INVESTIGATING STRUCTURAL INDEPENDENCE IN PREFERENCE-BASED UTILITY INSTRUMENTS USING GRAPHICAL MODELS

Purpose: The construction of preference based utility instruments relies on multi-attribute utility theory, one of the most important components of which is structural independence among the attributes. This means that overlap between items is minimized so that every combination of health states is possible. For example, severe pain with excellent emotional well-being is possible, if unlikely, but high levels of function are not compatible with low mobility, since function and mobility are highly correlated. This property is rarely tested empirically.  We used patient data and graphical models - advanced statistical methods used for modelling multivariate associations and interdependencies among random variables - to test the structural independence of a prostate cancer-specific instrument, Patient-Oriented Prostate Utility Scale (PORPUS-U). 

Method: We used patient-level data from one cross-sectional and one longitudinal dataset, the latter capturing three time points representing different states in disease/treatment trajectory.  In the models, the items are represented by nodes, which are connected with edges whenever there is a conditional dependence between them, given the rest of the item responses. We tested the conditional dependence with a chi-square based statistical test, correcting for multiple testing. We also performed model selection, starting with the saturated model (with all possible connections present) and applying stepwise backward selection and the Bayesian Information Criterion (BIC), in order to obtain the best-fitted model structure.

Result: Using the statistical tests and the selected models we identified a number of conditional dependencies among the item responses. Out of the 45 possible connections among the 10 items of the PORPUS-U, 22 were included in the selected model based on the cross-sectional dataset. Using the longitudinal data at the three time points identified 16, 20 and 20 connections respectively. Similar results were obtained by the statistical tests. Five item pairs were identified as highly correlated in all 4 models.

Conclusion: Graphical models are powerful statistical tools that can be used for investigating possible deviations from the claimed structural independence among items of utility instruments. As such they can potentially improve the design and use of these instruments. In this study we identified dependencies among a number of items in a prostate cancer utility instrument. Further investigation using alternative testing and modeling strategies, applied to data from other instruments is needed.