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At least 19 recordsLinked to original sources
PubMed1994

ROC curve regression analysis: the use of ordinal regression models for diagnostic test assessment.

Diagnostic tests commonly are characterized by their true positive (sensitivity) and true negative (specificity) classification rates, which rely on a single decision threshold to classify a test result as positive. A more complete description of test accuracy is given by the receiver operating characteristic (ROC) curve, a graph of the false positive and true positive rates obtained as the decision threshold is varied. A generalized regression methodology, which uses a class of ordinal regression models to estimate smoothed ROC curves has been described. Data from a multi-institutional study comparing the accuracy of magnetic resonance (MR) imaging with computed tomography (CT) in detecting liver metastases, which are ideally suited for ROC regression analysis, are described. The general regression model is introduced and an estimate for the area under the ROC curve and its standard error using parameters of the ordinal regression model is given. An analysis of the liver data that highlights the utility of the methodology in parsimoniously adjusting comparisons for covariates is presented.

Algorithms↗
PubMed2006

Ordinal regression model and the linear regression model were superior to the logistic regression models.

OBJECTIVE: Ordinal scales often generate scores with skewed data distributions. The optimal method of analyzing such data is not entirely clear. The objective was to compare four statistical multivariable strategies for analyzing skewed health-related quality of life (HRQOL) outcome data. HRQOL data were collected at 1 year following catheterization using the Seattle Angina Questionnaire (SAQ), a disease-specific quality of life and symptom rating scale. STUDY DESIGN AND SETTING: In this methodological study, four regression models were constructed. The first model used linear regression. The second and third models used logistic regression with two different cutpoints and the fourth model used ordinal regression. To compare the results of these four models, odds ratios, 95% confidence intervals, and 95% confidence interval widths (i.e., ratios of upper to lower confidence interval endpoints) were assessed. RESULTS: Relative to the two logistic regression analysis, the linear regression model and the ordinal regression model produced more stable parameter estimates with smaller confidence interval widths. CONCLUSION: A combination of analysis results from both of these models (adjusted SAQ scores and odds ratios) provides the most comprehensive interpretation of the data.

Adolescent↗
PubMed2002

A review of ordinal regression models applied on health-related quality of life assessments.

There has been increasing emphasis in medical research on the design and analysis of quality of life scales. Many quality of life scales are ordinal and statistical methods such as ordinal regression models have been reviewed on a number of occasions. However, when such models are applied, the way the data have been generated is often overlooked. In this paper we illustrate the use of ordinal regression models, in particular the proportional odds model, the partial proportional odds model and the stereotype model in the MRC Cognitive Function and Ageing Study (MRC CFAS). The partial proportional odds and the stereotype models are often under-utilized, perhaps due to the lack of available software. However, in this paper, analysis based on these models has been carried out using the popular statistical software package SAS and macros devised in SAS. Furthermore, bootstrapping techniques have been applied to obtain valid estimates of the standard errors of the parameters in the stereotype model. Strikingly different results were obtained using the different ordinal regression models. We conclude that the way the data have been generated is particularly important for the analysis of quality of life assessments. Different methods of generating scores yield data with different properties. It is now possible to fit a variety of ordinal regression models and so select the appropriate one that correctly models the data.

Data Interpretation, Statistical↗
PubMed1994

A SAS macro for residual deviance of ordinal regression analysis.

In this paper, a SAS macro is described for calculating the likelihood of the 'saturated' model in the analysis of ordinal regression. The outcome variable is multinomial on an ordinal scale, while the explanatory variables can be nominal or ordinal. Several ordinal regression models may be fitted to the data. One method of testing for the goodness of fit of these regression models is by comparing the residual deviance with the chi 2 distribution. In SAS, PROC LOGISTIC may be used to fit this type of data with proportional odds model. Unfortunately, the residual deviance is not available from the output. Our SAS macro will supplement the SAS output so that the residual deviance test may be carried out. The data from an ongoing HIV study is used as an illustration.

Bias↗
PubMed1994

A random-effects ordinal regression model for multilevel analysis.

A random-effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data. This model is developed for both the probit and logistic response functions. The threshold concept is used, in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects. A maximum marginal likelihood (MML) solution is described using Gauss-Hermite quadrature to numerically integrate over the distribution of random effects. An analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random-effects analysis of clustered ordinal data, while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random-effects approach for longitudinal ordinal data.

Adolescent↗
PubMed2000

Random effects in censored ordinal regression: latent structure and Bayesian approach.

This paper discusses random effects in censored ordinal regression and presents a Gibbs sampling approach to fit the regression model. A latent structure and its corresponding Bayesian formulation are introduced to effectively deal with heterogeneous and censored ordinal observations. This work is motivated by the need to analyze interval-censored ordinal data from multiple studies in toxicological risk assessment. Application of our methodology to the data offers further support to the conclusions developed earlier using GEE methods yet provides additional insight into the uncertainty levels of the risk estimates.

