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Decision and Cost-Effectiveness Analysis

Elective, Training in Clinical Research

UCSF Department of Epidemiology and Biostatistics EPI 213

Jan-Feb 2004

ATCR DCEA Lecture 2, January 13, 2004, Dr. Caughey / substitute:
Decision Analysis: Utilities and QALYs

PRIVATE Objectives:tc  \l 1 "Objectives"

·                    To understand techniques to measure utilities

·                    seq level0 \h \r0 seq level1 \h \r0 seq level2 \h \r0 seq level3 \h \r0 seq level4 \h \r0 seq level5 \h \r0 seq level6 \h \r0 seq level7 \h \r0 To understand how to calculate Quality-Adjusted Life Years

·                    To understand discounting


Shlipak MG, Chapter 2. Decision Analysis, in Friedland DJ et al Evidence-Based Medicine: A Framework for Clinical Practice. Appleton & Lange, 1998.

In the last lecture, we introduced decision analysis and went through the steps of making a decision tree. In this lecture, we’ll move on to some important refinements in DA. The topics are

1. Utilities/utility measurement

2. Quality-adjusted life years

3. Discounting

1. Utilities and utility measurment

Utility is a quantitative measure of the strength of a patient’s preference for a particular state of health, or outcome.

In other words, how do we value our health compared with other potential states of health?


Disability from a stroke

stable exertional angina

chronic pain

Why do this quantitatively?

Let’s return to aneurysm example. There are two parts of the analysis that require good utility assessments.

            As discussed, clipping surgery can cause disability. The quality of life depends on the severity of the disability – mild vs. moderate/severe.

            Also, being at risk of an aneurysm rupture can cause anxiety that reduces quality of life, and hence reduces the utility of being in the at-risk state. Considering this factor makes the no surgery arm less attractive. This anxiety does not affect the surgery arm; clipping reduces risk to zero, and thus is assumed to reduce the anxiety to zero.

            We’ll return to how these utilities are assessed at the end of the lecture.

How do you decide what the utility of health states is?

3 common methods used for estimating utilities:

Visual analog scale/Interval scaling


Standard Gamble


Time trade-off



To illustrate these methods, consider the following clinical scenario:

            A patient in the hospital has a serious infection of the lower leg.  The surgeon advises a below-the-knee amputation (BKA), rather than medical management. The reason she gives is that the infection has about a 20% chance of spreading further up the leg, and an 80% chance of being cured, with medical management. If the infection spreads, the procedure would have to be an above-the-knee amputation (AKA), a more serious procedure. The chance of dying is about 10% if the infection were to spread; the mortality from a BKA is only 1%. Which option (BKA or medical management) is better? It turns out the right answer depends on how the patient values living with a BKA versus with an AKA.

Visual analog scale:

This method uses a simple linear scale to determine a patient’s relative preferences. (It’s basically a ruler.)

(death 0-----------------------------1.0 cure)

                                    Where is the AKA?

(AKA--------------------------------1.0 cure)

                                    Where is the BKA?



Easy to understand



May bias values to the middle.

Seems disconnected from medical reality.

Standard Gamble:

Method of utility assessment that forces patients to choose between

a.                  a certain outcome

b.                  a gamble to achieve a better outcome while risking ending up with a worse outcome

Sort of like the old game show, “Lets make a deal.”

How it works:

Choice A: You live with a BKA

Choice B: Take a chance – you might have a cure; you might die.

Which do you choose? Doesn’t it depend on the likelihood of cure vs. death? What risk of death would you accept to avoid living with the BKA? How does this lead us to the utility?

Remember the concept expected utility. If you cannot decide between the 2 choices, then your expected utility is the same for both (Choice A = Choice B).  The choice is represented like this:

Steps in the Standard Gamble.

(The other methods have steps too; we show standard gamble because it’s the most complicated.)

Ask the “subject” to

1. Rank the 3 outcomes (perfect health, BKA, death).


2. Imagine that they have the intermediate outcome (BKA); you provide details about limitations on mobility, etc.

Tell the subject that

3. You are doing this to try to determine the relative value they place on living with this intermediate state (BKA), by comparison with the best (perfect health) and the worst (death).


4. There is a procedure (or pill, or test) that has the possibility of restoring them to perfect health (or whatever the best outcome is). However, there is a down side to this procedure. Sometimes, it results in death (or whatever the worst outcome is).

Then determine “100- p.”

5. “I’m now going to ask you what chance of dying you would be willing to take with this procedure. Remember, if it works, you will be restored to perfect health.”

6. Approach it from the bottom (“Would you be willing to take a one in a million chance of dying?”) and from the top (“...a 1 in 2 chance of dying?”). Keep narrowing: a one in 10,000 chance? a 1 in 5 chance? until you arrive at the point where the subject has a hard time deciding.

