QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured

อ่านฉบับภาษาไทย (Thai version)

Abstract

A hospital committee must decide whether a knee replacement is worth 450,000 THB more than medicines and physiotherapy. It adds no years of life but turns 10 years with a painful knee into 10 years of full health. Pricing that gain needs a weight for a year with the knee, from 1 for full health to 0 for death; a QALY, a quality-adjusted life year, is a year weighted this way. Trading years gives 0.70, a gamble with death 0.85, the Thai scoring table gives 0.751, and a rating line 0.60 (not a valid weight, because nothing is given up for it). So each QALY gained costs 150,000, 300,000, 180,723 or, from the invalid rating, 112,500 THB, either side of a 160,000 THB benchmark. A DALY, a disability-adjusted life year, counts healthy life lost: with a disability weight of 0.20, the 10 years lose 2.0 healthy years, not the 3.0 that 1 minus 0.70 suggests.

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One knee, ten years, four answers

A hospital committee is deciding whether to fund knee replacement for patients with severe osteoarthritis of the knee. Take one patient. Without the operation, this patient is expected to live 10 more years with moderate knee pain, slight problems walking and slight trouble with daily work. With it, in this illustrative case, the same 10 years are lived in full health.

The operation and its rehabilitation cost 450,000 THB (Thai baht) more than continuing medicines and physiotherapy. It does not change how long the patient lives. Counted in years of life, it gains nothing: 10 years either way. What it changes is how good those 10 years are.

To weigh that against 450,000 THB, the committee needs one number: how much is a year with this knee worth, compared with a year in full health? Ask in four ways and you get four numbers. A question that trades years gives 0.70, and a question with a gamble gives 0.85. A rating line gives 0.60, and the Thai scoring table for the patient's questionnaire answers gives 0.751.

Over the 10 years, those four numbers say the operation adds 3.0, 1.5, 4.0 or 2.49 years of full health. So the same 450,000 THB pays 150,000, 300,000, 112,500 or 180,723 THB for each year it adds.

Is that good value? The committee compares the price with a benchmark, usually called the threshold: the most the health system is willing to pay for one extra year of full health, here 160,000 THB. A price below it counts as good value, so two answers say yes and two say no.

The amounts are illustrative, for teaching, except the Thai table's 0.751. This article shows where each number comes from, which ones can be used, and why a measure of health lost gives yet another answer.

What is a year with this knee worth?

Start with a scale whose two ends nobody disputes: a year in full health counts 1, and death counts 0. A year with the knee sits somewhere between, worse than full health and far better than death.

Suppose the knee is worth 0.70 on that scale; this is the answer from trading years, explained in the next section. Then each year with the knee counts as 0.70 of a healthy year and loses 0.30. Over 10 years that is 0.70 × 10 = 7.0 years of full health. The operation lifts each year to 1, so it adds (1 − 0.70) × 10 = 3.0.

A year weighted this way has a name. A QALY, a quality-adjusted life year, is a year of life weighted by the quality of that health, from 1 for full health to 0 for death [2]. The weight itself is called a utility, or a health-state value; for the knee it is 0.70. So the knee's 10 years are 7.0 QALYs, and the operation gains 3.0 QALYs although it adds no year of life.

When the weight changes, add period by period. If the knee worsened after 5 years to 0.50, the 10 years would give 5 × 0.70 + 5 × 0.50 = 3.5 + 2.5 = 6.0 QALYs. In symbols, with $u_t$ the weight in period $t$, $\Delta t$ its length in years, and $\sum_t$ meaning add over all periods:

$$\text{QALYs}=\sum_t u_t\,\Delta t$$

Survival enters the same way: years after death add nothing, so a treatment that keeps people alive longer gains QALYs by adding periods. The scale can also go below 0. A state judged worse than death gets a negative weight, and a year in it takes QALYs away.

