Analysis of Multiple Partially Ordered Responses to Belief Items with Don't Know Option

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.

Longitudinal partially ordered data analysis for preclinical sarcopenia

Sarcopenia is a geriatric syndrome characterized by significant loss of muscle mass. Based on a commonly used definition of the condition that involves three measurements, different subclinical and clinical states of sarcopenia are formed. These states constitute a partially ordered set (poset). This article focuses on the analysis of longitudinal poset in the context of sarcopenia. We propose an extension of the generalized linear mixed model and a recoding scheme for poset analysis such that two submodels-one for ordered categories and one for nominal categories-that include common random effects can be jointly estimated. The new poset model postulates random effects conceptualized as latent variables that represent an underlying construct of interest, that is, susceptibility to sarcopenia over time. We demonstrate how information can be gleaned from nominal sarcopenic states for strengthening statistical inference on a person's susceptibility to sarcopenia.

Gleaning Information for Cognitive Operations from Don't Know Responses in Cognitive and Noncognitive Assessments

The Don't Know (DK) response - taking the form of an omitted response or not-reached at the end of a cognitive test, or explicitly presented as a response option in a social survey - contains important information that is often overlooked. Direct psychometric modeling efforts for DK responses are few and far between. In this article, the linear logistic test model (LLTM) is proposed for delineating the impacts of cognitive operations for a test that contains DK responses. We assume that the DK response is a valid response. The assumption is reasonable for many situations, including low-stakes cognitive tests and attitudinal assessments. By extracting information embedded in the DK response, the method shows how DK can inform the latent construct of interest and the cognitive operations underlying the response to stimuli. Using a proven recoding scheme, the LLTM could be implemented through commonly used programs such as PROC GLIMMIX. Two simulation experiments to evaluate how well the parameters can be recovered were conducted. In addition, two real data examples, from a noncognitive test of health belief assessment and a cognitive test of knowledge in diabetes, are also presented as case studies to illustrate the LLTM for DK response.

Resolve conflicting rankings of outcomes in network meta-analysis: Partial ordering of treatments

Network meta-analysis has evolved into a core method for evidence synthesis in health care. In network meta-analysis, 3 or more treatments for a given medical condition are compared, based on a number of clinical studies, usually randomized controlled trials. Often, many different endpoints are investigated, related to different aspects of the patient's outcome, such as efficacy, safety, acceptability, or costs of a treatment. Different outcomes may lead to different rankings of the treatments. We use the existing theory of partially ordered sets and show how the relations between the treatments in a network meta-analysis can be illustrated by Hasse diagrams, that is, directed graphs showing the partial order relations, and by structured scatter plots and biplots.