Extending the Qaly Model to Incorporate Goals that Are Not Time Modulated

1. Extending the Qaly Model to Incorporate Goals that Are Not Time Modulated Gordon Hazen Northwestern University

2. QALY Model • QALYs are the most important and broadly used method for evaluating health quality. • Panel on Cost Effectiveness in Health and Medicine (Gold et al. 1996): Medical CE studies should incorporate morbidity and mortality consequences into a single measure using QALYs.

3. Problems with QALYs • Numerous studies have demonstrated that the correlation between one’s current health and the time-tradeoff or standard gamble utility for that health state is at best modest. (Tsevat 2000)

4. Problems with QALYs (cont.) • Willingness to trade away time often much less than one might expect. • Miyamota and Eraker (1988): Subjects might accept a tradeoff of life duration for improved health quality when remaining lifetime was long, but decline such tradeoffs if remaining lifetime was short. • This behavior cannot be accommodated within the QALY model.

5. Problems with QALYs (cont.) • Maximum endurable time: Subjects can tolerate no more than a particular time in an undesirable health state, beyond which each additional increment of time decreases overall utility. • Miyamoto et al (1998) report a patient who regarded his health state as almost intolerable, but who wanted to live at least 5 more years to see his son graduate from high school. • Such behavior cannot be accommodated within the QALY model.

6. Health Quality vs. Life Quality • Hypothesis (Tsevat): QALYs capture quality of health, but not quality of life. • Goals related to quality of health tend to be ongoing – their impact is modulated by duration • increase mobility • eliminate pain • reduce emotional stress.

7. Health Quality vs. Life Quality (cont.) • Goals related to quality of life may be extrinsic – their impact is not modulated by duration: • an author might want to complete a book; • a politician might strive to achieve higher office; • an engineer or architect might endeavor to see a project to completion; • many individuals seek to have children and raise families.

8. QALY model and Extrinsic Goals • In the QALY model, quality of health is given weight proportional to health duration. • It follows that the QALY model cannot directly account for extrinsic goals, whose importance is by definition independent of duration.

9. Assumptions underlying the QALY model (Miyamoto et al 1998) Quality/life duration pairs (q,t). Theorem (Miyamoto et al 1998): A1 + A2  U(q,t) = UQ(q)UT(t) (Generalized QALY model)

10. Assumptions underlying the QALY model (Miyamoto et al 1998) Quality/life duration pairs (q,t). A1. The zero condition: Preferences between states of health disappear when survival duration is zero, that is, for all states q, q of health, (q,0) ~ (q,0). A2. Generalized utility independence (GUI) for lifetime/ Standard gamble independence.

11. Revised assumptions allowing for extrinsic goals Goal/ quality/ life-duration triples (g,q,t). B1. Conditional zero condition: For each level g of extrinsic goal achievement, preferences for health quality disappear when life duration is zero, that is, for all health states q, q, (g,q,0) ~ (g, q,0). B2. Generalized utility independence (GUI) for lifetime. B3. Conditional utility independence of extrinsic goal attainment and health quality given life duration.

12. Revised assumptions allowing for extrinsic goals Goal / quality / life-duration triples (g,q,t). Theorem (Hazen 2003): B1+B2+B3 implies U(g,q,t) = UQ(q)UT(t)  kG(1UG(g))

13. Utility function incorporating extrinsic goals The utility model: U(g,q,t) = UQ(q)UT(t)  kG(1UG(g)) Interpretation: UQ(q)UT(t) QALYs UG(g) Utility for goal achvmnt level g kG(1UG(g)) Penalty for less-than-full goal achievement kG Tradeoff weight for goal achvmt

14. Survival-duration surrogate for extrinsic goal achievement • Achievement of an extrinsic goal may require time commitment – say estimated time commitment is tG. • Simple and convenient surrogate for goal achievement: Whether survival exceeds tG. Only two levels of goal achievement  Can take UG(g) = g.

15. Interpretation of kGwhen there is a tG-survival duration surrogate U(g,q,t) = UQ(q)UT(t) – kG(1 – g) kG / tG = Quality of life increment that one would be just willing to sacrifice to increase survival from slightly below tG to slightly above tG.

16. Goal model allows max endurable time Health profile h: Survive for duration t in unde-sirable health state with utility uQ < 0. U(h) = uQt  kG(1 g) Utility of h decreases until t exceeds tG, where time goal is achieved.

17. Goal model allows tradeoff reluctance UQ(q0) = 0.30, tG = 1 yr • If reduction in survival time interferes with goal achievement, then it may make sense not to trade away time for health improvement.

18. Example Decision Analysis • Decision to undergo carotid endarterectomy – a Markov chain analysis performed by Matchar & Pauker (1986) • We add an extrinsic goal represented by survival-duration surrogate tG = 6 yr. • We take goal weight kG= 1.2 yr. (Willing to decrease health quality by 0.20 in order to increase survival duration from just below the 6-year survival goal to just above it.)

19. Example Decision Analysis Results tG = 6 years, kG = 1.2 years

20. Conclusion • Von Neuman-Morganstern utility functions that include an extrinsic goal component • can account for observed violations of the QALY model (maximum endurable time preference, reluctance to trade off time for quality) • can do so prescriptively, thereby providing a coherent basis for including such goals in decision and cost-effectiveness analyses.