A comparison of methods for correlated ordinal measures with ophthalmic applications

For many clinical trials and epidemiologic investigations in the field of ophthalmology, paired ordinal data are often collected through the detailed grading of retinal photographs. One method for analysis of these data is the extension of the generalized estimating equation (GEE) methodology to multinomial data with cumulative link functions. Prior to the development of this advanced technique, however, ophthalmologists developed a method of combining the ordinal responses of both eyes of a patient into a single person-level response on a new ordinal scale. A relationship between the regression coefficients of these two methods is derived as a function of the correlation between eyes. We investigate the applicability of this result and the relationship of the standard errors in simulation experiments and in an example from the Wisconsin Epidemiologic Study of Diabetic Retinopathy.     

Analysis of matched case-control data with multiple ordered disease states: possible choices and comparisons

In an individually matched case-control study, effects of potential risk factors are ascertained through conditional logistic regression (CLR). Extension of CLR to situations with multiple disease or reference categories has been made through polychotomous CLR and is shown to be more efficient than carrying out separate CLRs for each subgroup. In this paper, we consider matched case-control studies where there is one control group, but there are multiple disease states with a natural ordering among themselves. This scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease, for example, according to different stages of cancer. We explore several popular models for ordered categorical data in this context. We first adopt a cumulative logit or equivalently, a proportional-odds model to account for the ordinal nature of the data. The important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum-specific nuisance parameters cannot be eliminated in this model via the conditional-likelihood approach. We discuss a Mantel-Haenszel approach for analysing such data. We point out possible difficulties with standard likelihood-based approaches with the cumulative logit model when applied to case-control data. We then consider an alternative conditional adjacent-category logit model. We illustrate the methods by analysing data from a matched case-control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control. A simulation study compares the different ordinal methods with methods ignoring sub-classification of the ordered disease states.     

Fitting stratified proportional odds models by amalgamating conditional likelihoods

Classical methods for fitting a varying intercept logistic regression model to stratified data are based on the conditional likelihood principle to eliminate the stratum-specific nuisance parameters. When the outcome variable has multiple ordered categories, a natural choice for the outcome model is a stratified proportional odds or cumulative logit model. However, classical conditioning techniques do not apply to the general K-category cumulative logit model (K>2) with varying stratum-specific intercepts as there is no reduction due to sufficiency; the nuisance parameters remain in the conditional likelihood. We propose a methodology to fit stratified proportional odds model by amalgamating conditional likelihoods obtained from all possible binary collapsings of the ordinal scale. The method allows for categorical and continuous covariates in a general regression framework. We provide a robust sandwich estimate of the variance of the proposed estimator. For binary exposures, we show equivalence of our approach to the estimators already proposed in the literature. The proposed recipe can be implemented very easily in standard software. We illustrate the methods via three real data examples related to biomedical research. Simulation results comparing the proposed method with a random effects model on the stratification parameters are also furnished.     

Ordered multinomial regression for genetic association analysis of ordinal phenotypes at Biobank scale

Logistic regression is the primary analysis tool for binary traits in genome-wide association studies (GWAS). Multinomial regression extends logistic regression to multiple categories. However, many phenotypes more naturally take ordered, discrete values. Examples include (a) subtypes defined from multiple sources of clinical information and (b) derived phenotypes generated by specific phenotyping algorithms for electronic health records (EHR). GWAS of ordinal traits have been problematic. Dichotomizing can lead to a range of arbitrary cutoff values, generating inconsistent, hard to interpret results. Using multinomial regression ignores trait value hierarchy and potentially loses power. Treating ordinal data as quantitative can lead to misleading inference. To address these issues, we analyze ordinal traits with an ordered, multinomial model. This approach increases power and leads to more interpretable results. We derive efficient algorithms for computing test statistics, making ordinal trait GWAS computationally practical for Biobank scale data. Our method is available as a Julia package OrdinalGWAS.jl. Application to a COPDGene study confirms previously found signals based on binary case–control status, but with more significance. Additionally, we demonstrate the capability of our package to run on UK Biobank data by analyzing hypertension as an ordinal trait.     

A new model for ordinal pain data from a pharmaceutical study

For the pain data analysed previously by Cox and Chuang, this paper proposes a new model that assumes monotone scores for ordered response categories. This proposed model possesses several attractive features and allows a stochastic ordering of the drugs under comparison. Such a model also provides insight regarding the ordinal scale used to classify response. Estimation of the parameters in the model is obtained by use of BMDP3R.     

