Inference for odds ratio regression models with sparse dependent data

Suppose the number of 2 x 2 tables is large relative to the average table size, and the observations within a given table are dependent, as occurs in longitudinal or family-based case-control studies. We consider fitting regression models to the odds ratios using table-level covariates. The focus is on methods to obtain valid inferences for the regression parameters beta when the dependence structure is unknown. In this setting, Liang (1985, Biometrika 72, 678-682) has shown that inference based on the noncentral hypergeometric likelihood is sensitive to misspecification of the dependence structure. In contrast, estimating functions based on the Mantel-Haenszel method yield consistent estimators of beta. We show here that, under the estimating function approach, Wald's confidence interval for beta performs well in multiplicative regression models but unfortunately has poor coverage probabilities when an additive regression model is adopted. As an alternative to Wald inference, we present a Mantel-Haenszel quasi-likelihood function based on integrating the Mantel-Haenszel estimating function. A simulation study demonstrates that, in medium-sized samples, the Mantel-Haenszel quasi-likelihood approach yields better inferences than other methods under an additive regression model and inferences comparable to Wald's method under a multiplicative model. We illustrate the use of this quasi-likelihood method in a study of the familial risk of schizophrenia.     

Convex hull test for ordered categorical data

When testing for stochastic order in ordered 2 x J contingency tables, it is common to select the cutoff required to declare significance so as to ensure that the size of the test is exactly alpha conditionally on the margins. It is valid, however, to use the margins to select not only the cutoff but also the form of the test. Linear rank tests, which are locally most powerful and frequently used in practice, suffer from the drawback that they may have power as low as zero to detect some alternatives of interest when the margins satisfy certain conditions. The Smirnov and convex hull tests are shown, through exact conditional power calculations and simulations, to avoid this drawback. The convex hull test is also admissible and palindromic invariant and minimizes the required significance level to have limiting power of one as the alternative moves away from the null in any direction.     

Ordinal invariant measures for individual and group changes in ordered categorical data

Subjective judgements of complex variables are commonly recorded as ordered categorical data. The rank-invariant properties of such data are well known, and there are various statistical approaches to the analysis and modelling of ordinal data. This paper focuses on the non-additive property of ordered categorical data in the analysis of change. A rank-invariant non-parametric method of analysis is presented that is valid regardless of the number of response categories. The unique feature of this method is the augmented ranking approach that is related to the joint distribution of paired observations. This approach makes it possible to measure separately the individual order-preserved categorical changes, which are attributable to the group change, and the individual categorical changes that are not consistent with the pattern of group change. The method is applied to analysis of change in a three-point scale and in a visual analogue scale of continuous ordinal responses.     

Issues for covariance analysis of dichotomous and ordered categorical data from randomized clinical trials and non-parametric strategies for addressing them

Analysis of covariance is an effective method for addressing two considerations for randomized clinical trials. One is reduction of variance for estimates of treatment effects and thereby the production of narrower confidence intervals and more powerful statistical tests. The other is the clarification of the magnitude of treatment effects through adjustment of corresponding estimates for any random imbalances between the treatment groups with respect to the covariables. The statistical basis of covariance analysis can be either non-parametric, with reliance only on the randomization in the study design, or parametric through a statistical model for a postulated sampling process. For non-parametric methods, there are no formal assumptions for how a response variable is related to the covariables, but strong correlation between response and covariables is necessary for variance reduction. Computations for these methods are straightforward through the application of weighted least squares to fit linear models to the differences between treatment groups for the means of the response variable and the covariables jointly with a specification that has null values for the differences that correspond to the covariables. Moreover, such analysis is similarly applicable to dichotomous indicators, ranks or integers for ordered categories, and continuous measurements. Since non-parametric covariance analysis can have many forms, the ones which are planned for a clinical trial need careful specification in its protocol. A limitation of non-parametric analysis is that it does not directly address the magnitude of treatment effects within subgroups based on the covariables or the homogeneity of such effects. For this purpose, a statistical model is needed. When the response criterion is dichotomous or has ordered categories, such a model may have a non-linear nature which determines how covariance adjustment modifies results for treatment effects. Insight concerning such modifications can be gained through their evaluation relative to non-parametric counterparts. Such evaluation usually indicates that alternative ways to compare treatments for a response criterion with adjustment for a set of covariables mutually support the same conclusion about the strength of treatment effects. This robustness is noteworthy since the alternative methods for covariance analysis have substantially different rationales and assumptions. Since findings can differ in important ways across alternative choices for covariables (as opposed to methods for covariance adjustment), the critical consideration for studies with covariance analyses planned as the primary method for comparing treatments is the specification of the covariables in the protocol (or in an amendment or formal plan prior to any unmasking of the study.     

