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The Cost-effectiveness The Cost-effectiveness AnalysisAnalysis
Introduction/MotivationIntroduction/Motivation Two measures in a cost-effectiveness Two measures in a cost-effectiveness
analysisanalysis
ScenarioScenario You are the pharmacy director for a 1.5 million You are the pharmacy director for a 1.5 million
member health insurance organization. The detail member health insurance organization. The detail person from Merp Inc. comes calling with news that person from Merp Inc. comes calling with news that their new pain relief drug “Arafex” has just been their new pain relief drug “Arafex” has just been approved for persons with osteoarthritis. It’s reported approved for persons with osteoarthritis. It’s reported benefits are lower incidence of GI bleeding and (an benefits are lower incidence of GI bleeding and (an unexpected outcome of the clinical trial) an apparent unexpected outcome of the clinical trial) an apparent modest improvement in LDL cholesterol. Given these modest improvement in LDL cholesterol. Given these purported benefits, the detail person states that at purported benefits, the detail person states that at the price, Arafex “blows away” the other Cox II the price, Arafex “blows away” the other Cox II inhibitor products, such as celecoxib and rofecoxibinhibitor products, such as celecoxib and rofecoxib
The cost of Arafex is $95 per 30 day supplyThe cost of Arafex is $95 per 30 day supply The cost of celecoxib is $82The cost of celecoxib is $82 The cost of rofecoxib is $74The cost of rofecoxib is $74 Question: Should you add Arafex to the formularyQuestion: Should you add Arafex to the formulary
(Taken from S. Ramsey)
IntroductionIntroduction
Scarcity of resourcesScarcity of resources Choices need to be madeChoices need to be made Decision need to be made based Decision need to be made based
costs and effectscosts and effects Cost-effectiveness analysis (CEA) is a Cost-effectiveness analysis (CEA) is a
way to mingle way to mingle costcost and and effectivenesseffectiveness of a study of a study
Examples Of Effectiveness Examples Of Effectiveness Measures Used In Cost-Measures Used In Cost-effectiveness Analyseseffectiveness Analyses
Study Reference
Clinical Field
Effectiveness measure
Logan et al. (1981) Treatment of hypertension MmHg blood pressure reduction
Schulman et al. (1990) Treatment of hypercholesterolaemia
% serum cholesterol reduction
Hull et al. (1981) Diagnosis of deep vein thrombosis
Cases of DVT detected
Sculpher and Buxton (1993)
Asthma Episode-free days
Mark et al (1995) Thrombosis Years of life gained
Two Commonly Used Two Commonly Used StatisticsStatistics
Incremental cost-effectiveness ratio Incremental cost-effectiveness ratio (ICER):(ICER):
Net health benefit (NHB):Net health benefit (NHB):
Where Where λλ=Willingness to pay=Willingness to pay
01
01
ee
ccICER
0101
1cceeNHB
0 treatmentofeffect avg.
1 treatmentofeffect avg.
0 treatmentofcost avg.
1 treatmentofcost avg.