Measuring inequality in self-reported health-discussion of a recently suggested approach using Finnish data

Health surveys often include a general question on self-assessed health (SAH), usually measured on an ordinal scale with three to five response categories, from 'very poor' or 'poor' to 'very good' or 'excellent'. This paper assesses the scaling of responses on the SAH question. It compares alternative procedures designed to impose cardinality on the ordinal responses. These include OLS, ordered probit and interval regression approaches. The cardinal measures of health are used to compute and decompose concentration indices for income-related inequality in health. Results are provided using Finnish data on 15D and the SAH questions. Further evidence emerges for the internal validity of a method used in a pioneering study by van Doorslaer and Jones which was based on Canadian data on the McMaster Health Utility Index Mark III (HUI) and SAH. The study validates the conclusions drawn by van Doorslaer and Jones. It confirms that the interval regression approach is superior to OLS and ordered probit regression in assessing health inequality. However, regarding the choice of scaling instrument, it is concluded that the scaling of SAH categories and, consequently, the measured degree of inequality, are sensitive to characteristics of the chosen scaling instrument.     

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.     

A goodness‐of‐fit test for the ordered stereotype model

This paper presents a new goodness‐of‐fit test for an ordered stereotype model used for an ordinal response variable. The proposed test is based on the well‐known Hosmer–Lemeshow test and its version for the proportional odds regression model. The latter test statistic is calculated from a grouping scheme assuming that the levels of the ordinal response are equally spaced which might be not true. One of the main advantages of the ordered stereotype model is that it allows us to determine a new uneven spacing of the ordinal response categories, dictated by the data. The proposed test takes the use of this new adjusted spacing to partition data. A simulation study shows good performance of the proposed test under a variety of scenarios. Finally, the results of the application in two examples are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Meta-analysis of ordinal outcomes using individual patient data

Meta-analyses are being undertaken in an increasing diversity of diseases and conditions, some of which involve outcomes measured on an ordered categorical scale. We consider methodology for undertaking a meta-analysis on individual patient data for an ordinal response. The approach is based on the proportional odds model, in which the treatment effect is represented by the log-odds ratio. A general framework is proposed for fixed and random effect models. Tests of the validity of the various assumptions made in the meta-analysis models, such as a global test of the assumption of proportional odds between treatments, are presented. The combination of studies with different definitions or numbers of response categories is discussed. The methods are illustrated on two data sets, in a classical framework using SAS and MLn and in a Bayesian framework using BUGS. The relative merits of the three software packages for such meta-analyses are discussed.     

Regression with an ordered categorical response

A survey on Mseleni joint disease in South Africa involved the scoring of pelvic X-rays of women to measure osteoporosis. The scores were ordinal by construction and ranged from 0 to 12. It is standard practice to use ordinary regression techniques with an ordinal response that has that many categories. We give evidence for these data that the constraints on the response result in a misleading regression analysis. McCullagh's proportional-odds model is designed specifically for the regression analysis of ordinal data. We demonstrate the technique on these data, and show how it fills the gap between ordinary regression and logistic regression (for discrete data with two categories). In addition, we demonstrate non-parametric versions of these models that do not make any linearity assumptions about the regression function.     

Continuity of care in a family practice residency program. Impact on physician satisfaction

One of the primary benefits of continuity of care is its influence upon patient and physician satisfaction. This prospective pilot study involved a cohort of 14 second- and third-year family practice residents and 4 full-time faculty at a community hospital-based family practice residency in Cleveland, Ohio. Rates of continuity that physicians experience were calculated using the usual provider continuity (UPC) measure of continuity, and were correlated with physician satisfaction with outpatient care using a practice satisfaction scale (PSS) developed specifically for this purpose. Residents and faculty were also asked to rank order the importance of several aspects of outpatient care, including continuity of care. The results indicate that both residents and faculty value continuity of care highly compared with other aspects of outpatient care. The average continuity rates were 59% for second-year residents, 54% for third-year residents, and 82% for faculty. The UPC continuity measure correlated highly with the PSS scores (corrected r2 = .55; P less than .001). The data support the hypothesis that continuity of care with patients is an important determinant of resident and faculty physician satisfaction with their outpatient experience.     