Real evaluations add one more step for time. Discounting is converting a future cost or health gain into its value today, shrinking it by the discount rate for each year away. At 3% a cost of 1,834 THB due in year 3 is worth 1,678 THB today; the full lesson is in Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting.

QALYs in later years shrink the same way: each period in the sum is multiplied by $(1+r)^{-t}$, where $r$ is the discount rate and $t$ is how many years away the period is. This article leaves that step out so that every number can be checked by hand.

# The knee: 10 years at a weight of 0.70, where full health is 1 and death is 0.
years <- 10
weight <- 0.70
cat("Each year with the knee loses:", formatC(1 - weight, format = "f", digits = 2), "\n")
cat("10 years with the knee:", formatC(weight * years, format = "f", digits = 1), "QALYs\n")
cat("Full health for the 10 years gains:", formatC((1 - weight) * years, format = "f", digits = 1),
    "QALYs\n")
# If the knee worsened: 5 years at 0.70, then 5 years at 0.50, added period by period.
periods <- c(5 * 0.70, 5 * 0.50)
total <- sum(periods)
cat("5 years at 0.70, then 5 at 0.50:", periods, "->", formatC(total, format = "f", digits = 1),
    "QALYs\n")
# The recap of the step that values later years: 1,834 THB due in year 3, at 3% a year.
today <- formatC(1834 / 1.03^3, format = "f", digits = 0, big.mark = ",")
cat("1,834 THB due in year 3 is worth today:", today, "THB\n")

Each year with the knee loses: 0.30
10 years with the knee: 7.0 QALYs
Full health for the 10 years gains: 3.0 QALYs
5 years at 0.70, then 5 at 0.50: 3.5 2.5 -> 6.0 QALYs
1,834 THB due in year 3 is worth today: 1,678 THB

Three ways to ask the question

The 0.70 came from somewhere: a person answered a question. Health has no price tag, so a weight has to come from asking people. Three questions are common, and they do not give the same answer.

Rating the knee on a line

The simplest question shows a line from 0 for the worst health you can imagine to 100 for the best, and asks the patient to mark today's health. Our patient marks 60, and dividing by 100 gives 0.60. This is called a visual analogue scale, or VAS.

A VAS asks for a rating, not a choice: the patient gives up nothing to move the mark. Its ends also differ, because the best and worst imaginable health are not full health and death. So 0.60 is a reading on another ruler, and dividing by 100 only rescales it. An equation fitted to trade-off or gamble answers can convert ratings, but the result still starts from a rating, not from the choice that a weight for QALYs needs [1].

Trading years for health

The second question offers a trade. Would you rather live 10 years with this knee, or fewer years in full health? The interviewer changes the number of healthy years until the patient cannot choose between the two. Our patient is torn at 7 years, so 10 years with the knee are worth 7 in full health, and the weight is 7 / 10 = 0.70.

This is the time trade-off, or TTO. If $t$ years in the state are judged equal to $x$ years in full health, then $u = x/t$. The patient pays for better health with time, so the answer is a real choice. The plain version assumes the state is better than death; a state worse than death needs a changed question.

Taking a gamble

The third question offers a risk instead. Imagine a treatment that gives full health for the 10 years with chance $p$, or immediate death otherwise. Would you take it, or keep 10 sure years with the knee?

The interviewer changes the chance until the patient cannot choose, and our patient is torn at 85%. The weight is that chance, 0.85. This is the standard gamble, or SG, and here $u = p$.

It rests on a simple rule for valuing a risky choice: weight each outcome by its chance, so $p\times 1+(1-p)\times 0=p$. People dislike risking death, so they accept the gamble only when the chance of full health is high, which pushes gamble weights up [1].

So the same knee is worth 0.60, 0.70 or 0.85, depending on the question. Gamble weights are often above trade-off weights, and trade-off weights above ratings, but that order is a tendency, not a rule [1]. None of the three is a measuring error: each correctly answers a different question.