0
1
0
1
c
e
c
c
Graphical RepresentationGraphical Representation
01 cc
01 ee
The ΔE- ΔC plane
Graphical RepresentationGraphical Representation
001 cc
01 cc
001 ee
The ΔE- ΔC plane
01 ee
Slope = ICER
Graphical RepresentationGraphical Representation
001 cc
01 cc
001 ee
The ΔE- ΔC plane
01 ee
Graphical RepresentationGraphical Representation
001 cc
01 cc
001 ee
The ΔE- ΔC plane
01 ee
001 cc
001 ee
Graphical RepresentationGraphical Representation0
01 cc
01 cc 0
01 ee
The ΔE- ΔC plane
01 ee
Slope=λ=30,000
ICER=50,000
EstimationEstimation Incremental cost-effectiveness ratio Incremental cost-effectiveness ratio
(ICER):(ICER):
Net health benefit (NHB):Net health benefit (NHB):
01
01ˆEE
CCREIC
01011ˆ CCEEBHN
PropertiesPropertiesICER NHBICER NHB
Natural interpretation Natural interpretation (price/unit of product)(price/unit of product)
Analysis independent Analysis independent of of λλ
Economic foundationEconomic foundation
Negative ICER is Negative ICER is problematicproblematic
Undefined value Undefined value possible for CIspossible for CIs
Biased, not sufficientBiased, not sufficient
NHB properly orderedNHB properly ordered Interpretation is not Interpretation is not
ambiguous like ambiguous like negative ICERnegative ICER
UnbiasedUnbiased Easy extension to Easy extension to
more than two more than two comparatorscomparators
Dependent on λDependent on λ No natural No natural
interpretationinterpretation
Inference: Existing Inference: Existing TechniquesTechniques ICER NHB ICER NHB Normal theory via Normal theory via
CLTCLT BootstrapBootstrap Confidence box Confidence box Fieller’s method Fieller’s method
(1954)(1954) Hinkley’s method Hinkley’s method
(1969)(1969)
Normal theory via Normal theory via CLTCLT
BootstrapBootstrap
Inference: Existing TechniquesInference: Existing TechniquesConfidence BoxConfidence Box
01 cc
The ΔE- ΔC plane
01 ee
Inference: Existing Inference: Existing TechniquesTechniques
Fieller’s method (1954):Fieller’s method (1954):
The C.I. can be obtained by equating the The C.I. can be obtained by equating the formula and solve for R:formula and solve for R:
)1,0(~)r(av
NERC
ERC
ICERR
2/1)r(av
z
ERC
ERC
Inference: Existing Inference: Existing TechniquesTechniques
Hinkley’s method (1969):Hinkley’s method (1969): Distribution of ratio of two correlated random Distribution of ratio of two correlated random
normal variablesnormal variables Can be applied to the ICER if we assume the Can be applied to the ICER if we assume the
numerator and the denominator of the ICER numerator and the denominator of the ICER are bivariate normalare bivariate normal
Has not been applied to inference for the Has not been applied to inference for the ICERICER
Previous StudiesPrevious Studies
Briggs, et al. (1999)Briggs, et al. (1999) CLT-based (Taylor’s), Fieller’s, CLT-based (Taylor’s), Fieller’s,
confidence box, bootstrap (normal confidence box, bootstrap (normal approximation, percentile, BC, BCa, approximation, percentile, BC, BCa, parametric bootstrap)parametric bootstrap)
Conclusion: Fieller’s appears best; Conclusion: Fieller’s appears best; parametric bootstrap and BCa are best parametric bootstrap and BCa are best among the bootstrap methodsamong the bootstrap methods
Previous StudiesPrevious Studies
Fan & Zhou (Outcome Research Fan & Zhou (Outcome Research Methodology, 2006)Methodology, 2006) CLT-based (Taylor’s), Fieller’s, confidence CLT-based (Taylor’s), Fieller’s, confidence
box, bootstrap (normal approximation, box, bootstrap (normal approximation, percentile, bootstrap-t, BCa, parametric percentile, bootstrap-t, BCa, parametric bootstrap)bootstrap)
