Due to this close connection with the widely used LRM, we focus on the CLM with probit link when developing an estimate for the difference in mean scores from the CLM. If the terms in Equation are the thresholds that determine which ordinal score would be assigned for a specific (unobserved), ie, w=1 when, w= j when for and w= J when, then the β parameter in Equations and is identical 10, 11 (see top two rows of Figure 2 for a visual illustration) provided the error term in the LRM has a standard normal distribution. Where the independent error term,, has a standard normal distribution, ie. We outline the steps when applying our approach, compare the performance of the estimates from the CLM and LRM in simulation studies, and in a real data application investigating the effect of time since diagnosis on fatigue among breast cancer survivors. This approach allows both statistical and clinical significance to be assessed in a simple two-step workflow that is appropriate for analyzing ordinal scores. In this paper, we propose a new procedure for assessing the proxy assumption with the CLM, and when the assumption is adequate, a valid estimate of the difference in the means of an ordinal score between groups of individuals is obtained from the CLM. The authors commented that this transformation of the CLM estimate was based on the assumption that the ordinal score was a good proxy for an underlying continuous variable in this example, but did not suggest a formal assessment of this assumption. Specifically, when comparing the effect of an exposure on the ordinal outcome estimated from the LRM and the CLM (with probit link), the authors found that the CLM estimate multiplied by the standard deviation of the ordinal outcome was similar to the LRM estimate. 10, 11 Although the CLM models the cumulative probabilities of discrete ordinal categories, 10, 11 a real data application 12 suggested the potential of transforming the CLM estimates to express the effect of an exposure on an ordinal outcome as the difference in the mean score. The cumulative link model (CLM) is a well-established regression model that assumes an ordinal score is an ordered category that arises from the application of thresholds to a latent continuous variable. Given the relevance of the difference in mean QoL scores as a measure of clinical importance, 8, 9 we propose an alternative to the LRM that assesses the proxy assumption and enables the reporting of the estimates of mean differences when the assumption is adequate. However, there is currently no procedure in LRM analysis that allows the assessment of this proxy assumption, although it is critical to the validity of such inferences. Thus, the estimated change in the mean of the QoL score per unit change in the exposure variable is being used to infer the change in the underlying unobserved QoL level that is attributable to the exposure, thereby viewing the QoL score as a rounded value of the QoL level. When analyzing an ordinal QoL score as the outcome of interest in the LRM, there is an implicit assumption that the ordinal score is a good proxy for an underlying (unobserved) continuous QoL level. 2–4 A number of studies have examined the performance of the LRM in assessing the presence of an association between an exposure and an ordinal score, 2, 5–7 but few have investigated its validity in estimating the measure of association as the difference in means of an ordinal score that is used to assess the clinical importance of the effect. Because of these characteristics, conventional methods for continuous outcomes, such as the linear regression model (LRM), may be inappropriate for analysis of ordinal variables such as QoL measures. 1 Although the ordered categories are often represented by integer values ranging from 1 to a maximum “score”, the difference between any two consecutive categories does not necessarily reflect the same change in perceived well-being. #' cplot #' Conditional predicted value and average marginal effect plots for models #' Draw one or more conditional effects plots reflecting predictions or marginal effects from a model, conditional on a covariate.Quality of life (QoL) scores from questionnaires are often ordinal variables.
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