2. Discounting and the Time Trade Off Method: (Refer to the lecture notes for Lectures 10 and 11 for information on how to interpret the parameters in this question .) Consider a Time Trade Off where the health state to be evaluated is H, the discount rate r = 5%/year , A = 10 years and the point of indifference is at B = 3 years. The temporary state for which QALY is known, S, is 'Heartburn', which has a QALY value of 0.82. Given the above information , calculate the QALY value of H by comparing Option 1: A years in health state S, to : i. Option 2: B years in state H, followed by (A - B) years of full health . The value of Option 1, A years in health state S, is S S 0?17? 1 = S + 1+r (1 + r) 2 + 7 ( 1 + r ) ?-1 The 'A 1' is because we don't discount the first year . For our values , 0.82 0.82 0.82 071177 1 = 0.82 + 1 + 0.05 (1 + 0.05)2 + (1 + 0.05)9 = 6.65 Since full health has QALY = 1, the value of Option 2, B years in state H followed by (A - B) years of full health , is 1 ?-1 ?-1 H 1 07117? 2 = [ (1 + r) t (1 + r) * 1=0 For our values , 2 H H 071177 2 = E (1 + 0.05): 2 (1 + 0.05) (1 + 0.05), + 5.25 1=0 1=3 1=0 If the user is indifferent between the two options, then Option 1 = Option 2. We can use trial and error to change H until Option 2 and Option 1 are equal to each other (see companion spreadsheet). It is possible to use more advanced techniques than trial and error to find this value , but those techniques are beyond the scope of this course Solving , H = 0.49