Ordinal Outcome Data Research Articles

Statistical reanalysis of vascular event outcomes in primary and secondary vascular prevention trials

BackgroundVascular prevention trials typically use dichotomous event outcomes although this may be inefficient statistically and gives no indication of event severity. We assessed whether ordinal outcomes would be more efficient and how to best analyse them.MethodsChief investigators of vascular prevention randomised controlled trials that showed evidence of either benefit or harm, or were included in a systematic review that overall showed benefit or harm, shared individual participant data from their trials. Ordered categorical versions of vascular event outcomes (such as stroke and myocardial infarction) were analysed using 15 statistical techniques and their results then ranked, with the result with the smallest p-value given the smallest rank. Friedman and Duncan’s multiple range tests were performed to assess differences between tests by comparing the average ranks for each statistical test.ResultsData from 35 trials (254,223 participants) were shared with the collaboration. 13 trials had more than two treatment arms, resulting in 59 comparisons. Analysis approaches (Mann Whitney U, ordinal logistic regression, multiple regression, bootstrapping) that used ordinal outcome data had a smaller average rank and therefore appeared to be more efficient statistically than those that analysed the original binary outcomes.ConclusionsOrdinal vascular outcome measures appear to be more efficient statistically than binary outcomes and provide information on the severity of event. We suggest a potential role for using ordinal outcomes in vascular prevention trials.

Bayesian Approach to Multivariate Component-Based Logistic Regression: Analyzing Correlated Multivariate Ordinal Data

Applications of component-based models have gained much attention as a means of accompanying dimension reduction in the regression setting and have been successfully implemented to model a univariate outcome in the behavioral and social sciences. Despite the prevalence of correlated ordinal outcome data in the fields, however, most of the extant component-based models have been extended to address the multivariate ordinal issue with a simplified but unrealistic assumption of independence, which may lead to biased statistical inferences. Thus, we propose a Bayesian methodology for a component-based model that accounts for unstructured residual covariances, while regressing multivariate ordinal outcomes on pre-defined sets of predictors. The proposed Bayesian multivariate ordinal logistic model re-expresses ordinal outcomes of interest with a set of latent continuous variables based on an approximate multivariate t-distribution. This contributes not only to developing an efficient Gibbs sampler, a Markov Chain Monte Carlo algorithm, but also to facilitating the interpretation of regression coefficients as log-transformed odds ratio. The empirical utility of the proposed method is demonstrated through analyzing a subset of data, extracted from the 2009 to 2010 Health Behavior in School-Aged Children study that investigates risk factors of four different forms of bullying perpetration and victimization: physical, social, racial, and cyber.

Network meta-regression for ordinal outcomes: Applications in comparing Crohn's disease treatments.

Crohn's disease (CD) is a life-long condition associated with recurrent relapses characterized by abdominal pain, weight loss, anemia, and persistent diarrhea. In the US, there are approximately 780000 CD patients and 33000 new cases added each year. In this article, we propose a new network meta-regression approach for modeling ordinal outcomes in order to assess the efficacy of treatments for CD. Specifically, we develop regression models based on aggregate covariates for the underlying cut points of the ordinal outcomes as well as for the variances of the random effects to capture heterogeneity across trials. Our proposed models are particularly useful for indirect comparisons of multiple treatments that have not been compared head-to-head within the network meta-analysis framework. Moreover, we introduce Pearson residuals and construct an invariant test statistic to evaluate goodness-of-fit in the setting of ordinal outcome data. A detailed case study demonstrating the usefulness of the proposed methodology is carried out using aggregate ordinal outcome data from 16 clinical trials for treating CD.

Statistical tests for biosimilarity based on relative distance between follow-on biologics for ordinal endpoints

Investigations of biosimilarity between reference drugs and test drugs required statistical tests; in addition, statistical tests to evaluate biosimilarity have been recently proposed. Ordinal outcome data has been observed in research; however, appropriate statistical tests to deal with ordinal endpoints for biosimilar have not yet been proposed. This paper extends existing design for ordinal endpoints. Using measure of nominal-ordinal association and relative distances between drugs are defined so that testing procedures are developed. Through simulation studies, we investigate type I error rate and power to show the performance of our suggested method. Furthermore, a comparison between the statistical tests and other designs is proviede to show significance of ordinal endpoints.