Animals↗
PubMed1994

A robust goodness-of-fit test statistic with application to ordinal regression models.

We propose a goodness-of-fit test statistic for linear regression with heterogeneous variance, which is asymptotically chi-square if the given model is correct. The test statistic is computed as a quadratic form of observed minus predicted responses. We apply the method to a linear regression for an ordinal categorical response, the wheezing status of a child (no wheeze, wheeze with cold, wheeze apart from cold) as a function of maternal smoking and city of residence.

Child↗
PubMed1996

Ordinal regression methodology for ROC curves derived from correlated data.

We present an approach for the analysis of correlated ROC data, using ordinal regression models in conjunction with generalized estimating equations. The approach applies to the analysis of degree-of-suspicion data derived from multiple interpretations of the same diagnostic study and from the examination of the same patients with multiple diagnostic modalities. The regression models make it possible to incorporate patient and reader characteristics into the analysis, without having to resort to stratification. We illustrate the potential of the approach with analysis of data from two studies in diagnostic oncology.

Diagnosis↗
PubMed2001

Application of random effect ordinal regression model for outcome evaluation of two randomized controlled trials.

Cluster randomization is often used in intervention trials, yet when individuals nested within clusters are considered as the units of analysis for outcome evaluation, it cannot be assumed that the observations are statistically independent. Observations that are not statistically independent also result when repeated measures are taken over time for the same individual. Ignoring clustered observations when performing data analysis can lead to the erroneous conclusion that the intervention under study had a statistically significant effect. Moreover, individual responses are often collected on ordinal scales; thus models for continuous or categorical data are usually not appropriate. We applied a random effect ordinal regression model to data sets from two randomized controlled intervention trials that measured graded scale non-independent responses. The first trial compared two school programmes for AIDS prevention in terms of impact (i.e., changes in the frequency of condom use). The second trial used the MOS-HIV questionnaire to measure the quality of life of new AIDS cases four times over a one-year follow-up period (only results of the role-functioning scale are reported). Regarding the first data set, the effect of the intervention was not significant, and the post-intervention frequency of condom use was mainly attributable to the pre-intervention frequency (p<0.01), with no differences among schools. Regarding the second data set, a borderline significant increase in the role-functioning scale scores was observed over the follow-up period; the results differed only slightly by intervention group; a significant (p<0.01) intra-individual correlation of 0.4 was found.

Acquired Immunodeficiency Syndrome↗
PubMed1989

Ordinal regression models for epidemiologic data.

Health status is often measured in epidemiologic studies on an ordinal scale, but data of this type are generally reduced for analysis to a single dichotomy. Several statistical models have been developed to make full use of information in ordinal response data, but have not been much used in analyzing epidemiologic studies. The authors discuss two of these statistical models--the cumulative odds model and the continuation ratio model. They may be interpreted in terms of odds ratios, can account for confounding variables, have clear and testable assumptions, and have parameters that may be estimated and hypotheses that may be tested using available statistical packages. However, calculations of asymptotic relative efficiency and results of simulations showed that simple logistic regression applied to dichotomized responses can in some realistic situations have more than 75% of the efficiency of ordinal regression models, but only if the ordinal scale is collapsed into a dichotomy close to the optimal point. The application of the proposed models to data from a study of chest x-rays of workers exposed to mineral fibers confirmed that they are easy to use and interpret, but gave results quite similar to those obtained using simple logistic regression after dichotomizing outcome in the conventional way.

Asbestos, Amphibole↗
PubMed1989

A measurement-error model for binary and ordinal regression.

Exposure assessment poses special problems in air pollution epidemiology. This paper proposes a probit regression model for binary and ordinal outcomes that uses exposure validation information to develop estimates for the coefficient of the true exposure when only the inaccurate 'surrogate' measure of exposure is available for the individuals in the health study. This method is closely related to recently developed measurement-error methods, and is based on the assumption that the outcome and the surrogate exposure are conditionally independent given the true exposure. A test statistic is proposed for checking this conditional independence assumption when more than one surrogate is available, and an interpretation of the coefficient estimate is provided in the event that the assumption is violated. The methods are applied to an example involving nitrogen dioxide exposure and wheeze in children.

Air Pollution↗
PubMed1996

MIXOR: a computer program for mixed-effects ordinal regression analysis.

MIXOR provides maximum marginal likelihood estimates for mixed-effects ordinal probit, logistic, and complementary log-log regression models. These models can be used for analysis of dichotomous and ordinal outcomes from either a clustered or longitudinal design. For clustered data, the mixed-effects model assumes that data within clusters are dependent. The degree of dependency is jointly estimated with the usual model parameters, thus adjusting for dependence resulting from clustering of the data. Similarly, for longitudinal data, the mixed-effects approach can allow for individual-varying intercepts and slopes across time, and can estimate the degree to which these time-related effects vary in the population of individuals. MIXOR uses marginal maximum likelihood estimation, utilizing a Fisher-scoring solution. For the scoring solution, the Cholesky factor of the random-effects variance-covariance matrix is estimated, along with the effects of model covariates. Examples illustrating usage and features of MIXOR are provided.