Regression analysis of the log odds ratio: a method for retrospective studies

Quantification of the dependence of the odds ratio on concomitant variables associated with each of several 2 X 2 tables, using a regression model proposed by Zelen [1971], is an important tool for retrospective studies in epidemiology, An "exact" analysis may be based on the conditional likelihood obtained by fixing all the marginal totals. A symptotically this approach is equivalent to use of an unconditional log-linear model. The method is used to reanalyze data reported by Kneale [1971] on the relationship between obstetric radiation and childhood cancer.     

Multiple regression analysis for categorical data with an illustrative application in personnel selection.

Discusses a unified approach to the analysis of categorical data. The procedure is appropriate whenever 1 set of categorical variables can be regarded as dependent and a 2nd set is identified as predictor variables. The approach is identical to the traditional logit analysis model, but for computational convenience the procedure can be modeled in the more general log-linear framework. (16 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of estimation methods on making trait-level inferences from ordered categorical items for assessing psychopathology.

In assessments of attitudes, personality, and psychopathology, unidimensional scale scores are commonly obtained from Likert scale items to make inferences about individuals' trait levels. This study approached the issue of how best to combine Likert scale items to estimate test scores from the practitioner's perspective: Does it really matter which method is used to estimate a trait? Analyses of 3 data sets indicated that commonly used methods could be classified into 2 groups: methods that explicitly take account of the ordered categorical item distributions (i.e., partial credit and graded response models of item response theory, factor analysis using an asymptotically distribution-free estimator) and methods that do not distinguish Likert-type items from continuously distributed items (i.e., total score, principal component analysis, maximum-likelihood factor analysis). Differences in trait estimates were found to be trivial within each group. Yet the results suggested that inferences about individuals' trait levels differ considerably between the 2 groups. One should therefore choose a method that explicitly takes account of item distributions in estimating unidimensional traits from ordered categorical response formats. Consequences of violating distributional assumptions were discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes

Logistic regression is used frequently in cohort studies and clinical trials. When the incidence of an outcome of interest is common in the study population (>10%), the adjusted odds ratio derived from the logistic regression can no longer approximate the risk ratio. The more frequent the outcome, the more the odds ratio overestimates the risk ratio when it is more than 1 or underestimates it when it is less than 1. We propose a simple method to approximate a risk ratio from the adjusted odds ratio and derive an estimate of an association or treatment effect that better represents the true relative risk.     

Estimation of excess risk from case-control data using Aalen's linear regression model

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.     

Moderated multiple regression for interactions involving categorical variables: A statistical control for heterogeneous variance across two groups.

Moderated multiple regression (MMR) arguably is the most popular statistical technique for investigating regression slope differences (interactions) across groups (e.g., aptitude–treatment interactions in training and differential test score–job performance prediction in selection testing). However, heterogeneous error variances can greatly bias the typical MMR analysis, and the conditions that cause heterogeneity are not uncommon. Statistical corrections that have been developed require special calculations and are not conducive to follow-up analyses that describe an interaction effect in depth. A weighted least squares (WLS) approach is recommended for 2-group studies. For 2-group studies, WLS is statistically accurate, is readily executed through popular software packages (e.g., SAS Institute, 1999; SPSS, 1999), and allows follow-up tests. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