Modified spatial scan statistics using a restricted likelihood ratio for ordinal outcome data

Spatial scan statistics are widely used as a technique to detect geographical disease clusters for different types of data. It has been pointed out that the Poisson-based spatial scan statistic tends to detect rather larger clusters by absorbing insignificant neighbors with non-elevated risks. We suspect that the spatial scan statistic for ordinal data may also have similar undesirable phenomena. In this paper, we propose to apply a restricted likelihood ratio to spatial scan statistics for ordinal outcome data to circumvent such a phenomenon. Through a simulation study, we demonstrated not only that original spatial scan statistics have the over-detection phenomenon but also that our proposed methods have reasonable or better performance compared with the original methods. We illustrated the proposed methods using a real data set from the 2014 Health Screening Program of Korea with the diagnosis results of normal, caution, suspected disease, and diagnosed with disease as an ordinal outcome.

Occupation-focused interventions for well older people: An exploratory randomized controlled trial

Objective: The aim of this exploratory randomised controlled trial (RCT) was to evaluate three different occupation-focused interventions for well older people by estimating effect sizes for leisure engagement and ability in activities of daily living (ADL) and thereby identifying the most effective interventions. Methods: One hundred and seventy seven persons, 77–82 years old, living alone and without home help, were randomized to a control group (CG), an individual intervention (IG), an activity group (AG), and a one-meeting discussion group (DG). All interventions focused on occupational engagement and how persons can cope with age-related activity restrictions in order to enhance occupational engagement. Data were collected by blinded research assistants at baseline, three, and 12 months. Ordinal outcome data were converted, using Rasch measurement methods, to linear measures of leisure engagement and ADL ability. Standardized between-group effect sizes, Cohen’s d, were calculated. Results: While all groups showed a decline in leisure engagement and ADL over time, the IG and the DG were somewhat effective in minimizing the decline at both three and 12 months. However, the effect sizes were small. Conclusions: The findings indicate that occupation-focused interventions intended to minimize a decline in leisure engagement and ADL were sufficiently promising to warrant their further research.

Log-Link Regression Models for Ordinal Responses

The adjacent-categories, continuation-ratio and proportional odds logit-link regression models provide useful extensions of the multinomial logistic model to ordinal response data. We propose fitting these models with a logarithmic link to allow estimation of different forms of the risk ratio. Each of the resulting ordinal response log-link models is a constrained version of the log multinomial model, the log-link counterpart of the multinomial logistic model. These models can be estimated using software that allows the user to specify the log likelihood as the objective function to be maximized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the unconstrained models produced valid coefficient estimates and standard errors, and the constrained models produced plausible results. Models with a single continuous covariate performed well in data simulations, with low bias and mean squared error on average and appropriate confidence interval coverage in admissible solutions. In an application to real data, practical aspects of the fitting of the models are investigated. We conclude that it is feasible to obtain adjusted estimates of the risk ratio for ordinal outcome data.

Spatial cluster detection for ordinal outcome data

In geographical disease surveillance, spatial scan statistics are used to identify areas having unusually high or low rates of disease outcomes and to determine the statistical significance of detected clusters. The spatial scan statistic for ordinal data such as stage of cancer has been developed to detect clusters representing areas with high rates of more serious stages compared with the surrounding areas. Such areas were expressed using likelihood ratio ordering, which is a rather strict order restriction, and hence, the method might fail to detect spatial clusters with high rates of worse categories (e.g., later stage). In this paper, we relax the order restriction using stochastic ordering and examine differences between the two approaches in detecting spatial clusters. Through simulation studies, we show that the stochastic ordering-based approach has higher power, sensitivity, and positive predictive value under several scenarios. We illustrate the two methods with the use of a real data example.

