Rearrangement of Table 2
 
Treatments being compared in the cost effectiveness assessment
Undiscounted event rate with the first treatment
(A) 
Relative risk of the second treatment v placebo (B) 
Undiscounted absolute event rate with the second treatment (C=A´B)
Discounted absolute event rate with the first treatment (D)*
Discounted absolute event rate with the second treatment (E)*
Undiscounted absolute gain in the event rate (column (F=A- C) 
Discounted absolute gain in the event rate 
(G=D-E)
Discounted cost per patient with the first treatment (£) (H) *
Discounted cost per patient with the second treatment (£) (I)*
Discounted cost effectiveness ratio(pounds per event averted) (J=(I- H)/G)
Placebo v aspirin
0.1
0.75
0.075
0.09272
0.06954
0.025
0.02318
0
85 3667
Aspirin v aspirin+diuretic and b blocker
0.075
0.83
0.06225
0.06954
0.05772
0.01275
0.01182
85
228 12 096
Aspirin+diuretic and b blocker v aspirin+diuretic and b blocker+enalapril
0.06225
0.81
0.05042
0.05772
0.04675
0.01183
0.01097
228
602 34 103
Aspirin+diuretic and b blocker v aspirin+diuretic and b blocker+enalapril v Aspirin+diuretic and b blocker v aspirin+diuretic and b blocker+enalapril +statin
0.05042
0.69
0.03479
0.04675
0.03226
0.01563
0.01449
602
2385 123 022

*Discount rates are 6% per year for costs and 1.5% per year for benefits. All event rates (normalised to 1 patient) and all costs (normalised to 1 patient) are at five years.

Each value of the relative risk refers to adjunctive drug (considered in each individual row of table) v placebo. Contradiction arises because relative risks (obtained from either clinical studies or meta-analyses) compare drug under examination (adjunctive drug) with placebo, whereas cost effectiveness assessment in same row compares combination with absence of adjunctive drug v combination with presence of adjunctive drug (with no comparison v placebo). Hence, comparators in relative risk assessment (adjunctive drug v placebo) differ from those used for cost effectiveness comparison (absence v presence of adjunctive drug). Contradiction is only apparent because relative risks are applied in a chain of subsequent multiplications throughout the table. For example, if cost effectiveness comparison of aspirin v aspirin+diuretic and b blocker appears with relative risk of placebo v diuretic and b blocker (RR=0.83), there is no error because relative risk of aspirin v placebo (RR=0.75) has already been incorporated as multiplicative factor in previous row and its presence affects all subsequent rows (including comparison of aspirin v aspirin+diuretic and b blocker).
 




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