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

Table 2 Observed, purified and theoretical estimates of health utility for the 20 most prevalent co-morbid conditions (descending) in cycle 1.1 of CCHS

Two conditions reported together on CCHS		Observed^Φ HUI3	Purified^† HUI3	Theoretical^‡ utility
Non-Food Allergies	Asthma	0.93 (0.01)	1.00 (0.01)	0.98 (0.01)
Non-Food Allergies	Back Problems*	0.86 (0.01)	0.92 (0.01)	0.94 (0.01)
Food Allergies	Non-Food Allergies	0.92 (0.01)	0.99 (0.01)	0.99 (0.01)
Arthritis/Rheumatism	Back Problems*	0.78 (0.01)	0.83 (0.01)	0.88 (0.01)
Non-Food Allergies	Migraine Headaches	0.91 (0.01)	0.98 (0.01)	0.97 (0.01)
Arthritis/Rheumatism	High Blood Pressure	0.85 (0.01)	0.91 (0.01)	0.93 (0.01)
Non-Food Allergies	Arthritis/Rheumatism	0.83 (0.02)	0.89 (0.02)	0.94 (0.01)
Back Problems*	Migraine Headaches	0.82 (0.01)	0.88 (0.01)	0.91 (0.01)
Non-Food Allergies	High Blood Pressure	0.92 (0.01)	0.98 (0.01)	0.98 (0.01)
Back Problems*	High Blood Pressure	0.86 (0.02)	0.92 (0.02)	0.92 (0.01)
High Blood Pressure	Diabetes	0.89 (0.02)	0.96 (0.02)	0.96 (0.01)
Non-Food Allergies	Thyroid Condition	0.92 (0.01)	0.99 (0.01)	1.00 (0.01)
High Blood Pressure	Heart Disease	0.91 (0.02)	0.97 (0.02)	0.95 (0.01)
Arthritis/Rheumatism	Migraine Headaches	0.84 (0.02)	0.90 (0.02)	0.91 (0.01)
Food Allergies	Back Problems*	0.88 (0.01)	0.94 (0.01)	0.93 (0.01)
Asthma	Back Problems*	0.87 (0.02)	0.93 (0.02)	0.92 (0.01)
High Blood Pressure	Migraine Headaches	0.84 (0.02)	0.90 (0.02)	0.95 (0.01)
Food Allergies	Asthma	0.92 (0.01)	0.98 (0.02)	0.97 (0.01)
Arthritis/Rheumatism	Thyroid Condition	0.90 (0.02)	0.96 (0.02)	0.94 (0.01)
Food Allergies	Migraine Headaches	0.91 (0.01)	0.98 (0.02)	0.96 (0.01)

Notes:
Standard error is shown in brackets following the estimate.
Conditions are shown in descending order of prevalence of the observed co-morbidity.
* Back problems excluding fibromyalgia & arthritis.
Φ Observed refers to the average, age-sex standardized HUI3 of the pair of conditions reported together on CCHS before being purified.
† Purified refers to the average observed utility after division by the average utility of those reporting no conditions.
‡ Theoretical refers to the utility estimated from the multiplicative rule (no synergy), using the purified HUI3 of the two conditions reported alone (Table 1).