Conclusion: nonparametric bootstrap-t is best Conclusion: nonparametric bootstrap-t is best in term of coverage accuracy; next are the in term of coverage accuracy; next are the Fieller’s and among the bootstrap methods, Fieller’s and among the bootstrap methods, parametric bootstrap and BCa are bestparametric bootstrap and BCa are best
Limitation of Existing Limitation of Existing TechniquesTechniques
CLT-based: may not be appropriate for small CLT-based: may not be appropriate for small sample skewed-data (Briggs, 1999; Fan & sample skewed-data (Briggs, 1999; Fan & Zhou, 2006)Zhou, 2006)
Bootstrap: may be time-consuming, may not Bootstrap: may be time-consuming, may not provide proper coverage (Fan & Zhou, 2005)provide proper coverage (Fan & Zhou, 2005)
Confidence box: does not provide proper Confidence box: does not provide proper coverage (Briggs, et al, 1999)coverage (Briggs, et al, 1999)
Fieller’s and Hinkley’s: based on bivariate Fieller’s and Hinkley’s: based on bivariate normal, Fieller’s may not be closed intervalnormal, Fieller’s may not be closed interval
Inference: Alternative Inference: Alternative ApproachApproach
Purpose:Purpose: To explain what play a role in the To explain what play a role in the
normal approximationnormal approximation To help improve inferenceTo help improve inference
Edgeworth Expansion: NHBEdgeworth Expansion: NHB
NHB: LetNHB: Let
where,where,
22 ˆ
ˆ
NHBBHN
T
12
2/12 )()()()( NOxxqNxxTP
3
2222
2
3
1111
1
2
21
12
221
2/32
2
,
),var(
,)1(
1),12(
6)(
EC
EPEC
EP
TAsympQ
nn
nPP
QAx
Axq
EC
EC
Edgeworth Expansion: ICEREdgeworth Expansion: ICER ICER: LetICER: Let
wherewhere
AA11 and A and A22 depends on the asymptotic depends on the asymptotic variance of Tvariance of T11 and skewness of costs and and skewness of costs and effectseffects
11
2/11 )()()()( NOxxqNxxTP
11 ˆ
ˆ
ICERREIC
T
)1(
6
64)( 221
211 xAA
AAxq
Edgeworth Expansion for ICER Edgeworth Expansion for ICER and NHBand NHB
ICER:ICER:
NHB:NHB:
N
OxxqN
xxTP1
)()(1
)()( 11
N
OxxqN
xxTP1
)()(1
)()( 22
Alternative Confidence Alternative Confidence IntervalsIntervals
Similar to the two-sample problem, we can Similar to the two-sample problem, we can introduce three new transformational introduce three new transformational intervalsintervals
3. 2, 1,ifor
,ˆ)(ˆ
ˆ)(ˆ
2/2/112/1
02/12/112/1
zNhN
zNhN
i
i
SimulationSimulation Bivariate normalBivariate normal
Bivariate lognormalBivariate lognormal
Bivariate mixtureBivariate mixture
Simulation: ICERSimulation: ICERCoverage of 95% Confidence Coverage of 95% Confidence
intervalsintervalsNormal Fieller Hinkley Boot-t New1 New2 New3
.8556(247.53)
.9037(266.87)
.9037(265.69)
.9030(385.72)
.8961(363.12)
.8609(244.59)
.8944(245.40)
.8583(111.36)
.8636(116.91)
.8636(116.90)
.8956(170.36)
.8731(136.81)
.8637(110.53)
.8937(110.10)
.8520(242.38)
.8980(256.34)
.8979(256.30)
.9059(394.79)
.8957(355.36)
.8557(239.85)
.8829(238.10)
.8875(183.21)
.9171(190.09)
.9172(190.27)
.9171(243.31)
.9084(244.94)
.8924(181.59)
.9175(181.67)
Simulation: NHBSimulation: NHB Coverage of 95% Confidence intervalsCoverage of 95% Confidence intervals
Normal Boot-t BCa New1 New2 New3
0.9025 (60.88)
0.9262 (76.77)
0.9052(64.40)
0.8767 (85.87)
0.8971 (61.06)
0.9355(64.61)
0.8965(61.05)
0.9229 (77.24)
0.9027(64.57)
0.8704 (86.23)
0.8913 (61.23)
0.9304 (64.79)
0.8930(60.21)
0.9272(77.03)
0.9021(63.85)
0.8621(86.55)
0.8864(60.35)
0.9204(62.35)
0.9192 (45.55)
0.9269 (52.50)
0.9142(47.51)
0.9008 (57.61)
0.9159 (45.63)
0.9388 (47.29)
SimulationSimulation The modelThe model
Specify Specify λλ, , ββ, , γγ Generate X ~ uniformGenerate X ~ uniform εε ~ normal(0, 1) ~ normal(0, 1) gg22(Z(Zii, , γγ) = exp(Z) = exp(Zii
TTγγ)) Objective: estimate E(Y|xObjective: estimate E(Y|x00))
iiTii ZgXyh );();(
SimulationSimulationnn λλ CoveragCoverag
ee
95% CI.95% CI.
