DALY/QALY↔WELLBY Conversion

Funders cannot wait for perfect measurement. If you must allocate $1M between a malaria program and a mental health program this year, you are implicitly adopting some conversion—even if that conversion is "treat them as incomparable" (which is itself a choice).

The practical question is: given imperfect information, what mapping structure leads to least regret?[17]"Least regret" (or "minimax regret") is a formal criterion from decision theory: choose the action that minimizes the maximum regret across possible states of the world. Here, it means choosing conversion assumptions that minimize expected decision error across plausible true values. This is different from asking "what is the true conversion factor?"—a question that may not have a coherent answer.

• Founders Pledge: Compares interventions across their four "ways of doing good" (lives, DALYs, WELLBYs, income doublings)[6]Founders Pledge internal framework; they explicitly flag DALY↔WELLBY conversion as a key uncertainty.
• Happier Lives Institute: Uses WELLBY-based cost-effectiveness analysis for mental health interventions[16]HLI has developed explicit WELLBY→monetary conversion methods, controversially applied to StrongMinds.
• GiveWell: Primarily DALY-based but engages with WELLBY evidence when evaluating mental health[11]GiveWell's StrongMinds analysis explicitly discusses the WELLBY→DALY mapping problem.
• UK Government: Uses WELLBYs for policy appraisal via Green Book guidance[7]HM Treasury (2021) provides explicit QALY↔WELLBY conversion methodology.

Disability weights are elicited through population surveys using choice-based methods:

• Paired comparison: "Which of these two health states would you consider worse?"
• Population health equivalence: "Which is worse: 1000 people with condition X or 2000 with condition Y?"

The GBD 2019 study collected ~60,000 responses from 9 countries to set disability weights for 234 health states.

Importantly, respondents are asked about health loss specifically—not overall welfare, social functioning, or quality of life. This is a deliberate methodological choice that makes DALYs narrower than some alternatives.

DALYs and QALYs are often treated as "opposites" (DALYs measure burden; QALYs measure benefit), but the relationship is more complex:

• Disability weights ≠ 1 − utility weights. The elicitation methods are different, and empirical mappings show poor correspondence at the extremes.
• Reference states differ. DALYs reference "full health"; QALYs allow negative values for "worse than death."
• Aggregation differs. DALYs are population-summed burdens; QALYs are individual-level benefit calculations.

For conversion purposes, 1 DALY averted ≈ 1 QALY gained is a common working assumption, but it's not definitionally true.

The standard OECD/ONS question is:

"Overall, how satisfied are you with your life nowadays?"
(0 = "Not at all satisfied" to 10 = "Completely satisfied")

This is an evaluative measure—it asks for a cognitive assessment of one's life, not a measure of current mood or momentary affect.

Other common SWB questions (happiness, worthwhileness, anxiety) capture different constructs and don't combine into WELLBYs the same way.

WHO's methods documentation explicitly states that the DALY framework evolved from earlier "welfare/quality of life" framing toward quantifying loss of health (departures from perfect health). Disability weights are intended to reflect health states, not social value, stigma, or general quality-of-life.

This means DALYs and WELLBYs are measuring different targets, even in principle. A "conversion" is really a mapping between proxies, not a unit transformation within the same construct.

The Happier Lives Institute (HLI) ranked StrongMinds—a mental health NGO—as potentially more cost-effective than GiveWell's top charities, primarily based on WELLBY-measured impacts from group therapy.[16]HLI (2023). StrongMinds cost-effectiveness analysis. Available at happierlivesinstitute.org.

GiveWell's reanalysis raised several concerns:

• Depression → LS mapping: Studies measured depression severity (PHQ-9), not life satisfaction. Converting requires assumptions about the depression-LS relationship.
• Effect durability: What persistence should we assume for psychotherapy effects? HLI's assumptions were more optimistic.
• Spillover effects: HLI counted benefits to household members; GiveWell was more skeptical of the evidence base.

This controversy illustrates how DALY↔WELLBY mapping issues can materially affect charity recommendations, not just academic debates.

Refusing to make a conversion explicit doesn't avoid the problem—it just hides it. Common implicit approaches include:

• "Only compare within metrics": This effectively assigns infinite value to one metric and zero to the other across boundaries.
• "Fund both categories proportionally": This implicitly assumes some conversion ratio equal to budget shares, regardless of cost-effectiveness.
• "Use expert judgment case-by-case": This may embed inconsistent conversions across decisions.

Making conversion assumptions explicit—even with wide uncertainty ranges—is almost always preferable to leaving them implicit.

Fixed factor is appropriate when you need a simple baseline for sensitivity analysis, or when communicating to audiences who need a single number.

Anchor-span is preferred when you have good estimates of LS at health extremes and want a traceable derivation. The UK Green Book makes this approach explicit.

Monetary peg works when both metrics already have established £/$ valuations (e.g., from health technology assessment). Useful for policy consistency.

Empirical crosswalk is ideal when you have datasets measuring both health status and life satisfaction for the same individuals. This allows population-specific calibration.

Multi-metric sensitivity is recommended for final decision-making when conversion is contested. It makes uncertainty visible rather than hidden.

