Signature
QALY_AUC = sum_(t=1)^T [(u_start_t + u_end_t) / 2 * d_t]
| Inputs | Definition | Unit |
|---|---|---|
u_start_t | Utility observed at the start of interval t | utility (dimensionless) |
u_end_t | Utility observed at the end of interval t | utility (dimensionless) |
d_t | Time between the two observations that bound interval t | years |
QALY_AUC | Undiscounted QALYs estimated as the area under the linearly interpolated utility curve | QALYs per person |
|---|
TNumber of intervals between consecutive utility observations (count)
Function
Quality-adjusted survival function
Maps a profile of health-state utility over time to quality-adjusted life years, the area under the utility-over-time curve.
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Implementations
Excel
Trapezoidal QALYs
Excel averages the start and end utility of each interval, multiplies by the interval length in years and adds the products.
=SUMPRODUCT((StartUtilities+EndUtilities)/2,IntervalYears)
Assumptions
Linear change between observations
Utility moves in a straight line between consecutive measurements. Other interpolation rules can give different totals, so the rule is stated and tested in sensitivity analysis.
Contiguous intervals
The end observation of each interval is the start observation of the next, and together the intervals cover the follow-up period without gaps or overlaps.
Baseline utility controlled in trial comparisons
Baseline utility contributes to the area and is often imbalanced between trial arms, so incremental QALYs are estimated with adjustment for baseline utility, for example by regression.
Worked examples
Three observations over one year
Utility is 0.50 at baseline, 0.70 at six months and 0.80 at twelve months. The first interval contributes the mean of 0.50 and 0.70 multiplied by 0.5 years, which is 0.30 QALYs, and the second contributes the mean of 0.70 and 0.80 multiplied by 0.5 years, which is 0.375 QALYs. The total is 0.675 QALYs.
T = 2; u_start_t = [0.50,0.70]; u_end_t = [0.70,0.80]; d_t = [0.5,0.5]; QALY_AUC = 0.675
Common errors
Ignoring baseline imbalance
Comparing unadjusted mean areas between trial arms lets chance differences in baseline utility bias incremental QALYs, which can give a misleading ICER.
Interpolating silently across a missed visit
Joining the observations on either side of a missed visit applies the linear-change assumption over a longer interval. The rule is reported and its effect tested rather than left implicit.
Sources
Baseline utility in trial-based QALYs
Manca A, Hawkins N, Sculpher MJ. Estimating mean QALYs in trial-based cost-effectiveness analysis: the importance of controlling for baseline utility. Health Economics. 2005;14(5):487-496.
Review of QALY calculation methods
Richardson G, Manca A. Calculation of quality adjusted life years in the published literature: a review of methodology and transparency. Health Economics. 2004;13(12):1203-1210.
Methods textbook for area-under-the-curve QALYs
Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.
Canonical Identity
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