Life Years Gained

Life Years Gained in Survival Modelling and Cost-Effectiveness Analysis

Life years gained is a long-standing natural unit of effect in cost-effectiveness analysis and sits inside almost every model that reports the QALY, because a model has to work out how long people live before it can weight that time by quality of life. The estimate is the difference in mean survival between two arms, which makes it the area between two survival curves over the time horizon of the model, and a large share of that area often lies beyond the end of trial follow-up. NICE and ICER, which both rely on QALYs, still ask to see the life years behind them, NICE in the base-case results table of its company submission template and ICER in its reference case, where life years appear beside QALYs and the equal value of life years gained. The term here means the incremental survival produced by an intervention in an economic evaluation, as opposed to population measures of premature death such as potential years of life lost.

Mean survival and the area between two curves

A survival curve gives the proportion of a cohort still alive at each point in time, and the area under that curve is the mean time alive per person. The NICE Decision Support Unit's Technical Support Document 14 (TSD 14), written by Latimer, explains that the mean survival of a trial population equals the area under its survival curve. Economic models use the mean because costs and health effects are averaged over every patient, including the long survivors in the tail.

Life years gained follow by subtraction. With survival functions for the intervention and the comparator, the gain over a time horizon is the area between the two curves.

$$\Delta LY = \int_{0}^{T} \left[ S_{1}(t)-S_{0}(t) \right] dt$$

where $\Delta LY$ is the life years gained per person, $S_{1}(t)$ and $S_{0}(t)$ are the proportions alive at time $t$ under the intervention and the comparator, and $T$ is the time horizon of the analysis.

In a cohort state transition model or a partitioned survival model the integral becomes a sum. Each cycle contributes the proportion of the cohort alive during the cycle multiplied by the cycle length, and the life years in each arm are the total of those contributions. Drummond and colleagues treat years of life gained as a natural unit of effect in cost-effectiveness analysis, and the same survival trace is reused when the model weights each cycle by a utility to count QALYs.

Restricted means within a trial and extrapolation beyond it

Trials rarely follow every patient until death, so the observed curves stop while many patients are still alive. The area that can be measured directly is a restricted mean, the mean survival up to the end of follow-up, and the difference between two restricted means is a within-trial estimate of life years gained.

Royston and Parmar proposed the restricted mean survival time, and a test of the difference in restricted means, as an alternative measure of treatment effect to the hazard ratio when proportional hazards may not hold. That measure answers a question about a fixed period, and a decision model usually needs the full gain. TSD 14 warns that if analysis stays within the trial, estimates of the survival benefit will be restricted to what was observed directly, which is likely to underestimate the true survival gain. Its recommendation is that the base case use extrapolation of a fitted probability distribution, while results based only on the observed data can be presented for context.

Extrapolation brings its own risk. Latimer and Adler note that extrapolation beyond the trial period is usually needed to estimate long-term effects, and warn that different parametric survival models fitted to the same trial data can give widely varying results, which carry through to estimates of clinical effectiveness and cost effectiveness. The overall survival data from the trial and its Kaplan-Meier curve therefore fix only the early part of the life years gained, and the choice of tail often decides the rest.

Discounting life years under NICE and ICER methods

A life year gained in the distant future counts for less in present-value terms, in the same way as a future cost. NICE and ICER both discount life years at the rate they apply to costs and other health effects, following the general logic of discounting, and undiscounted figures show how much of the gain lies far ahead.

The NICE technology appraisal and highly specialised technologies manual (PMG36) states that for the reference case, costs and health effects should be discounted at the same rate of 3.5% per year. The manual also allows the committee to consider analyses using a non-reference-case rate of 1.5% per year for both costs and health effects when all of a set of listed criteria are met. ICER's reference case sets a rate of 3% per year for costs and outcomes and asks for life years to be tabulated both undiscounted and discounted.

