Background: Cost-effectiveness analyses (CEA) assess the impact of an intervention on the likelihood of causing individual health states (IHS) and then measuring utilities for those IHS. Clinically, IHS often occur jointly, generating joint health states (JHS). Given the mathematics involved, a few IHS can generate many JHS. Current approaches estimate JHS utilities from IHS utilities from models with unknown empirical validity: Additive (ADD): JHS=B0+B1*IHS1+B2*IHS2; Multiplicative (MULT): ln(JHS)=B0+B1*ln(IHS1)+B2*ln(IHS2); and Minimum State Equivalence (MSE): JHS = Min(IHS1,IHS2).

Purpose: To compare ratings of JHS utilities to component IHS utilities and to compare three models of JHS utility computation for “logical” and “illogical” responses from a prostate cancer CEA.

Methods: Utilities were assessed at prostate biopsy at two University-based urology clinics using the time-tradeoff (TTO) method. IHS utilities were elicited for impotence (IMP), incontinence (INC), asymptomatic localized disease (ALD), and post-prostatectomy (PP). Three JHS utilities were elicited by adding “impotence” to INC, PP, and ALD. Group and individual-level “logical” consistency was assessed (i.e. JHS rated no worse than component IHS). Linear regressions comparing models for JHS were tested for fit in both the full and “logical” sample.

Results: The IHS full sample (n = 124) mean utilities were: PP – 0.82, ALD – 0.82, IMP – 0.74; INC – 0.68. The JHS mean utilities were: IMP & PP – 0.70; IMP & ALD – 0.69; IMP & INC – 0.64. The percentage of “logical” responses at the individual-level were: IMP & ALD – 72%, IMP & INC – 63%, IMP & PP – 60%. In linear regressions of JHS utilities on component HIS utilities, R-square for model fit (ADD/MULT/MSE) were: IMP & INC – 0.561/0.648/0.566; IMP & PP – 0.615/0.669/0.650; IMP & ALD – 0.560/0.658/0.600. Including only “logical responses” improves fits, but introduces a downward bias.

Conclusions: At the group level, each JHS mean utility is lower than the IHS utilities of which it is composed, and men are “logical,” on average. At the individual level, 60 – 72% of respondents give “logical” responses. The multiplicative model fits the data best, even better than the commonly-used “minimum state” model. Additionally, if the “minimal state” model is used, “correcting” illogical responses introduces a downward bias to the JHS calculation. We suggest the multiplicative model for JHS utility calculation when not directly elicited.