Patient satisfaction and selected physician behaviors: does the type of practice make a difference?

This study was designed to show what specific physician characteristics lead to patient satisfaction and to compare satisfaction of patients using either prepaid or fee-for-service modes of payment within the same settings. We surveyed 1142 patients in five family practice clinics in rural and suburban areas of the North Central United States. Regression analysis of a seven-item satisfaction scale showed four significant factors that accounted for variance: sensitivity, is on time for appointments, follows up promptly, and provides personalized medical care. No meaningful differences were found between health-maintenance-organization and fee-for-service patients on these satisfactions. This study expands findings from previous research and raises more questions about reliable rating scales for complex physician/patient relations. Our methods can be used to investigate the effects of newer types of prepaid plans (including individual practice associations and preferred provider organizations) on patient satisfaction. The challenge for future investigations is to test and build reliable predictive models showing how physician characteristics, patient satisfaction, and quality of medical care affect each other in these more complex models of practice and reimbursement.     

Factors influencing consumers' selection of a primary care physician

There is a growing body of literature regarding patient choice of health care plans, patient satisfaction, and patient evaluation of health care quality, but there is little information concerning the factors that influence the initial selection of a primary care physician (PCP). This exploratory study identifies and conceptualizes the physician selection dimensions which include: physician reputation/manner, physician record, physician search, consumer self-awareness, physician location, physician qualifications, physician demographics, office atmospherics, house calls/insurance, and valuing patient opinion. The study also develops and tests a scale for PCP selection using factor analysis which is demonstrated to be valid, and determines significant differences of variables, which include education level, gender, and age, using a summated scale. The study is of use to physicians in their targeting and communication strategies, and to researchers seeking to refine the scale.     

Does telephone follow-up predict patient satisfaction and readmission?

Nursing telephone calls after hospital discharge are commonly adopted as a tool to improve patient satisfaction and continuity of care. Previous research, however, has been inconclusive on the impact of telephone follow-up. The purpose of this study was to comparatively examine patients who received telephone follow-up for response differences on a mail satisfaction survey and 30-day readmission rates for a large health system in southeast Texas. Telephone follow-up, patient satisfaction, and administrative billing data from 2008 to 2009 were retrospectively examined across 10 nursing units that routinely performed calls after patient discharge. Patients eligible to receive a nursing call (N = 10,559) were categorized based on responses to nursing questions or if no contact was made. Logistic regression was used to evaluate whether call data significantly predicted survey response and 30-day readmission rates. Nonparametric analysis was used to evaluate whether survey ratings varied between groups. Completion of telephone follow-up was a significant (P < 0.01) predictor of patient response to the mail survey, with 62% more patients returning surveys after contact. Completion of a nursing call with a patient who reported a physician appointment was a significant predictor (P = 0.04) of lower 30-day readmissions. Readmission rates were 10.8% for patients who did not receive telephone follow-up compared to 9.5% for patients who received a call and who had a scheduled physician appointment. Mean nursing and overall satisfaction scores varied minimally between groups and telephone follow-up was not a significant predictor of patient satisfaction. Telephone follow-up shows significant predictive value for mail survey response and 30-day readmission rates but does not correlate with patient satisfaction scores in the hospital setting.     

Classification to ordinal categories using a search partition methodology with an application in diabetes screening.

A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obtained. The approach is applied to ordinal categories of glucose tolerance to discriminate between diabetes, impaired glucose tolerance and normal states. The results are compared with analysis by ordinal logistic regression and by classification trees.     

Factors Influencing Consumers' Selection of a Primary Care Physician

Abstract

There is a growing body of literature regarding patient choice of health care plans, patient satisfaction, and patient evaluation of health care quality, but there is little information concerning the factors that influence the initial selection of a primary care physician (PCP). This exploratory study identifies and conceptualizes the physician selection dimensions which include: physician reputation/manner, physician record, physician search, consumer self-awareness, physician location, physician qualifications, physician demographics, office atmospherics, house calls/insurance, and valuing patient opinion. The study also develops and tests a scale for PCP selection using factor analysis which is demonstrated to be valid, and determines significant differences of variables, which include education level, gender, and age, using a summated scale. The study is of use to physicians in their targeting and communication strategies, and to researchers seeking to refine the scale.     

