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Motivation

Motivation.

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Motivation

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  1. Motivation • You are the pharmacy director for a 1.5 million member health insurance organization. The detail person from Merp Inc. comes calling with news that their new pain relief drug “Arafex” has just been approved for persons with osteoarthritis. It’s reported benefits are lower incidence of GI bleeding and (an unexpected outcome of the clinical trial) an apparent modest improvement in LDL cholesterol. Given these purported benefits, the detail person states that at the price, Arafex “blows away” the other Cox II inhibitor products, such as celecoxib and rofecoxib (Taken from S. Ramsey)

  2. Motivation, continued • The cost of Arafex is $95 per 30 day supply • The cost of celecoxib is $82 • The cost of rofecoxib is $74 • Question: Should you add Arafex to the formulary

  3. Introduction • Scarcity of resources • Choices need to be made • Decision need to be made based costs and effects • Cost-effectiveness analysis (CEA) is a way to mingle cost and effectiveness of a study

  4. Examples Of Effectiveness Measures Used In Cost-effectiveness Analyses

  5. Two Commonly Used Statistics • Incremental cost-effectiveness ratio (ICER): • Net health benefit (NHB): Where λ=Willingness to pay

  6. Graphical Representation The ΔE- ΔC plane

  7. Graphical Representation Slope = ICER The ΔE- ΔC plane

  8. Graphical Representation The ΔE- ΔC plane

  9. Graphical Representation The ΔE- ΔC plane

  10. Graphical Representation ICER=50,000 Slope=λ=30,000 The ΔE- ΔC plane

  11. Estimation • Incremental cost-effectiveness ratio (ICER): • Net health benefit (NHB):

  12. Natural interpretation (price/unit of product) Analysis independent of λ Economic foundation Negative ICER is problematic Undefined value possible for CIs Biased, not sufficient NHB properly ordered Interpretation is not ambiguous like negative ICER Unbiased Easy extension to more than two comparators Dependent on λ No natural interpretation PropertiesICER NHB

  13. Normal theory via CLT Bootstrap Confidence box Fieller’s method (1954) Hinkley’s method (1969) Normal theory via CLT Bootstrap Inference: Existing Techniques ICER NHB

  14. Inference: Existing TechniquesConfidence Box The ΔE- ΔC plane

  15. Inference: Existing Techniques • Fieller’s method (1954): • The C.I. can be obtained by equating the formula and solve for R:

  16. Inference: Existing Techniques • Hinkley’s method (1969): • Distribution of ratio of two correlated random normal variables • Can be applied to the ICER if we assume the numerator and the denominator of the ICER are bivariate normal • Has not been applied to inference for the ICER

  17. Previous Studies • Briggs, et al. (1999) • CLT-based (Taylor’s), Fieller’s, confidence box, bootstrap (normal approximation, percentile, BC, BCa, parametric bootstrap) • Conclusion: Fieller’s appears best; parametric bootstrap and BCa are best among the bootstrap methods

  18. Previous Studies • Fan & Zhou (Outcome Research Methodology, 2006) • CLT-based (Taylor’s), Fieller’s, confidence box, bootstrap (normal approximation, percentile, bootstrap-t, BCa, parametric bootstrap) • Conclusion: nonparametric bootstrap-t is best in term of coverage accuracy; next are the Fieller’s and among the bootstrap methods, parametric bootstrap and BCa are best

  19. Limitation of Existing Techniques • CLT-based: may not be appropriate for small sample skewed-data (Briggs, 1999; Fan & Zhou, 2006) • Bootstrap: may be time-consuming, may not provide proper coverage (Fan & Zhou, 2005) • Confidence box: does not provide proper coverage (Briggs, et al, 1999) • Fieller’s and Hinkley’s: based on bivariate normal, Fieller’s may not be closed interval

  20. Inference: Alternative Approach • Purpose: • To explain what play a role in the normal approximation • To help improve inference

  21. Edgeworth Expansion: NHB • NHB: Let where,

  22. Edgeworth Expansion: ICER • ICER: Let • where • A1 and A2 depends on the asymptotic variance of T1 and skewness of costs and effects

  23. Edgeworth Expansion for ICER and NHB • ICER: • NHB:

  24. Alternative Confidence Intervals • Similar to the two-sample problem, we can introduce three new transformational intervals