7. Verify by re-phrasing to determine p  (“...a 999,999 in a million chance of living through the surgery?”; “ ...a 1 in 2 chance of living?”, etc.)

Once you find the probability “p” of cure at which A = B, then from the equating of expected utility value

Utility (BKA) x Probability (BKA) = Utility(cure) x (p) + Utility(death) x (1-p)

you can demonstrate that the utility of BKA = p:

Utility (BKA)    = [Utility(cure) x (p) + Utility(death) x (1-p)] / Probability (BKA)

                        = [1.0 * p + 0 * (1-p)] / 1.0 = p


Reflects the uncertainty of the future.

Portrays the element of risk.


Hard for some people to understand, especially those who have never gambled.

Involves a math equation.

Time Trade-off:

This method of utility assessment involves trading off the quality of life vs. length of time alive.

Simple concept:

Time A * Utility A = Time B * Utility B

So, let’s say you have a life expectancy of 30 years of life with a BKA; how much time would you give-up to live in your current state?

Would you give up 5 years? 3 years? 1 year?


30 years * Utility (BKA) = (30-x) years * 1.0


If you’re willing to give up 3 years, that means the utility of BKA is 0.9 [= (30-3)/ 30].




Portrays long-term outcomes.

Easy to understand.

Helpful for portraying chronic diseases.


Does not reflect the element of risk.

Makes all years in the future appear to be equal.

Final thoughts on Utilities:

1.                   Very subjective. To some extent this is desirable – capturing patient preferences even if apparently nonrational. But some subjectivity represents measurement problems (the methods may yield inconsistent results with no “gold standard”, and are hard to standardize). Research to improve measurement is ongoing.

2.                   Important to realize that the utilities can change over time.

3.                   It really matters who is deriving the utility. In some situations the patient should, and their rankings  will depend on who they are. For example, for BKA -- teenagers, vascular surgeons, patients, professional athletes. Some economists say society should decide utility values, which may overstate disutility (eg, people living with AIDS rate their quality of life as higher than those in society contemplating living with AIDS).

2. Quality-adjusted life-years:

What does this term mean? What’s a Quality-Adjusted Life Year (QALY)? It’s really pretty straightforward:

QALY(s) = Year(s) * Quality (i.e., utility)

Example: 2 years * 0.9 utility = 1.8 QALYs.

Another example:


Patient A

Patient B






















QALYs = 3.6


QALYs = 3.6

Are QALYs better than Life Years?

Given how subjective utilities are, how does measuring QALYs help? It represents the best estimate of the quality of life. To not use QALYs ignores the obvious differences in the desirability of different health states. Utility assessments and QALYs, though imperfect, begin to quantify these differences.

For the aneurysm example, there are no definitive published studies for the health states with disutility* (disability due to brain surgery and anxiety due to risk of rupture). Nor were there resources to conduct utility assessments (these studies are expensive!).  So another approach was used: applying the most relevant estimates from the literature.

        Gage and colleagues used time tradeoff and standard gamble methods to obtain utility valuations for permanent disability states after stroke for 83 patients with atrial fibrillation (Gage 96). Utility for mild strokes was 0.76, and for moderate and major strokes averaged 0.25. Since these two levels of disability occur with equal frequency after surgery, the tree uses 0.50 as the utility. The risk of death is 3-fold higher with disability (Strauss 98), so we lowered life expectancy by 2/3. Thus, QALYs are reduced by 83% (50% reduction for disutility; a further 67% reduction for shorter life).

Thus, with QALYs substituted for utilities (but not yet portraying worry), the tree looks like below. Note that the disability branch reflects decreases due to lower utility and lower life expectancy. Other branches have utility = 1.0; differences in QALYs reflect unequal life years.

Here’s how worry is incorporated:

Prior cost-effectiveness analyses of aneurysm treatment assumed that untreated patients would be burdened by concern that their aneurysm could rupture, and estimated a utility of 0.95 (Kallmes 98, King 95). This burden should depend on rupture rates, so we assumed that the utility for untreated patients would vary with the rupture rates as follows: RU = 1 – 5 * (Rupture rate). The factor 5 is an estimate of the emotional dimension of living with a low-risk, high consequence condition (Gage 96). For an aneurysm with 1% yearly rupture rate, this reproduces the prior estimate of 0.95 and is similar to the mildly impaired emotional state (“occasionally fretful, angry, irritable, anxious, depressed, or suffering” = 0.93) in the Health Utilities Index Mark 2 (Torrance 96). For an aneurysm with 0.05% yearly rupture rate (our example), the formula produces a utility of 0.9975.