Calculation of Numbers-Needed-To-Treat in Parallel Group Trials Assessing Ordinal Outcomes: Case Examples from Acute Stroke and Stroke Prevention

Number-needed-to-treat describes the magnitude of the effect of an intervention, underpins health economic analyses, and is typically calculated for binary events. Ordered categorical outcomes provide more clinical information and their analysis using ordinal approaches is usually more efficient statistically. However, to date, techniques to calculate number-needed-to-treat based on ordinal outcomes for parallel group trials have had important limitations. Aims Numbers-needed-to-treat may be calculated for ordinal data from parallel group trials by using an unmatched comparison of all subjects or by generating matched pairs of patients nested within the study. The above approaches were assessed and compared with numbers-needed-to-treat calculated for binary outcomes using individual patient data from acute and prevention stroke trials testing the effect of interventions of varying utility and efficacy. Numbers-needed-to-treat were generally lower numerically for ordinal vs. binary, and matched vs. unmatched analyses, and the lowest in highly efficacious interventions: hemicraniectomy, ordinal matched 2.4 vs. ordinal unmatched 2.5 vs. binary matched 12 vs. binary unmatched 9 (one trial, 12 month outcome); alteplase, 4.5 vs. 6.6 vs. 8.4 vs. 8.4 (one trial with two parts, three-months); aspirin, 42 vs. 58 vs. 76 vs. 80 (one trial, six-months); and stroke units, 3.6-5.3 vs. 6.2 vs. 4.7-5.9 vs. 6.3-7.0 (two trials, three- to 60 months). Similar trends were seen for aspirin/dipyridamole vs. aspirin in secondary prevention, 22 vs. 20 vs. 31 vs. 31 (one trial, 24 months). Number-needed-to-treat may be calculated for ordinal outcome data derived from parallel group stroke trials; such numbers-needed-to-treat are lower than those calculated for binary outcomes. Their use complements the use of ordinal statistical approaches in the analysis of ordered categorical data.

Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation.

Previous research has compared methods of estimation for fitting multilevel models to binary data, but there are reasons to believe that the results will not always generalize to the ordinal case. This article thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data include a small to moderate number of clusters (i.e., ≤ 50 clusters).

A simulation study evaluating approaches to the analysis of ordinal outcome data in randomized controlled trials in traumatic brain injury: results from the IMPACT Project

Clinical trials in traumatic brain injury have a disappointing track record, with a long history of 'negative' Phase III trials. One contributor to this lack of success is almost certainly the low efficiency of the conventional approach to the analysis, which discards information by dichotomizing an ordinal outcome scale. Our goal was to evaluate the potential efficiency gains, which can be achieved by using techniques, which extract additional information from ordinal outcome data - the proportional odds model and the sliding dichotomy. In addition, we evaluated the additional efficiency gains, which can be achieved through covariate adjustment. The study was based on simulations, which were built around a database of patient-level data extracted from eight Phase III trials and three observational studies in traumatic brain injury. Two different putative treatment effects were explored, one which followed the proportional odds model, and the other which assumed that the effect of the intervention was to reduce the risk of death without changing the distribution of outcomes within survivors. The results are expressed as efficiency gains, reported as the percentage reduction in sample size that can be used with the ordinal analyses without loss of statistical power relative to the conventional binary analysis. The simulation results show substantial efficiency gains. Use of the sliding dichotomy allows sample sizes to be reduced by up to 40% without loss of statistical power. The proportional odds model gives modest additional gains over and above the gains achieved by use of the sliding dichotomy. As with any simulation study, it is difficult to know how far the findings may be extrapolated beyond the actual situations that were modeled. Both ordinal techniques offer substantial efficiency gains relative to the conventional binary analysis. The choice between the two techniques involves subtle value judgments. In the situations examined, the proportional odds model gave efficiency gains over and above the sliding dichotomy, but arguably, the sliding dichotomy is more intuitive and clinically appealing.