5050 11 1616 15.9315.93 0.9480.948
5050 .5.5 72.9372.93 72.0472.04 0.9270.927
200200 .5.5 72.9372.93 72.5572.55 0.8940.894
20002000 .5.5 72.9372.93 72.7972.79 0.9480.948
5050 .2.2 1094.1094.33
1011.1011.99
0.8440.844
200200 .2.2 1094.1094.33
1040.1040.88
0.8310.831
20002000 .2.2 1094.1094.33
1081.1081.77
0.9350.935
)|( 0xYE )|(ˆ0xYE
Application to a real Application to a real exampleexample
IN 2002, Katon et al. (2002) conducted a randomized IN 2002, Katon et al. (2002) conducted a randomized trial to evaluate the cost effectiveness of a trial to evaluate the cost effectiveness of a collaborative care intervention, compared to the collaborative care intervention, compared to the usual primary care setting, in patients with panic usual primary care setting, in patients with panic disorder. disorder.
Panic disorder occurs in 4–6% of patients in primary Panic disorder occurs in 4–6% of patients in primary care. This severe anxiety disorder is associated with care. This severe anxiety disorder is associated with high use of medical services, high costs, and a high use of medical services, high costs, and a variety of unexplained medical symptoms. variety of unexplained medical symptoms.
Patients with panic disorder often do not receive an Patients with panic disorder often do not receive an accurate diagnosis in primary care and even when accurate diagnosis in primary care and even when diagnosis is assigned, few patients receive diagnosis is assigned, few patients receive appropriate treatment or psychotherapy (Katon et appropriate treatment or psychotherapy (Katon et al., 2002). al., 2002).
Application to real example, Application to real example, contcont
One objective of the study is to determine One objective of the study is to determine the incremental cost effectiveness of a the incremental cost effectiveness of a collaborative care program for primary care collaborative care program for primary care patients with panic disorder compared with patients with panic disorder compared with the usual primary care setting.the usual primary care setting.
To demonstrate our methods, we consider To demonstrate our methods, we consider total outpatient nonmental health costs, and total outpatient nonmental health costs, and for measure of effectiveness, we consider for measure of effectiveness, we consider the number of days a patient experiences the number of days a patient experiences panic disorder during the 1-year study panic disorder during the 1-year study period. period.
The summary statisticsThe summary statistics
Estimated ICER = 15.33, NHB = 77.08Estimated ICER = 15.33, NHB = 77.08 Control group (Control group (nn1 = 54) Intervention group (1 = 54) Intervention group (nn2 = 53) 2 = 53)
Mean SD Skewness Mean SD Mean SD Skewness Mean SD
SkewnessSkewness Cost(U.S.$) 2507.42 4460.44 4.93 1325.48 1785.67 3.46Cost(U.S.$) 2507.42 4460.44 4.93 1325.48 1785.67 3.46 Effectiveness (days with anxiety attack) Effectiveness (days with anxiety attack) 211.52 139.68 −0.30 134.42 134.55 0.71211.52 139.68 −0.30 134.42 134.55 0.71
Application, contApplication, cont
Costs in both groups are highly skewed Costs in both groups are highly skewed with the coefficient of skewness 4.93 for with the coefficient of skewness 4.93 for the control group and 3.46 for the the control group and 3.46 for the intervention group. intervention group.
On average, the control group incurred On average, the control group incurred $1181.95 and 77.1 days of panic attack $1181.95 and 77.1 days of panic attack more than the intervention group. more than the intervention group.
The estimated ICER is 15.33, indicating The estimated ICER is 15.33, indicating that the intervention arm is dominant. that the intervention arm is dominant.
