Another component of cost-benefit analysis includes Quality-Adjusted Life Years (QALYs); the extra dollar cost of providing one additional year of life expectancy for evaluating health programs.

Equation:

FV=PV (1+r)i where FV = future value, PV = present value

r = the interest rate

n = the number of time periods into the future

If you want instead to calculate how much money you would need today (present value) to achieve a particular future value (say $100 in five years), the equation can be rearranged:

PV = FV/(1 = r)ⁿ

Case Study: Patient BN is a 36-year-old female with a type of organ failure that reduces her quality of life to half of what it would be in good health. Without treatment she can expect to live only two years. With a successful transplant, BN can expect to live four years and have a quality of life that is near (80 percent) of what she would enjoy in good health. However, the transplant costs $100,000, plus $10,000 each year for drugs and follow-up care, and carries a 15 percent risk of rejection resulting in immediate death. What is the cost per additional year of life gained (without discounting for time or quality of life)? What is the cost per discounted QALY gained (assuming a 5 percent time discount rate)?

The three key parts to this evaluation are the risk of death, the adjustment to quality of life, and discounting for time. The calculations below follow Table 2.5 in the text.

	Year 1		Year 2		Year 3	Year 4	Total
Time discount factor (at 5%)	1.00		0.952		0.907	0.864
Baseline (2 year survival)
Quality of life	0.5		0.5		(death)	(death)	(1.00 QALY)
Discounted value	0.5		0.48		0	0	0.98 QALY
Successful transplant (4 year survival)
Quality of life	0.8		0.8		0.8	0.8	(3.20 QALY)
Discounted value	0.8		0.76		0.73	0.69	2.98 QALY
Annual cost of care	$10,000		$10,000		$10,000	$10,000	$40,000
Discounted value	$10,000		$9,520		$9,070	$8,640	$37,230
CALCULTED FROM TABLE ABOVE (*Use this data below to calculate the 2 questions related to Cost per Qualy Gained). Initial cost of surgery = $100,000 Surgical mortality = 15% (i.e., 85% realize successful transplant life expectancy, 15% lose the baseline life expectancy)
Unadjusted for quality or time				= [0.85*(4.0) + 0.15*(0.0)] - 2.0 = 1.4
Discounted for Quality only Discounted for QALY and time				= [0.85*(3.2) + 0.15*(0.0)] - 0.98 = 1.7 = [0.85*(2.98) + 0.15*(0.0)] - 0.98 = 1.55
Undiscounted cost				= 0.85($140,000) + 0.15($100,000) = $134,000
Time Discounted cost				= 0.85($137,200) + 0.15($100,000) = $131,620

Answers the following questions

(*You are using the data above to answer the following questions)

2.a. Cost per QUALY gained Undiscounted:

2.b. Cost per QUALY gained Discounted: