Reconsidering the use of rankings in the valuation of health states: a model for estimating cardinal values from ordinal data

BACKGROUND: In survey studies on health-state valuations, ordinal ranking exercises often are used as precursors to other elicitation methods such as the time trade-off (TTO) or standard gamble, but the ranking data have not been used in deriving cardinal valuations. This study reconsiders the role of ordinal ranks in valuing health and introduces a new approach to estimate interval-scaled valuations based on aggregate ranking data. METHODS: Analyses were undertaken on data from a previously published general population survey study in the United Kingdom that included rankings and TTO values for hypothetical states described using the EQ-5D classification system. The EQ-5D includes five domains (mobility, self-care, usual activities, pain/discomfort and anxiety/depression) with three possible levels on each. Rank data were analysed using a random utility model, operationalized through conditional logit regression. In the statistical model, probabilities of observed rankings were related to the latent utilities of different health states, modeled as a linear function of EQ-5D domain scores, as in previously reported EQ-5D valuation functions. Predicted valuations based on the conditional logit model were compared to observed TTO values for the 42 states in the study and to predictions based on a model estimated directly from the TTO values. Models were evaluated using the intraclass correlation coefficient (ICC) between predictions and mean observations, and the root mean squared error of predictions at the individual level. RESULTS: Agreement between predicted valuations from the rank model and observed TTO values was very high, with an ICC of 0.97, only marginally lower than for predictions based on the model estimated directly from TTO values (ICC = 0.99). Individual-level errors were also comparable in the two models, with root mean squared errors of 0.503 and 0.496 for the rank-based and TTO-based predictions, respectively. CONCLUSIONS: Modeling health-state valuations based on ordinal ranks can provide results that are similar to those obtained from more widely analyzed valuation techniques such as the TTO. The information content in aggregate ranking data is not currently exploited to full advantage. The possibility of estimating cardinal valuations from ordinal ranks could also simplify future data collection dramatically and facilitate wider empirical study of health-state valuations in diverse settings and population groups

Logit tree models for discrete choice data with application to advice-seeking preferences among Chinese Christians

Logit models are popular tools for analyzing discrete choice and ranking data. The models assume that judges rate each item with a measurable utility, and the ordering of a judge’s utilities determines the outcome. Logit models have been proven to be powerful tools, but they become difficult to interpret if the models contain nonlinear and interaction terms. We extended the logit models by adding a decision tree structure to overcome this difficulty. We introduced a new method of tree splitting variable selection that distinguishes the nonlinear and linear effects, and the variable with the strongest nonlinear effect will be selected in the view that linear effect is best modeled using the logit model. Decision trees built in this fashion were shown to have smaller sizes than those using loglikelihood-based splitting criteria. In addition, the proposed splitting methods could save computational time and avoid bias in choosing the optimal splitting variable. Issues on variable selection in logit models are also investigated, and forward selection criterion was shown to work well with logit tree models. Focused on ranking data, simulations are carried out and the results showed that our proposed splitting methods are unbiased. Finally, to demonstrate the feasibility of the logit tree models, they were applied to analyze two datasets, one with binary outcome and the other with ranking outcome

A Componential Interpretation of the General Factor in Human Intelligence

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A recursive partitioning method for the prediction of preference rankings based upon Kemeny distances

Multivariate analysis of psychological dat