# Three answers about the same knee, the same operation and the same extra cost.
cost <- 450000
years <- 10
threshold <- 160000
weight <- c(TTO = 7 / 10, SG = 0.85, VAS_shortcut = 60 / 100)
gained <- (1 - weight) * years
price <- cost / gained
for (m in names(weight)) {
  cat(m, "weight", formatC(weight[m], format = "f", digits = 2), "| QALYs gained",
      formatC(gained[m], format = "f", digits = 1), "| THB per QALY gained",
      formatC(price[m], format = "f", digits = 0, big.mark = ","), "\n")
}
cat("Threshold, THB per QALY gained:", formatC(threshold, format = "d", big.mark = ","), "\n")

TTO weight 0.70 | QALYs gained 3.0 | THB per QALY gained 150,000
SG weight 0.85 | QALYs gained 1.5 | THB per QALY gained 300,000
VAS_shortcut weight 0.60 | QALYs gained 4.0 | THB per QALY gained 112,500
Threshold, THB per QALY gained: 160,000

Whose answer counts? The questionnaire and the Thai scoring table

Running a trade-off interview with every patient in every study is not practical. Instead, patients describe their health on a short questionnaire, and a scoring table turns the description into a weight. The most widely used questionnaire of this kind is the EQ-5D-5L.

It asks about five things, always in this order: mobility, self-care, usual activities, pain or discomfort, and anxiety or depression. Each has five levels, from 1, no problems, to 5, extreme problems or unable. Our patient answers 2, 1, 2, 3 and 2: slight problems walking, none with washing or dressing, slight problems with usual activities, moderate pain and slight anxiety. Written together, the profile 21232 describes this knee.

The profile 21232 is a description, not a weight. A scoring table built from the answers of a country's general public turns it into one. Thailand's table comes from interviews in which members of the Thai public valued EQ-5D-5L states with trade-off and choice questions [4]. In the rounded form printed as Table 4.29 of a compendium of value sets [5], it starts at 1 and subtracts one amount, called a decrement, for each answer above level 1:

So the weight is 1 − 0.249 = 0.751. These are rounded decrements, and the unrounded equation can differ slightly. With 0.751, the operation gains (1 − 0.751) × 10 = 2.49 QALYs, and each costs 450,000 / 2.49 = 180,723 THB, over the threshold. A scoring rule like this one is called a value set, or tariff: it turns questionnaire answers into weights.

Notice whose preferences went in. The patient described the knee; the Thai public valued it. Guidance on the standard way to run an evaluation (the reference case) usually asks for such general-public values, because the decision spends everyone's money [3]. A patient who has adapted to the knee may value it higher than the public does, so the patient's own answer is a different number, not a better or worse one.

Sometimes the patient cannot answer, for example with severe dementia. Then a proxy, such as a carer, fills in the questionnaire; record who answered and whether they gave their own view or the patient's.

Many value sets give the worst profiles weights below 0. Keep them, because cutting them to 0 hides real loss.

A value set from another country brings that country's preferences as well as its arithmetic. Check that it fits the people the decision is for.

# The patient's answers, 21232, scored with the Thai value set: rounded decrements (Table 4.29).
decrement <- c(mobility = 0.066, self_care = 0, usual_activities = 0.058,
               pain_discomfort = 0.067, anxiety_depression = 0.058)
lost <- sum(decrement)
weight <- 1 - lost
gained <- (1 - weight) * 10
cat("The five decrements add up to:", formatC(lost, format = "f", digits = 3), "\n")
cat("Weight for 21232:", formatC(weight, format = "f", digits = 3), "\n")
cat("QALYs gained over 10 years:", formatC(gained, format = "f", digits = 2), "\n")
price <- 450000 / gained
cat("THB per QALY gained:", formatC(price, format = "f", digits = 0, big.mark = ","), "\n")

The five decrements add up to: 0.249
Weight for 21232: 0.751
QALYs gained over 10 years: 2.49
THB per QALY gained: 180,723

What the questionnaire cannot see, and two conditions at once

A questionnaire can only see what it asks about. After the operation, many patients choose level 1 on all five questions, the top of the scale. A patient who goes on to hike or play sport cannot score any higher, so improvements beyond that point are invisible. This is called a ceiling effect.