基于属性值集中度的分类数据聚类有效性内部评价指标

针对分类数据,通过数据对象在属性值上的集中程度定义了新的基于属性值集中度的类内相似度(similarity based on concentration of attribute values,CONC),用于衡量聚类结果中类内各数据对象之间的相似度;通过不同类的特征属性值的差异程度定义了基于强度向量差异的类间差异度(dissimilarity based on discrepancy of SVs,DCRP),用于衡量两个类之间的差异度.基于CONC和DCRP提出了新的分类数据聚类有效性内部评价指标(clustering validation based on concentration of attribute values,CVC),它具有以下3个特点:(1)在评价每个类内相似度时,不仅依靠类内各数据对象的特征,还考虑了整个数据集的信息;(2)采用几个特征属性值的差异评价两个类的差异度,确保评价过程不丢失有效的聚类信息,同时可以消除噪音的影响;(3)在评价类内相似度及类间差异度时,消除了数据对象个数对评价过程的影响.采用加州大学欧文分校提出的用于机器学习的数据库(UCI)进行实验,将CVC与类别效用(category utility,CU)指标、基于主观因素的分类数据指标(categorical data clustering with subjective factors,CDCS)指标和基于信息熵的内部评价指标(information entropy,IE)等内部评价指标进行对比,通过外部评价指标标准交互信息(normalized mutual information,NMI)验证内部评价效果.实验表明相对其他内部评价指标,CVC指标可以更有效地评价聚类结果.此外,CVC指标相对于NMI指标,不需要数据集以外的信息,更具实用性.     

转炉炼钢过程静态控制模型的改进

简要介绍了采用统计回归方法建立增量多元回归方程,从而建立达到对冶炼终点进行控制目的的转炉炼钢静态控制模型,并通过采集到的某钢厂120 t转炉的实际生产数据,对模型进行了验证.     

A Markov mixed effect regression model for drug compliance

Patient compliance (adherence) with prescribed medication is often erratic, while clinical outcomes are causally linked to actual, rather than nominal medication dosage. We propose here a hierarchical Markov model for patient compliance. At the first stage, conditional upon individual random effects and a set of individual-specific nominal daily dose times, we assume that (i) the subject-specific probability of taking zero, one, or more than one dose associated with a given nominal dose time depends on the value of certain covariates, and on the number of doses associated with the immediate previous time, but is independent of any other previous or future dosing events (the Markov hypothesis); and (ii) the set of 'errors' between actual dose times associated with each nominal time is multivariate normally distributed, conditional on covariates and the number of such actual dose times, as in (i). At the second stage, a multivariate normal distribution is assumed for the individual random effects. We fit this model by maximum likelihood to data collected over three months using an electronic system for recording actual dose times in HIV-positive patients assigned to a regimen of zidovudine thrice daily. Beyond its value for describing and quantifying compliance behaviour, as illustrated here, the model may prove useful for explanatory analyses of clinical trials.     

基于属性值集中度的分类数据聚类有效性内部评价指标

针对分类数据, 通过数据对象在属性值上的集中程度定义了新的基于属性值集中度的类内相似度(similarity based on concentration of attribute values, CONC), 用于衡量聚类结果中类内各数据对象之间的相似度; 通过不同类的特征属性值的差异程度定义了基于强度向量差异的类间差异度(dissimilarity based on discrepancy of SVs, DCRP), 用于衡量两个类之间的差异度.基于CONC和DCRP提出了新的分类数据聚类有效性内部评价指标(clustering validation based on concentration of attribute values, CVC), 它具有以下3个特点: (1)在评价每个类内相似度时, 不仅依靠类内各数据对象的特征, 还考虑了整个数据集的信息; (2)采用几个特征属性值的差异评价两个类的差异度, 确保评价过程不丢失有效的聚类信息, 同时可以消除噪音的影响; (3)在评价类内相似度及类间差异度时, 消除了数据对象个数对评价过程的影响.采用加州大学欧文分校提出的用于机器学习的数据库(UCI)进行实验, 将CVC与类别效用(category utility, CU)指标、基于主观因素的分类数据指标(categorical data clustering with subjective factors, CDCS)指标和基于信息熵的内部评价指标(information entropy, IE)等内部评价指标进行对比, 通过外部评价指标标准交互信息(normalized mutual information, NMI)验证内部评价效果.实验表明相对其他内部评价指标, CVC指标可以更有效地评价聚类结果.此外, CVC指标相对于NMI指标, 不需要数据集以外的信息, 更具实用性.      

