Deriving utility scores for co-morbid conditions: a test of the multiplicative model for combining individual condition scores

The co-morbidity of health conditions is becoming a significant health issue, particularly as populations age, and presents important methodological challenges for population health research. For example, the calculation of summary measures of population health (SMPH) can be compromised if co-morbidity is not taken into account. One popular co-morbidity adjustment used in SMPH computations relies on a straightforward multiplicative combination of the severity weights for the individual conditions involved. While the convenience and simplicity of the multiplicative model are attractive, its appropriateness has yet to be formally tested. The primary objective of the current study was therefore to examine the empirical evidence in support of this approach. The present study drew on information on the prevalence of chronic conditions and a utility-based measure of health-related quality of life (HRQoL), namely the Health Utilities Index Mark 3 (HUI3), available from Cycle 1.1 of the Canadian Community Health Survey (CCHS; 2000-01). Average HUI3 scores were computed for both single and co-morbid conditions, and were also purified by statistically removing the loss of functional health due to health problems other than the chronic conditions reported. The co-morbidity rule was specified as a multiplicative combination of the purified average observed HUI3 utility scores for the individual conditions involved, with the addition of a synergy coefficient s for capturing any interaction between the conditions not explained by the product of their utilities. The fit of the model to the purified average observed utilities for the co-morbid conditions was optimized using ordinary least squares regression to estimate s. Replicability of the results was assessed by applying the method to triple co-morbidities from the CCHS cycle 1.1 database, as well as to double and triple co-morbidities from cycle 2.1 of the CCHS (2003-04). Model fit was optimized at s = .99 (i.e., essentially a straightforward multiplicative model). These results were closely replicated with triple co-morbidities reported on CCHS 2000-01, as well as with double and triple co-morbidities reported on CCHS 2003-04. The findings support the simple multiplicative model for computing utilities for co-morbid conditions from the utilities for the individual conditions involved. Future work using a wider variety of conditions and data sources could serve to further evaluate and refine the approach.