confidence intervals for the ICER and the confidence intervals for the ICER and the NHBNHB
Methods Confidence intervals Interval lengthMethods Confidence intervals Interval length ICER Taylor's (−3.44, 34.10) 37.54 ICER Taylor's (−3.44, 34.10) 37.54 Fieller's (−1.43, 53.86) 55.28 Fieller's (−1.43, 53.86) 55.28 Hinkley's (−1.68, 52.44) 54.12 Hinkley's (−1.68, 52.44) 54.12 Bootstrap-Bootstrap-tt (4.50, 49.55) 45.05 (4.50, 49.55) 45.05 GG1 (3.33, 81.87) 78.54 1 (3.33, 81.87) 78.54 GG2 (−1.99, 35.22) 37.21 2 (−1.99, 35.22) 37.21 GG3 (0.35, 38.38) 38.033 (0.35, 38.38) 38.03 NHB Taylor's (25.12, 129.03) 103.92 NHB Taylor's (25.12, 129.03) 103.92 Bootstrap-Bootstrap-tt (21.68, 132.33) 110.65 (21.68, 132.33) 110.65 BCa (20.21, 125.52) 105.31 BCa (20.21, 125.52) 105.31 GG1 (26.78, 130.87) 104.10 1 (26.78, 130.87) 104.10 GG2 (25.46, 129.39) 103.92 2 (25.46, 129.39) 103.92 GG3 (32.84, 144.42) 111.58 3 (32.84, 144.42) 111.58
Results, contResults, cont
Both bootstrap-Both bootstrap-tt and and GG3 intervals are positive, 3 intervals are positive, showing that the intervention is significantly showing that the intervention is significantly dominant (the control group incurred more dominant (the control group incurred more cost and more days of panic disorder). cost and more days of panic disorder).
As anticipated, both Fieller's and Hinkley's As anticipated, both Fieller's and Hinkley's intervals are similar and the intervals are similar and the GG3 interval has 3 interval has shorter length than bootstrap-shorter length than bootstrap-tt. .
Because the estimated qBecause the estimated q11/sqrt(N)=0.9 , /sqrt(N)=0.9 , Taylor's interval is inadequate. Based on our Taylor's interval is inadequate. Based on our simulation results, we would recommend simulation results, we would recommend using the using the GG3 interval as the confidence 3 interval as the confidence interval for the ICER. interval for the ICER.
A common willingness-to-pay is λ = $50,000; A common willingness-to-pay is λ = $50,000; using this value, the estimated NHB is 77.08. using this value, the estimated NHB is 77.08.
Confidence intervals for the NHB are Confidence intervals for the NHB are presented in Table 6. All intervals are presented in Table 6. All intervals are relatively similar, especially relatively similar, especially GG1, 1, GG2, and 2, and Taylor's intervals. The coefficient qTaylor's intervals. The coefficient q22/sqrt(N) is /sqrt(N) is 0.05 in this setting, suggesting that Taylor's 0.05 in this setting, suggesting that Taylor's interval is adequate. interval is adequate.
All of these confidence intervals are strictly All of these confidence intervals are strictly positive indicating, again, that the positive indicating, again, that the intervention arm is cost effective.intervention arm is cost effective.
Conclusions on ICERConclusions on ICER
For the ICER, when data were generated from a For the ICER, when data were generated from a skewed distribution, our new intervals gave skewed distribution, our new intervals gave better coverages than Taylor's interval. better coverages than Taylor's interval.
They were comparable and sometimes better They were comparable and sometimes better than Fieller's and Hinkley's intervals. We found than Fieller's and Hinkley's intervals. We found that Hinkley's method, which has not been that Hinkley's method, which has not been adopted for the ICER, was similar to Fieller's adopted for the ICER, was similar to Fieller's method in terms of coverage accuracy and method in terms of coverage accuracy and interval length. interval length.
Intervals based on Intervals based on GG3 transformation were 3 transformation were comparable to the boott in terms of coverage but comparable to the boott in terms of coverage but were about one third narrower.were about one third narrower.
Conclusions on NHBConclusions on NHB
For the NHB, we saw that intervals based on the For the NHB, we saw that intervals based on the GG3 3 transformation gave good coverages in all cases transformation gave good coverages in all cases considered and were comparable to the boott. considered and were comparable to the boott. However, our intervals were narrower than the boott However, our intervals were narrower than the boott and required less computing in terms of bootstrap and required less computing in terms of bootstrap resampling.resampling.
When dealing with highly skewed data, our intervals When dealing with highly skewed data, our intervals based on the based on the GG3 transformation should be 3 transformation should be recommended.recommended.
The remaining question is what one should choose The remaining question is what one should choose between the ICER and the NHB. between the ICER and the NHB.
Each measure has its own advantages as well as Each measure has its own advantages as well as disadvantages. We leave it to the readers to decide disadvantages. We leave it to the readers to decide which measure is more appropriate for their purposes.which measure is more appropriate for their purposes.