locations such as the analysis of variance (ANOVA) or the Kruskal–Wallis (KW) test are violated. Alternatives that might be more appropriate are the median test (MED) and tests based on mutual information (MI). In simulation studies these approaches and a novel MI test are compared with ANOVA and KW. Location, dispersion and skewness parameters of the gene expression distributions given genotypes are varied as well as genotype frequencies. The MED test and the novel MI‐based method keep the nominal significance levels for comparing medians if gene expression data are non‐normally distributed. ANOVA and KW have substantially inflated type I errors. They are, however, optimal if standard model assumptions are fulfilled. The MED test generally has larger power than MI and is therefore recommended if model assumptions of standard procedures are violated. A 300 kb region on chromosome 9p21.3, which is associated with coronary artery disease, was analyzed using the HapMap data. Only the alternative approaches were able to identify three genes (ADM, FCGR3B and ADORA1) as promising candidates to clarify the molecular mechanism of the genetic association. Copyright © 2009 John Wiley & Sons, Ltd.     

Overdispersion models for correlated multinomial data: Applications to blinding assessment

Overdispersion models have been extensively studied for correlated normal and binomial data but much less so for correlated multinomial data. In this work, we describe a multinomial overdispersion model that leads to the specification of the first two moments of the outcome and allows the estimation of the global parameters using generalized estimating equations (GEE). We introduce a Global Blinding Index as a target parameter and illustrate the application of the GEE method to its estimation from (1) a clinical trial with clustering by practitioner and (2) a meta-analysis on psychiatric disorders. We examine the impact of a small number of clusters, high variability in cluster sizes, and the magnitude of the intraclass correlation on the performance of the GEE estimators of the Global Blinding Index using the data simulated from different models. We compare these estimators with the inverse-variance weighted estimators and a maximum-likelihood estimator, derived under the Dirichlet-multinomial model. Our results indicate that the performance of the GEE estimators was satisfactory even in situations with a small number of clusters, whereas the inverse-variance weighted estimators performed poorly, especially for larger values of the intraclass correlation coefficient. Our findings and illustrations may be instrumental for practitioners who analyze clustered multinomial data from clinical trials and/or meta-analysis.     

The exact distribution of Cochran's heterogeneity statistic in one-way random effects meta-analysis

The presence and impact of heterogeneity in the standard one-way random effects model in meta-analysis are often assessed using the Q statistic due to Cochran. We derive the exact distribution of this statistic under the assumptions of the random effects model, and also suggest two moment-based approximations and a saddlepoint approximation for Q. The exact and approximate distributions are then applied to obtain the corresponding distributions of the recently proposed heterogeneity measures I(2) and H(M)(2), the power of the standard test for the presence of heterogeneity and confidence intervals for the between-study variance parameter when the DerSimonian-Laird or the Hartung-Makambi estimator is used. The methodology is illustrated by revisiting a recent simulation study concerning the heterogeneity measures and applying all the proposed methods to four published meta-analyses.     

A random change point model for assessing variability in repeated measures of cognitive function

Some cognitive functions undergo transitions in old age, which motivates the use of a change point model for the individual trajectory. The age when the change occurs varies between individuals and is treated as random. We illustrate the properties of a random change point model and use it for data from a Swedish study of change in cognitive function in old age. Variance estimates are obtained from Markov chain Monte Carlo simulation using Gibbs sampling. The random change point model is compared with models within the family of linear random effects models. The focus is on the ability to capture variability in measures of cognitive function. The models make different assumptions about the variance over the age span, and we demonstrate that the random change point model has the most reasonable structure.     

Nested frailty models using maximum penalized likelihood estimation

The frailty model is a random effect survival model, which allows for unobserved heterogeneity or for statistical dependence between observed survival data. The nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects. Nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design. In such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data. We present a maximum penalized likelihood estimation (MPnLE) to estimate non-parametrically a continuous hazard function in a nested gamma-frailty model with right-censored and left-truncated data. The estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously. The simulation study demonstrates that this semi-parametric approach yields satisfactory results in this complex setting. In order to illustrate the MPnLE method and the nested frailty model, we present two applications. One is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping. The other application is based on recurrent infection times of patients from different hospitals. We illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates, with an overestimation of the variance of the random effects. We show that even when the frailty effects are fairly small in magnitude, they are important since they alter the results in a systematic pattern.     