Ordinal response prediction using bootstrap aggregation,with application to a high‐throughput methylation data set

Many investigators conducting translational research are performing high‐throughput genomic experiments and then developing multigenic classifiers using the resulting high‐dimensional data set. In a large number of applications, the class to be predicted may be inherently ordinal. Examples of ordinal outcomes include tumor‐node‐metastasis (TNM) stage (I, II, III, IV); drug toxicity evaluated as none, mild, moderate, or severe; and response to treatment classified as complete response, partial response, stable disease, or progressive disease. While one can apply nominal response classification methods to ordinal response data, in doing so some information is lost that may improve the predictive performance of the classifier. This study examined the effectiveness of alternative ordinal splitting functions combined with bootstrap aggregation for classifying an ordinal response. We demonstrate that the ordinal impurity and ordered twoing methods have desirable properties for classifying ordinal response data and both perform well in comparison to other previously described methods. Developing a multigenic classifier is a common goal for microarray studies, and therefore application of the ordinal ensemble methods is demonstrated on a high‐throughput methylation data set. Copyright © 2009 John Wiley & Sons, Ltd.     

Questionnaire to assess patient satisfaction with pharmaceutical care in Spanish language.

OBJECTIVE: To develop and validate a questionnaire, in Spanish, for assessing patient satisfaction with pharmaceutical care received in community pharmacies. DESIGN: Selection and translation of questionnaire's items; definition of response scale and demographic questions. Evaluation of face and content validity, feasibility, factor structure, reliability and construct validity. SETTING: Forty-one community pharmacies of the province of Santa Fe. Argentina. PARTICIPANTS: Questionnaire administered to patients receiving pharmaceutical care or traditional pharmacy services. MAIN OUTCOME MEASURE: Pilot test to assess feasibility. Factor analysis used principal components and varimax rotation. Reliability established using internal consistency with Cronbach's alpha. Construct validity determined with extreme group method. RESULTS: A self-administered questionnaire with 27 items, 5-point Likert response scale and demographic questions was designed considering multidimensional structure of patient satisfaction. Questionnaire evaluates cumulative experience of patients with comprehensive pharmaceutical care practice in community pharmacies. Two hundred and seventy-four complete questionnaires were obtained. Factor analysis resulted in three factors: Managing therapy, Interpersonal relationship and General satisfaction, with a cumulative variance of 62.51%. Cronbach's alpha for the whole questionnaire was 0.96, and 0.95, 0.88 and 0.76 for the three factors, respectively. Mann-Whitney test for construct validity did not showed significant differences between pharmacies that provide pharmaceutical care and those that do not, however, 23 items showed significant differences between the two groups of pharmacies. CONCLUSION: The questionnaire developed can be a reliable and valid instrument to assess patient satisfaction with pharmaceutical care in community pharmacies in Spanish. Further research is needed to deepen the validation process.     

Two-part models for repeatedly measured ordinal data with “don't know” category

Ordinal data (eg, “low,” “medium,” “high”; graded response on a Likert scale) with an additional “don't know” category are frequently encountered in the medical, social, and behavioral science literature. The handling of a “don't know” option presents unique challenges as it often “destroys” the ordinal nature of the data. Commonly, nominal models are employed which ignore the partial ordering and have a complicated interpretation, especially in situations with repeatedly measured outcomes. We propose two-part models that easily accommodate longitudinal partially ordered (semiordinal) data. The most easily interpretable formulation consists of a random effect logistic submodel for “don't know” vs all the other categories combined, and a random effect ordinal submodel for the ordered categories. Correlated random effects account for statistical dependence within individual. An extension allowing for nonproportionality of odds for the predictor effects in the ordinal submodel is also considered. Maximum likelihood estimation is performed using adaptive Gaussian quadrature in SAS PROC NLMIXED. A simulation study is performed to evaluate the performance of the estimation algorithm in terms of bias and efficiency, and to compare the results of joint and separate models of the two parts, and of proportional and nonproportional model formulations. The methods are motivated and illustrated on a dataset from a study of adolescents' perceptions of nicotine strength of JUUL e-cigarettes. Using the proposed approach we show that adolescents perceive 5% nicotine content as relatively low, a misconception more pronounced among past month nonusers than among past month users of JUUL e-cigarettes.