  25. Simulation • Bivariate normal • Bivariate lognormal • Bivariate mixture

  26. Simulation: ICERCoverage of 95% Confidence intervals

  27. Simulation: NHBCoverage of 95% Confidence intervals

  28. Simulation • The model • Specify λ, β, γ • Generate X ~ uniform • ε ~ normal(0, 1) • g2(Zi, γ) = exp(ZiTγ) • Objective: estimate E(Y|x0)

  29. Simulation

  30. Application to a real example • IN 2002, Katon et al. (2002) conducted a randomized trial to evaluate the cost effectiveness of a collaborative care intervention, compared to the usual primary care setting, in patients with panic disorder. • Panic disorder occurs in 4–6% of patients in primary care. This severe anxiety disorder is associated with high use of medical services, high costs, and a variety of unexplained medical symptoms. • Patients with panic disorder often do not receive an accurate diagnosis in primary care and even when diagnosis is assigned, few patients receive appropriate treatment or psychotherapy (Katon et al., 2002).

  31. Application to real example, cont • One objective of the study is to determine the incremental cost effectiveness of a collaborative care program for primary care patients with panic disorder compared with the usual primary care setting. • To demonstrate our methods, we consider total outpatient nonmental health costs, and for measure of effectiveness, we consider the number of days a patient experiences panic disorder during the 1-year study period.

  32. The summary statistics • Estimated ICER = 15.33, NHB = 77.08 • Control group (n1 = 54) Intervention group (n2 = 53) • Mean SD Skewness Mean SD Skewness • Cost(U.S.$) 2507.42 4460.44 4.93 1325.48 1785.67 3.46 • Effectiveness (days with anxiety attack) • 211.52 139.68 −0.30 134.42 134.55 0.71

  33. Application, cont • Costs in both groups are highly skewed with the coefficient of skewness 4.93 for the control group and 3.46 for the intervention group. • On average, the control group incurred $1181.95 and 77.1 days of panic attack more than the intervention group. • The estimated ICER is 15.33, indicating that the intervention arm is dominant.

  34. confidence intervals for the ICER and the NHB • Methods Confidence intervals Interval length • ICER  Taylor's (−3.44, 34.10) 37.54   • Fieller's (−1.43, 53.86) 55.28  • Hinkley's (−1.68, 52.44) 54.12   • Bootstrap-t   (4.50, 49.55)  45.05   • G1   (3.33, 81.87)  78.54   • G2   (−1.99, 35.22)   37.21   • G3   (0.35, 38.38)  38.03 • NHB  Taylor's  (25.12, 129.03) 103.92    • Bootstrap-t  (21.68, 132.33) 110.65   •  BCa  (20.21, 125.52) 105.31    • G1  (26.78, 130.87) 104.10    • G2  (25.46, 129.39) 103.92    • G3  (32.84, 144.42) 111.58

  35. Results, cont • Both bootstrap-t and G3 intervals are positive, showing that the intervention is significantly dominant (the control group incurred more cost and more days of panic disorder). • As anticipated, both Fieller's and Hinkley's intervals are similar and the G3 interval has shorter length than bootstrap-t. • Because the estimated q1/sqrt(N)=0.9 , Taylor's interval is inadequate. Based on our simulation results, we would recommend using the G3 interval as the confidence interval for the ICER.

  36. A common willingness-to-pay is λ = $50,000; using this value, the estimated NHB is 77.08. • Confidence intervals for the NHB are presented in Table 6. All intervals are relatively similar, especially G1, G2, and Taylor's intervals. The coefficient q2/sqrt(N) is 0.05 in this setting, suggesting that Taylor's interval is adequate. • All of these confidence intervals are strictly positive indicating, again, that the intervention arm is cost effective.

  37. Conclusions on ICER • For the ICER, when data were generated from a skewed distribution, our new intervals gave better coverages than Taylor's interval. • They were comparable and sometimes better than Fieller's and Hinkley's intervals. We found that Hinkley's method, which has not been adopted for the ICER, was similar to Fieller's method in terms of coverage accuracy and interval length. • Intervals based on G3 transformation were comparable to the boott in terms of coverage but were about one third narrower.

  38. Conclusions on NHB • For the NHB, we saw that intervals based on the G3 transformation gave good coverages in all cases considered and were comparable to the boott. However, our intervals were narrower than the boott and required less computing in terms of bootstrap resampling. • When dealing with highly skewed data, our intervals based on the G3 transformation should be recommended. • The remaining question is what one should choose between the ICER and the NHB. • Each measure has its own advantages as well as disadvantages. We leave it to the readers to decide which measure is more appropriate for their purposes.

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