A Linear Index for Predicting Joint Health States Utilities from Single Health States Utilities

1. A Linear Index for Predicting Joint Health States Utilities from Single Health States Utilities Anirban Basu, University of Chicago William Dale, University of Chicago Arthur Elstein, University of Illinois at Chicago David Meltzer, University of Chicago Academy Health Annual Research Meeting Orlando, June 5, 2007

2. Calculation of QALYs in CEA Health at any time  combination of the presence and also of the levels of various “health conditions” or “attributes”  “multi-attribute” in nature Combinatorial explosion of health states if all “health conditions” are considered.  Substantial interview burden to collect utilities  Cognitive burden for eliciting preferences on “multi-attribute” heath states. However, some “multi-attribute” health states are sufficiently prevalent ignoring them may influence CEA.

3. Goal To develop an empirical model to predict the utilities for a “bi-attribute” health state (JOINT STATE) based on the utilities of single-attribute health states. Single-attribute health states • Only one health condition is present (or has a fixed level) AND all other health conditions are either absent or fixed at some innocuous levels. Example: Predict utility of a health state where patient experience both impotence and incontinence, based on the utilities of health states where either impotence or incontinence is present.

4. Traditional Models SS = Single state, JS= Joint State u(.)= Utility, l (.) = 1 – u(.) = Disutility or Loss Most commonly used models: 1) Additive, 2) Multiplicative and 3) Minimum. Each model is of the general form: l (JS) = f {l (SS1), l (SS2)} + ε i.e., E{l (JS) }= f {l (SS1), l (SS2)}

5. Traditional Models 1) Additive E{l (JS)} = l (SS1) + l (SS2)  E{u(JS)} = u(SS1) + u(SS2) - 1 2) Multiplicative E{l (JS)} = l (SS1) + l (SS2) - l (SS1)· l (SS2)  E{u(JS)} = u(SS1) u(SS2) 3) Minimum E{l (JS)} = Max {l (SS1), l (SS2)}  E{u(JS)} = Min {u(SS1), u(SS2)}

6. Traditional Models Previous research (Dale et al., MDM forthcoming) finds all three models produce biased prediction of E{u(JS)}, while the minimum model was the best of the three in terms of overall bias and efficiency. Other models : Based of additive/multiplicative utility function (Keeney and Raiffa, 1976, 1993) u(JS) = k1·u(SS1) + k2·u(SS2) + kk1k2·u(SS1) ·u(SS2) Also used by Torrence et al (1982, 1986) to develop HUI. Turns out for HUI II/III: E{l (JS)} = C· [l (SS1) + l (SS2) - l (SS1)· l (SS2)]

7. Proposed Models E{l(JS)} = α0 + α1·max{l(SS1), l(SS2)} + α2·min{l(SS1), l(SS2)} + α3·l(SS1)·l(SS2) Two unique features – 1) Parameters of the model are not tied to the specific health conditions 2) Encompasses all three traditional generic mapping functions α0 = 0, α1 = 1, α2 = 1, α3 = 0;  Additive model α0 = 0, α1 = 1, α2 = 1, α3 = -1;  Multiplicative model α0 = 0, α1 = 1, α2 = 0, α3 = 0;  Minimum model

8. Normative Constraints?

9. Data • Urology Clinics • University of Chicago (45% positive biopsy) • Northwestern (25% positive biopsy) • Time & Clinic Setting • 30 minutes between appointments • Embedded in larger survey • At time of biopsy, Referral for cause • 75% - elevated PSA (>4.0 ng/dL) • 25% - symptom, abnormal DRE, other

10. Data Single States • Impotence • Urinary Incontinence • Anxiety • High: Watchful Waiting • Low: Post-prostatectomy Joint States • Impotence & Incontinence • Impotence & Post-prostatectomy • Impotence & Asymptomatic Localized Disease Utilities elicited using time-tradeoff method, with ProSPEQT (Bayoumi , 2004)

11. MethodsAn iterated, bootstrapped, split-sample approach

12. RESULTS

13. Table 1. Descriptive statistics (n = 207)

14. Table 2. Utilities (n = 207)

15. Table 3. Parameter Estimates

16. Proposed linear indices • With theoretical restrictions E{l(JS)} = 0 + ·max{l(SS1), l(SS2)} - 0.043596· [min{l(SS1), l(SS2)} - l(SS1) ·l(SS2)] • Unrestricted E{l(JS)} = 0.05 + 0.72·max{l(SS1), l(SS2)} + 0.33·min{l(SS1), l(SS2)} – 0.18·l(SS1) ·l(SS2)

17. Table 4. Goodness-of Fit in Test (out-of sample) Datasets

18. Figure 1. Goodness-of Fit

19. Conclusions • Empirical models that can predict utilities for the joint states are of great value • Develop and validate a simple predictive model: • combines the utilities for patients of two single-attribute health states and predict utilities when these attributes occur jointly, resulting in a bi-attribute or joint state. • Proposed model outperforms the traditional models, and provides consistent estimates of joint state utilities. • Theoretical constraints produce suboptimal fit to stated utilities for joint states

20. Conclusions • Close resemblance to the additive/multiplicative formulation proposed by Keeney & Raiffa. • Also conforms with “evaluative hypothesis” in psychology comparing “joint evaluation mode” versus “separate evaluation model” (Hsee et al, 1999; Hsee and Zhang 2004) => puts more weight on bigger loss compared to the smaller one.

21. Limitation and Future Directions • Based on convenience sample in urology clinics. • Only evaluated for health states relevant to prostate cancer. • “Impotence” was a common SS in all the JS. • Further validation of this new function in other joint health states in other diseases is warranted. • Tackle issues of logical versus illogical predictions.