Sometimes a trial measured only a knee-specific score, not the EQ-5D-5L. Analysts can then predict the EQ-5D-5L weight from the knee score, using an equation estimated in other patients who answered both. This is called mapping. The prediction carries error, so the model should carry that error too, and the equation should come from patients like the ones in the decision.

A change can also be real but too small to matter to patients. The smallest change that patients notice as meaningful is called the minimal clinically important difference, or MCID. It depends on the questionnaire, the patients and the setting, so there is no single cut-off on the 0 to 1 scale.

Many patients carry more than one condition. Suppose our patient also has diabetes, a state valued 0.80 on its own, while the knee alone is 0.70. What are the two together worth? The best answer is a weight measured in people who have both.

When no such weight exists, analysts assume one of two rules. Multiplying the weights gives 0.70 × 0.80 = 0.56. Adding the losses gives 1 − (0.30 + 0.20) = 0.50. Neither is a measured value, so a report should say which rule it used and test the other.

# The knee (0.70) plus diabetes valued 0.80 on its own: two assumptions, not a measured value.
knee <- 0.70
diabetes <- 0.80
multiplied <- knee * diabetes
losses_added <- 1 - ((1 - knee) + (1 - diabetes))
cat("Losses on their own:", formatC(1 - knee, format = "f", digits = 2), "and",
    formatC(1 - diabetes, format = "f", digits = 2), "\n")
cat("Multiply the weights:", formatC(multiplied, format = "f", digits = 2), "\n")
cat("Add the losses, then take them from 1:", formatC(losses_added, format = "f", digits = 2), "\n")

Losses on their own: 0.30 and 0.20
Multiply the weights: 0.56
Add the losses, then take them from 1: 0.50

Counting healthy years lost: the DALY

So far the question was a committee's: is the operation worth its price? A health ministry ranking diseases asks something else: how much healthy life does each disease take from the population? That question counts loss, not value, and it uses another scale.

On this scale, 0 means no health lost and 1 means a loss as large as death. Each condition gets a disability weight on it. In our illustrative case the knee's disability weight is 0.20, so the patient's 10 years with the knee add 0.20 × 10 = 2.0 years of healthy life lost. These are called years lived with disability, or YLD.

Early death adds the other part. Each death counts the further years that a standard reference table expects a person of that age to live; a death at 70, where the table expects another 15 years, adds 15 years of life lost, or YLL. The operation changes no deaths, so for our patient the YLL is 0.

Add the two parts and you have the measure. A DALY, a disability-adjusted life year, counts healthy life lost: years lost to early death plus years lived with illness, weighted by a disability weight from 0 for full health to 1 for death [2]. In symbols, DALY = YLL + YLD; for the knee, 0 + 2.0 = 2.0 DALYs. After the operation the knee is in full health, with a disability weight of 0, so the operation averts all 2.0.

For our one patient, the YLD adds up all 10 future years with the knee. A burden study of a whole country usually counts one calendar year instead. It multiplies the people living with the condition that year by its disability weight, so it needs prevalence, not incidence; the difference is taught in Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models.

Older burden studies counted a year of life lived in young adulthood as worth more than a year at other ages, and shrank years further in the future. Current global burden studies do neither, so every year counts the same.

It is tempting to think the disability weight is just 1 minus the utility. It is not: 1 − 0.70 = 0.30, but the knee's disability weight is 0.20. The two come from different questions asked of different people.

A utility asks how good a year in the state is. The disability weights used in burden studies usually come from surveys in which members of the public judge which of two described people is healthier.

So the same operation gains 3.0 QALYs but averts 2.0 DALYs, and 450,000 / 2.0 = 225,000 THB per DALY averted. That price cannot be held against the 160,000 THB per QALY threshold, because it counts a different unit. A DALY is not a QALY with the sign flipped.