The tree below shows the effect of worry. Only the no surgery branches are affected. Given the low rupture rate in our example, worry doesn’t affect QALYs much. With a higher rupture rate (as we’ll examine in a later lecture), worry creates a larger effect. The “worry” factor amplifies the loss in QALYs by about 25%, compared with considering only the years of life lost due to aneurysm rupture.

3. Discounting

Is it right to simply add QALYs over time? Should we really treat present and future QALYs equally? The answer is no: We need to capture the real “time preference” people have – valuing events in the present more than events in the future.

Example: Let’s say (hypothetically), I agree to buy you an ice cream cone, or your equivalent favorite dessert…

Who would want the dessert today? Or in 5 years?

Most people want to delay bad events or health states, but have good events occur as soon as possible. (This holds true for all except physicians-in-training. We MD’s are pretty accepting of delayed gratification.)

Discounting is the method to adjust future health outcomes and costs to their value in the present. Value in the present is called “net present value”, or NPV. This technique has long been used to represent time preference for costs. Recently a consensus has been reached to discount health outcomes. Not doing so leads to some logical conundrums in CEAs. On average people exhibit time preferences for health outcomes similar to those for costs.

The recommended discount rate (for both health and costs) is 3% (0.03), suggested by the U.S. Panel on Cost-Effectiveness in Health and Medicine. Other rates can be used to reflect special conditions such as the discount rate used internally by an HMO for financial planning.

As we’ve talked about all along, everything in decision analysis has to be done quantitatively. Each year in the future will be de-valued at a constant rate (the discount rate). Here is the formula for discounting:

The NPV of a utility value occurring x years in the future  =



where D is the discount rate.

So, if D = 3%, then events occurring 1-5 years into the future are adjusted as follows:

0.97, 0.94, 0.92, 0.89, 0.86.

For Utility = 1.0, D = 3%, and x = 10 years, the NPV for a year of “perfect health” is:

1.0/(1+0.03)10 = 0.74.

This can get subtle: Events happening “in year x” of a simulation are not happening exactly “x years into the future”. More precisely, they are happening on average [x-0.5] years into the future. For example, events during “year 2” probably occur on average 1.5 years from the start of the analysis. Thus, a half-year adjustment is sometimes used:



                                                (1+D)[x – 0.5]


Thus, a utility of 1.0 in year 2 translates to a NPV of 1.0/(1+0.03)1.5 = 0.957. Alternatively, a full-year adjustment is sometimes used, so events in year x are discounted by (x-1); this may be slightly inaccurate but is acceptable.

In the aneurysm example, discounting is very important, because most of the health states occur substantially into the future. The QALY total without rupture, with life expectancy of 35 years, is discounted by 39% overall. This represents the discounting of each year, and then summing across years. The QALY total with rupture is discounted less (24%), since many individuals live only an average of 17.4 years. Life with disability is discounted least (17%) since it occurs in the near future.

The tree with discounted values is below. The drop in QALYs due to discounting is slightly larger for no surgery 13.4 (38.5%) than for clipping 12.3 (38.3%). As a result, the difference in QALYs between the strategies also decreases, from 2.77 to 1.63. Almost all of the change in the difference (93%) is due to the overall effects of discounting; just 7% is due to the differential effects of discounting on the two strategies

Quick Review:

Utilities – ways of measuring and valuing health states between perfect health and death.

Utility assessment – Visual analog scale, standard gamble, time trade-off

Quality-adjusted life expectancy – utility * time

Discounting – way of de-valuing future health states relative to the present

Additional reading / references

Kallmes DF et al. Guglielmi detachable coil embolization for unruptured aneurysms in non-surgical candidates: a cost-effectiveness exploration. Am J Neuroradiol 1998;18:167-176.

King JT et al. Elective surgey for asymptomatic, unruptured, intracranial aneurysms: a cost-effectiveness analysis. J Neurosurg 1995;83:403-412.

Strauss DJ et al. Long-term survival of children and adolescents after traumatic brain injury. Arch Phys Med Rehabil 1998;79:1095-1100.

Gage BF et al. Cost-effectiveness of warfarin and aspirin for prophylaxis of stroke in patients with nonvalvular atrial fibrillation. JAMA 1995;274:1839-1845.

Gage BF et al. The effect of stroke and stroke prophylaxis with aspirin or warfarin on quality of life. Arch Intern Med 1996;156:1829-1836.

  “Disutility” is the reduction in utility due to morbidity. For example, if living with a stroke has utility = 0.8, vs. 1.0 with no stroke, the disutility = 0.2.

 Perhaps the most interesting conundrum is that if only costs were discounted we would in theory always want to delay prevention: by waiting we decrease the net present value of implementation costs but not the net present value of improvements in health outcomes.