A bivariate survival model with modified gamma frailty for assessing the impact of interventions

Bivariate survival analysis models that incorporate random effects or 'frailty' provide a useful framework for determining the effectiveness of interventions. These models are based on the notion that two paired survival times are correlated because they share a common unobserved value of a random variate from a frailty distribution. In some applications, however, investigators may have some information that characterizes pairs and thus provides information about their frailty. Alternatively, there may be an interest in assessing whether the correlation within certain types of pairs is different from the correlation within other types of pairs. In this paper, we present a method to incorporate 'pair-wise' covariate information into the dependence parameter of the bivariate survival function. We provide an example using data from the Framingham Heart Study to investigate the times until the occurrence of two events within an individual: the first detection of hypertension and the first cardiovascular disease event. We model the dependence between these two events as a function of the age of the individual at the time of enrollment into the Framingham Study.     

A model for predicting the transmission rate of malaria from serological data

A model is developed to estimate the duration for which malaria antibody levels in the blood remain high in a closed population. This estimate can be used to calculate the transmission rate within a region, in conjunction with the serological information contained in the population. The model is used on data obtained from a study of malaria in the Philippines and shows excellent agreement. It is subsequently utilised for predictions and seems to be an appropriate vehicle for this purpose.     

Nonparametric alternatives for testing main effects hypotheses: A model for combining data across independent studies.

Describes G. A. Mack and J. H. Skillings's (1980) and A. Benard and P. Van Elteren's (1953) forms of the combined Kruskal-Wallis test, 2 nonparametric tests that can be used to make comparisons across K groups in a design with B blocks or in B independent studies. It is suggested that the dependent variables across studies may be alternative measures of the same underlying construct, and an application of the models to B. G. Davis's (1972, 1974) data on the clinical skills of 3 groups of nurses is described. (12 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A model for interval-censored tuberculosis outbreak data

As the incidence of tuberculosis (TB) has increased in the United States, occupationally acquired TB has increased among the health care workers (HCWs). This paper describes a model developed in response to the needs of an outbreak of multidrug-resistant TB. One of the goals of the outbreak investigation was to estimate the risk of tuberculin skin test (TST) conversion as a function of HCW job type and the period during which persons were employed over the study period. TST conversions were evaluated at periodic examinations and data are interval-censored. We present a generalized linear model that extends Efron's survival model for censored survival data to the case of interval-censored data.     

A laboratory model for dental radiographic studies

A 3-year-old girl with Down's syndrome and myelopathy caused by atlanto-axial subluxation (AAS) was treated by C-1 to C-2 posterior fusion with a one-piece cervical device (OPCD). Instrumentation was required because the posterior arch of C-1 was too tiny and fragile to tolerate wiring. Postoperative immobilization was another major problem in this mentally retarded young child, but a hard plastic cervical corset effectively restrained the neck. She had been confined to bed by severe quadriparesis, but became able to walk without assistance 8 months after surgery. We recommend OPCD instrumentation and postoperative immobilization using a hard plastic corset for the treatment of AAS associated with Down's syndrome in young children.     

Random-effects regression models for clustered data with an example from smoking prevention research.

Proposes a random-effects regression model for analysis of clustered data. Unlike ordinary regression analysis of clustered data, random-effects regression models do not assume that each observation is independent but do assume that data within clusters are dependent to some degree. The degree of this dependency is estimated along with estimates of the usual model parameters, thus adjusting these effects for the dependency resulting from the clustering of the data. A maximum marginal likelihood solution is described, and available statistical software for the model is discussed. An analysis of a dataset in which students are clustered within classrooms and schools is used to illustrate features of random-effects regression analysis, relative to both individual-level analysis that ignores the clustering of the data, and classroom-level analysis that aggregates the individual data. (PsycINFO Database Record (c) 2010 APA, all rights reserved)