# Health lost with the knee: a disability weight runs from 0 (full health) to 1 (death).
years <- 10
disability_weight <- 0.20
yld <- disability_weight * years
cat("Years lived with disability (YLD):", formatC(yld, format = "f", digits = 1), "\n")
# One death at 70, where the reference table expects 15 more years of life.
cat("YLL for one death at 70:", 15, "\n")
yll <- 0
cat("YLL for the knee, survival unchanged:", yll, "\n")
cat("DALYs, YLL + YLD:", formatC(yll + yld, format = "f", digits = 1), "\n")
cat("1 minus the utility 0.70 would give:", formatC(1 - 0.70, format = "f", digits = 2), "\n")
per_daly <- 450000 / (yll + yld)
cat("THB per DALY averted:", formatC(per_daly, format = "f", digits = 0, big.mark = ","), "\n")

Years lived with disability (YLD): 2.0
YLL for one death at 70: 15
YLL for the knee, survival unchanged: 0
DALYs, YLL + YLD: 2.0
1 minus the utility 0.70 would give: 0.30
THB per DALY averted: 225,000

Which number for which question

Use QALYs when a committee compares what an intervention costs with the health it adds, as here. Use DALYs to measure the burden of disease in a population and to set priorities between diseases. Either way, a number is only as clear as its label. Before using a health weight, write down beside it:

• the question or questionnaire: the EQ-5D-5L;
• the scoring table and its country: the Thai value set;
• who answered: the patient described the knee, the Thai public valued it;
• the result and its rounding: 0.751, from rounded decrements.

A reader can then see why another study of the same knee reports 0.70 or 0.85. Where to find published weights when local data are thin is the subject of Parameter Sourcing, Reference Cost Lists and Utility Catalogues When Local Data Are Sparse. What a QALY leaves out, such as who receives the health, is taken up in Cost-Effective Is Not Affordable, and Efficient Is Not Fair: Budget Impact and Equity. The next article turns the price of a QALY into a decision rule.

The series, in learning order

1. Health Economics Series Guide: Read the Evidence Before the Costs
2. Incidence, Prevalence and the Right Denominator: The Epidemiology Beneath Cost-of-Illness and Markov Models
3. Design, Model and Estimand: What Each Study Design Can Actually Estimate
4. Risk Ratio, Odds Ratio, Risk Difference and NNT: One 2×2 Table, Four Answers
5. The Hazard Ratio Is Not a Risk Ratio: Proportional Hazards, Restricted Mean Survival Time and Model Inputs
6. Chance, Bias and Confounding: Why an Association Is Not Yet a Treatment Effect
7. Beyond the Evidence Pyramid: GRADE Certainty and Choosing Effectiveness Inputs for Economic Models
8. From Sensitivity to Cost per Case Detected: Predictive Values, Prevalence and the Economics of Screening
9. Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting
10. QALY, DALY and the Utilities Behind Them: What Is Actually Being Measured (this article)
11. ICER, Dominance and the Cost-Effectiveness Plane: Reading the Thai Threshold of 160,000 Baht per QALY
12. Decision Trees, Markov Cohorts and Probabilistic Sensitivity Analysis: How a Model Turns Evidence into a Decision
13. Cost-Effective Is Not Affordable, and Efficient Is Not Fair: Budget Impact and Equity
14. Parameter Sourcing, Reference Cost Lists and Utility Catalogues When Local Data Are Sparse
15. Early Health Technology Assessment, Headroom Pricing and Benefit-Package Decisions
16. Communicating Health Economic Evidence: From Model Outputs to Policy Briefs

Related in the wiki: Whose Cost, in Which Year? Perspective, Opportunity Cost, Inflation and Discounting · ICER, Dominance and the Cost-Effectiveness Plane: Reading the Thai Threshold of 160,000 Baht per QALY · Cost-Effective Is Not Affordable, and Efficient Is Not Fair: Budget Impact and Equity