Residual plots for the censored data linear regression model

To be consistent, censored data linear regression estimators typically require a correctly specified linear regression function and independent and identically distributed errors. For uncensored data one can assess these model assumptions informally by examining plots of the residuals against the independent variables or fitted values. In this paper I propose plots for censored data analogous to these uncensored data residual plots. One can use such plots in the same way as their uncensored data counterparts for checking model assumptions; if the model assumptions are correct, then the plots should exhibit a random scatter. I show that the proposed plots are useful in selecting a linear regression model for the Stanford heart transplant data.     

Allowing for uncertainty due to missing data in meta-analysis--part 1: two-stage methods

Analysis of a randomized trial with missing outcome data involves untestable assumptions, such as the missing at random (MAR) assumption. Estimated treatment effects are potentially biased if these assumptions are wrong. We quantify the degree of departure from the MAR assumption by the informative missingness odds ratio (IMOR). We incorporate prior beliefs about the IMOR in a Bayesian pattern-mixture model and derive a point estimate and standard error that take account of the uncertainty about the IMOR. In meta-analysis, this model should be used for four separate sensitivity analyses which explore the impact of IMORs that either agree or contrast across trial arms on pooled results via their effects on point estimates or on standard errors. We also propose a variance inflation factor that can be used to assess the influence of trials with many missing outcomes on the meta-analysis. We illustrate the methods using a meta-analysis on psychiatric interventions in deliberate self-harm.     

随机区组设计方差分析中应注意的几个问题

目的探讨区组因素的概念及随机区组设计与分析的若干前提条件。方法对实例1进行配对、随机区组和单因素设计方差分析3种不同的处理,比较结果的异同。对实例2采取不考虑与考虑区组-处理交互作用两种不同的处理,比较结果的异同。结果实例1中3种分析方法前两种结果相同但与第3种方法的P值有所差异;实例2中,如果直接用随机区组设计的方差分析,会忽略可能存在的交互作用,使结果发生偏倚。结论随机区组设计属于单因素设计,配对设计是其特例。不主张抛开研究设计将区组方差分析变为单因素方差分析。利用残差散点图可对区组设计方差分析的前提条件进行考察,其中区组-处理之间是否存在交互作用可采用Turkey的单自由度检验进行判断。     

Assessing reproducibility for interval data in health-related quality of life questionnaires: Which coefficient should be used?

In contrast to other reliability estimates, test-retest reliability (or reproducibility) captures not only the measurement error of an assessment instrument, but also the stability of the construct measured. Consequently, one would expect any departure from identity (Y = X) of measurement pairs (X first, and Y second measurement) to be treated as 'error' by the respective reproducibility statistic, even if 'true' changes happened, e.g. worsening of a disease due to its natural course. The Pearson correlation, still often advocated for continuous measures in test-retest reliability studies, however captures the degree of linearity (Y = bX + a): perfect relationship can be computed, even if the measurement pairs differ not only by a additive constant 'a', but also because of a multiplication of the X-values with the slope 'b'. Therefore, intraclass correlation coefficients (ICCs) have been proposed as alternative statistics for reproducibility. However, only ICCs with absolute agreement definition of concordance capture the degree of identity. ICCs with a consistency definition of concordance measure the degree of additivity (Y = X + a). ICCs are calculated from repeated measures analyses of variance (ANOVAs), and a common population variance must be is assumed for the different measurements. Given this assumption, an ICC computed from a one-way ANOVA seems to be the best choice for this purpose. Otherwise, Lin's concordance correlation coefficient is recommended as identity measure.     

Sample size requirements for reliability studies

This paper provides exact power contours to guide the planning of reliability studies, where the parameter of interest is the coefficient of intraclass correlation rho derived from a one-way analysis of variance model. The contours display the required numbers of subjects k and number of repeated measurements n that provide 80 per cent power for testing Ho: rho less than or equal to rho 0 versus H1: rho greater than rho 0 at the 5 per cent level of significance for selected values of rho o. We discuss the design considerations of these results.     

组内相关系数及其软件实现

目的 介绍可靠性评价指标组内相关系数及其统计软件实现.方法 结合实例阐明各种不同类型组内相关系数的意义、计算和SAS、SPSS软件实现.结果 选择恰当的ICC取决于以下三个方面,选择的模型是one-waymodel或two-way model:采用single measure或average measure:选择absolute agreement或consistency.结论 研究者应根据资料类型和分析目的选择恰当的组内相关系数,SAS和SPSS可提供计算结果.