Characteristics and Performance of a Modified Version of the ADCS-CGIC CIBIC+ for Mild Cognitive Impairment Clinical Trials

The Alzheimer's Disease Cooperative Study-Clinical Global Impression of Change (ADCS-CGIC) was modified for use in mild cognitive impairment (MCI) trials and tested in the ADCS MCI randomized clinical trial of donepezil, vitamin E, and placebo. We assessed feasibility for its use by determining whether or not: (1) it distinguished a medication effect at 6 months and 12 months, (2) baseline demographic or clinical characteristics predicted change, (3) there was an association between MCI-CGIC and change in other clinical measures in order to evaluate external or concurrent validity. We used a generalized estimating equations approach for ordinal outcome data to test the effects of treatment, baseline characteristics, and change in clinical measures on the MCI-CGIC over 12 months, and ordinal logistic regression to assess the association between MCI-CGIC and change in clinical measures at 6 months and 12 months. On the MCI-CGIC overall, 12.9% and 10.6% were rated as having improved, and 31.6% and 39.8% as having worsened over 6 months and 12 months, respectively. The MCI-CGIC did not distinguish the donepezil or vitamin E groups from placebo at 6 and 12 months treatment. Variables at screening or baseline that were associated with worse CGIC scores over 6 and 12 months included white race, greater years of education, worse depression, dementia severity rating, cognitive, and daily activities scores, and lower memory domain scores on a neuropsychological battery. Rate of worsening on the MCI-CGIC over 12 months was associated with change on the Alzheimer Disease Assessment Scale-cognitive and on executive function. Worsening at 6 months and 12 months, separately, were associated with the corresponding change in Alzheimer Disease Assessment Scale-cognitive, Activities of Daily Living, Beck Depression Inventory, Mini-Mental State Examination, Clinical Dementia Rating sum of boxes, memory, and executive function. Change detected by the MCI-CGIC was associated with baseline clinical severity and with change in clinical ratings over 6 and 12 months, supporting the validity of a CGIC approach in MCI. The effect size of the donepezil-placebo difference was similar to that of other outcomes at 12 months. About 40% of MCI patients were judged worse and about 11% improved, consistent with clinical experience and other ratings.

Stroke trials

One of the most commonly used clinical outcomes in acute stroke trials is the 3-month modified Rankin Scale (mRS), an ordinal scale that ranges from 0 (no symptoms) to 6 (death). Traditionally, the mRS is dichotomized into excellent (0–1 vs 2–6) or good (0–2 vs 3–6) outcome. Alternately, shift analysis compares the distribution of outcomes between the treatment and control groups across the entire ordinal scale, thus answering the question of whether there is any measurable improvement on the mRS associated with treatment. The two approaches target different types of departures from the null hypothesis of no difference in outcome between treatment and control groups. Hence, applying the appropriate analytic strategy to the expected departure can increase power and reduce the number needed to prove a benefit in clinical trials. In this issue of Neurology ®, Saver and Gornbein1 explored statistical approaches to ordinal outcome data …

Likelihood‐based modelling of age‐related normal ranges for ordinal measurements: changes in visual acuity through early childhood

This paper investigates the construction of age-related standards for ordinal outcome data. Asymmetric logistic models are used to describe the age-related changes in the cumulative probabilities for each ordinal level. Maximum likelihood estimation of model parameters allows the use of likelihood ratio tests to ascertain the appropriate model complexity. In contrast to methodologies for constructing age-related standards where the outcome is continuous, we show how the methodology leads directly to centile estimation for individuals. The method is illustrated using visual acuity measurements collected from 2968 children between 2 and 9 years of age made on a 30-point ordinal scale. We show how, in this instance, smoothing of parameters across ordinal categories leads to reduced validity of the centiles, justifying the need for specialized methodology for non-continuous outcomes.

A study of the effect of dichotomizing ordinal data upon modeling

Investigators in health services research often analyze ordinal outcome data as if it were dichotomous by collapsing outcomes into two groups and using standard logistic regression, rather than an alternate discrete model. This paper assesses the degree to which parameters are inaccurately estimated and ower is lost when this is done. Simulations with a five level ordinal outcome variable demonstrated that the loss of precision and power can be very pronounced. Parameter estimates were especially poor in the presence of moderately sparse data, while the loss of power was most evident with balanced data. Polychotomous models are also examined and discussed. An example using length of hospital stay data grouped into discrete outcome levels is given.