Antipsychotic Agents↗
PubMedDate not supplied

Aquifer vulnerability assessment to heavy metals using ordinal logistic regression.

A methodology using ordinal logistic regression is proposed to predict the probability of occurrence of heavy metals in ground water. The predicted probabilities are defined with reference to the background concentration and the maximum contaminant level. The model is able to predict the occurrence due to different influencing variables such as the land use, soil hydrologic group (SHG), and surface elevation. The methodology was applied to the Sumas-Blaine Aquifer located in Washington State to predict the occurrence of five heavy metals. The influencing variables considered were (1) SHG; (2) land use; (3) elevation; (4) clay content; (5) hydraulic conductivity; and (6) well depth. The predicted probabilities were in agreement with the observed probabilities under existing conditions. The results showed that aquifer vulnerability to each heavy metal was related to different sets of influencing variables. However, all heavy metals had a strong influence from land use and SHG. The model results also provided good insight into the influence of various hydrogeochemical factors and land uses on the presence of each heavy metal. A simple economic analysis was proposed and demonstrated to evaluate the cost effects of changing the land use on heavy metal occurrence.

Forecasting↗
PubMed2006

Differential item functioning analysis with ordinal logistic regression techniques. DIFdetect and difwithpar.

INTRODUCTION: We present an ordinal logistic regression model for identification of items with differential item functioning (DIF) and apply this model to a Mini-Mental State Examination (MMSE) dataset. We employ item response theory ability estimation in our models. Three nested ordinal logistic regression models are applied to each item. Model testing begins with examination of the statistical significance of the interaction term between ability and the group indicator, consistent with nonuniform DIF. Then we turn our attention to the coefficient of the ability term in models with and without the group term. If including the group term has a marked effect on that coefficient, we declare that it has uniform DIF. We examined DIF related to language of test administration in addition to self-reported race, Hispanic ethnicity, age, years of education, and sex. METHODS: We used PARSCALE for IRT analyses and STATA for ordinal logistic regression approaches. We used an iterative technique for adjusting IRT ability estimates on the basis of DIF findings. RESULTS: Five items were found to have DIF related to language. These same items also had DIF related to other covariates. DISCUSSION: The ordinal logistic regression approach to DIF detection, when combined with IRT ability estimates, provides a reasonable alternative for DIF detection. There appear to be several items with significant DIF related to language of test administration in the MMSE. More attention needs to be paid to the specific criteria used to determine whether an item has DIF, not just the technique used to identify DIF.

Bias↗
PubMed1990

Assessing proportionality in the proportional odds model for ordinal logistic regression.

The proportional odds model for ordinal logistic regression provides a useful extension of the binary logistic model to situations where the response variable takes on values in a set of ordered categories. The model may be represented by a series of logistic regressions for dependent binary variables, with common regression parameters reflecting the proportional odds assumption. Key to the valid application of the model is the assessment of the proportionality assumption. An approach is described arising from comparisons of the separate (correlated) fits to the binary logistic models underlying the overall model. Based on asymptotic distributional results, formal goodness-of-fit measures are constructed to supplement informal comparisons of the different fits. A number of proposals, including application of bootstrap simulation, are discussed and illustrated with a data example.

Biometry↗
PubMedDate not supplied

Ordinal logistic regression in medical research.

Medical research workers are making increasing use of logistic regression analysis for binary and ordinal data. The purpose of this paper is to give a non-technical introduction to logistic regression models for ordinal response variables. We address issues such as the global concept and interpretation of logistic models, the model building procedure from a practical point of view, and the assessment of the model adequacy. For illustrative purposes we apply these methods to real data of a study investigating the association between glycosylated haemoglobin and retinopathy. We give some recommendations for the use and assessment of ordinal logistic regression models in medical research.

Analysis of Variance↗
PubMed1991

Using ordinal logistic regression to estimate the likelihood of colorectal neoplasia.

The utility of ordinal logistic regression in the prediction of colorectal neoplasia was demonstrated in a group of 461 consecutive patients undergoing colonoscopy in a community practice. One hundred twenty-nine patients had adenomatous polyps and 34 had colorectal adenocarcinoma. An ordinal logistic regression model developed in a random subset (292 patients) identified five predictors of colorectal neoplasia. Colorectal neoplasia risk could be predicted using the patient's age, sex, hematocrit, fecal occult blood test result and indication for colonoscopy. The risk of colorectal neoplasia in the remaining subset of patients (169) could be reliably estimated from the model. Ordinal logistic regression analysis in this select group of patients can accurately estimate the likelihood of colorectal neoplasia. Because the generalizability of our findings are unknown, the model should not be applied to other patients. However, application of this technique to an unselected group of patients not already referred for colonoscopy could provide unbiased estimates of colorectal neoplasia risk in individual patients.

Adenocarcinoma↗