The idea of estimating LS = f(health) from datasets that measure both seems straightforward, but complications include:

• Selection: People measured on both instruments may not be representative (e.g., patients vs. general population).
• Simultaneity: Health affects LS, but LS may also affect health behaviors and reporting.
• Ceiling effects: At high health levels, LS variation may reflect non-health factors.
• Instrument mismatch: EQ-5D measures "today," while LS measures "overall evaluation." Timing differences matter.

EEPRU's work (Mukuria et al., 2016) found that generic SWB measures are often less sensitive than disease-specific instruments for physical conditions, complicating simple crosswalks.[10]Mukuria, C., et al. (2016). EEPRU research report on SWB measures.

Peasgood et al. (2018), cited in the UK guidance, found an indifference point around LS = 2. Using this anchor:

$X = 8 - 2 = 6$ WELLBY per QALY

A one-point shift in the anchor changes the conversion factor by ~14%. This illustrates why the neutral/death-equivalence debate is not semantic—it is numerically load-bearing for mortality comparisons.

Plant (2025) provides a useful decomposition of the assumptions needed for cardinal WELLBY use:

• C1: Phenomenal cardinality (subjective experiences have inherent magnitudes)
• C2: Linearity (equal scale steps = equal welfare differences)
• C3: Intertemporal comparability (same person uses scale consistently over time)
• C4: Interpersonal comparability (different people's reports are comparable)

This framework helps locate which assumptions are most load-bearing for a given comparison.

Adaptation creates a fundamental tension between DALY and WELLBY accounting:

• DALY perspective: A person with chronic paraplegia accumulates ~0.3-0.4 YLD per year indefinitely (based on disability weights).
• WELLBY perspective: After initial adjustment, LS may return close to pre-injury levels (substantial evidence of hedonic adaptation).

If adaptation is complete, a simple conversion implies the person is "not losing welfare" each year—even though DALYs continue accruing. This is either:

• Evidence that DALYs over-count chronic morbidity (the WELLBY perspective wins), or
• Evidence that LS under-counts genuine welfare losses that people have adapted to accepting (the DALY perspective wins).

The correct interpretation is a substantive philosophical question, not just a measurement issue.[9]Frijters, P., et al. (2024). Discusses adaptation as a challenge for WELLBY interpretation.

Suppose you're comparing two interventions:

• Intervention A: $50/person, generates 0.3 WELLBYs/person
• Intervention B: $100/person, averts 0.05 DALYs/person

Cost-effectiveness in WELLBYs per $1000:

• A: 0.3 / $50 × 1000 = 6 WELLBYs/$1000
• B (converted): 0.05 × X / $100 × 1000 = 0.5 × X WELLBYs/$1000

B beats A when 0.5X > 6, i.e., when X > 12.

This tells you: if you believe the conversion factor is below 12, fund A; if above 12, fund B. The "indifference threshold" X* = 12 is the key number for decision-making, not the conversion factor itself.

When presenting cost-effectiveness analyses that involve DALY↔WELLBY conversion, consider including:

1. Base case: State your assumed conversion factor and cite the source (e.g., "7 WELLBYs/QALY per UK Green Book").
2. Sensitivity range: Report results at X = 4, 7, and 10 (or whatever range brackets the literature).
3. Threshold analysis: Report X* at which ranking reverses. State whether X* falls within the plausible range.
4. Robustness statement: "Intervention A is preferred under all conversion factors below [X*]" or "Ranking is sensitive to conversion assumptions."

This template makes your assumptions transparent and allows readers with different priors to interpret your results.

1. Beneficiary tradeoff studies:

• Use discrete choice experiments asking beneficiaries to choose between health improvements and income/wellbeing improvements.
• Could be embedded in existing RCT follow-up surveys at low marginal cost.

2. Joint measurement:

• Add LS questions (1-2 items) to health intervention trials that already measure EQ-5D or SF-6D.
• Cost: ~$1-5/participant for additional survey items; high value-of-information.

3. LMIC calibration:

• Benjamin et al. (2023) methods could be adapted for LMIC populations using vignettes in local languages.[13]Benjamin, D.J., et al. (2023). "Adjusting for Scale-Use Heterogeneity in Self-Reported Well-Being." NBER WP 31728.
• Could be combined with anchoring vignettes (King et al., 2004) for cross-population comparison.

If you believe WELLBYs have fundamental measurement problems (scale-use heterogeneity, demand effects, philosophical objections to hedonism), the conversion framework here still applies—just with much wider uncertainty ranges or higher weight on DALY-based evidence.

The practical value of making conversion explicit is that it lets you:

• See how much your skepticism matters for specific decisions (threshold analysis)
• Communicate your reasoning transparently to others with different priors
• Update systematically as new evidence arrives

"WELLBYs are too unreliable to use" is itself an implicit conversion assumption (X ≈ 0 or undefined). Making it explicit is more honest.

If you believe DALYs miss important welfare effects (mental health, non-health domains, adaptation, social context), you might prefer to:

• Use WELLBYs as the primary metric and convert DALYs to WELLBYs (rather than vice versa)
• Apply domain-specific adjustments to DALY-based estimates
• Flag DALY-only evidence as potentially understating welfare effects

The conversion framework accommodates this perspective—just flip the direction and acknowledge that mortality comparisons require additional neutral-point assumptions.