Stochastic cost-effectiveness
analysis
 Cost-effectiveness planes
 Cost-effectiveness ratio confidence
intervals
 Cost-effectiveness acceptability
 Net benefit approach
 The relevance of inference?
(-) Difference in costs (+)
Cost-effectiveness plane
Treatment
dominated
Costeffectiveness
ratio
Costeffectiveness
ratio
Treatment
dominates
(-) Difference in effects (+)
Cost-effectiveness plane
(-) Difference in costs (+)
CER
(-) Difference in effects (+)
CER = Cost-effectiveness Ratio
CER confidence intervals
CER confidence intervals
Problems
 Independent cost and effect confidence
intervals may give too wide an overall
confidence interval
 The probability distribution of a ratio of two
random variables does not have a known
distribution
 The ratio has discontinuities at the
boundaries between different quadrants
Some solutions
 The “box” method – separate distributions
 The “ellipse” method – joint distributions
 Fieller’s theorem
 Bootstrapping
Cost-effectiveness acceptability
Cost-effectiveness decision rule
ICER= C/E
Compare with “ceiling ratio” = Rc
If Rc > C/E, treatment is cost-effective
Rc can also be interpreted as the costeffectiveness threshold or the willingness to
pay for a unit of health effect
Cost-effectiveness acceptability
(-) Difference in costs (+)
At Rc, treatment
unacceptable
Treatment
never
acceptable
At Rc, treatment
acceptable
At Rc, treatment
unacceptable
Treatment
always
acceptable
At Rc, treatment
acceptable
(-) Difference in effects (+)
Cost-effectiveness acceptability
(-) Difference in costs (+)
Different thresholds for gains and losses in health
Treatment
acceptable
Treatment
acceptable
(-) Difference in effects (+)
Cost-effectiveness acceptability
Calculate the proportion of the distribution (P)
which lies below the line defining a particular
ceiling ratio (Rc)
Cost-effectiveness acceptability
Rc1, P1
(-) Difference in costs (+)
Rc2, P2
Rc3, P3
(-) Difference in effects (+)
Calculate Pi for each level of Rci
Cost-effectiveness acceptability
Cost-Effectiveness Acceptability Curve (CEAC)
Proportion acceptable
1.00
0.50
0.00
£3,000
£15,000
Ceiling ratio
£30,000
The Net Benefit Approach
ICER= C/E
where C is in £ and E is not
Net benefit = E - C
where C and E are in the same units
Rc can be used to convert costs to the same
units as effects, or effects to the same units as
costs:
Monetary net benefit (MNB):
MNB = Rc *E - C
Health net benefit (HNB):
HNB = E - C/Rc
The Net Benefit Approach
Cost-effectiveness decision rule
If Rc > C/E, treatment is cost-effective
Net benefits decision rule
Monetary net benefit:
If Rc *E - C > 0, treatment is cost-effective
Health net benefit:
If E - C/Rc > 0, treatment is cost-effective
Net Monetary Benefit Curve
Net Monetary Benefit
£30,000
£0
-£30,000
0
£15,000
Ceiling ratio
£30,000
The relevance of inference?
 Inference about CERs may lead to different
conclusions than inference about costs and
effects
 Are decisions based on statistical
significance perverse?
 Is quantifying uncertainty useful to decision
makers?
 Expected value of information