Discounting takes a larger share from a survival gain that arises late. A treatment that delays death by several years after a long plateau loses a larger share of its gain to discounting than one that prevents early deaths, so the discounted figure is the one to place in a ratio and the undiscounted figure shows the timing.

Life years gained beside QALYs in HTA reporting

NICE and ICER use the QALY as their main outcome but still report the survival component on its own. Showing the life years separately lets a committee see whether a gain comes from longer life, better life or both.

NICE's user guide for the company evidence submission template (PMG24) includes life years gained (LYG) in the base-case results table, alongside costs, QALYs and the ICER. ICER's reference case lists costs, life years, equal value life years gained (evLYG) and QALYs, each undiscounted and discounted, and includes a cost per life year where a treatment has effects on mortality, beside the cost per QALY and the cost per evLYG.

In the United States the use of QALYs in public programmes also has a legal side. The Inflation Reduction Act of 2022 (Public Law 117-169) bars the use of evidence from comparative clinical effectiveness research in Medicare drug price negotiation in a manner that treats extending the life of an elderly, disabled or terminally ill individual as of lower value than extending the life of an individual who is younger, nondisabled or not terminally ill. The Medicare bar on QALYs is older than the Act. Section 1182(e) of the Social Security Act, added by the Affordable Care Act of 2010, stops the Secretary using a dollars-per-QALY measure as a threshold for Medicare coverage, reimbursement or incentive programmes. CMS stated in its revised negotiation guidance of June 2023 that it will not use QALYs to determine any offer, and that it considers studies using QALYs only for other content permitted under sections 1194(e)(2) and 1182(e). ICER's 2023 Value Assessment Framework describes the evLYG as awarding the quality of life of the general population for the additional years of life gained, irrespective of the health state patients are in during those years.

Worked example with two illustrative survival curves

All numbers in this example are illustrative. A cohort model with annual cycles compares a new treatment with standard care for an advanced cancer. The table gives the proportion alive at the start of each year, and everyone has died by year 4 under standard care and by year 5 under the new treatment.

Step 1. Life years in each year. Taking the average of the proportions alive at the start and end of each year, standard care gives 0.80, 0.45, 0.20 and 0.05 life years in years 1 to 4. The new treatment gives 0.90, 0.65, 0.375, 0.175 and 0.05 in years 1 to 5.

Step 2. Undiscounted life years gained. Standard care totals 0.80 + 0.45 + 0.20 + 0.05 = 1.50 life years and the new treatment totals 0.90 + 0.65 + 0.375 + 0.175 + 0.05 = 2.15 life years, so the gain is 2.15 − 1.50 = 0.65 life years per patient.

Step 3. Discounting at 3.5 per cent. Year 1 is left undiscounted and year $k$ is multiplied by a discount factor of one over 1.035 raised to the power $k-1$, which gives 1.0000, 0.9662, 0.9335, 0.9019 and 0.8714. Standard care gives 0.80 + 0.4348 + 0.1867 + 0.0451 = 1.4666 discounted life years and the new treatment gives 0.90 + 0.6280 + 0.3501 + 0.1578 + 0.0436 = 2.0795, so discounted life years gained are 2.0795 − 1.4666 = 0.6129.

Step 4. Cost per life year gained. With a discounted incremental cost of GBP 12,000 per patient, the ratio is computed as follows.

$$\text{ICER}_{LY} = \frac{\Delta C}{\Delta LY} = \frac{12000}{0.6129} = 19579$$

where $\Delta C$ is the incremental cost in GBP and $\Delta LY$ is the discounted life years gained, giving GBP 19,579 per life year gained.

Step 5. The same gain as QALYs. If patients in both arms live with a utility of 0.6, the QALY gain is 0.6 × 0.6129 = 0.36774 and the cost per QALY is 12,000 / 0.36774 = 32,631, or GBP 32,631 per QALY.

Step 6. A trial that stops at two years. If follow-up ends at year 2, the restricted means are 0.80 + 0.45 = 1.25 and 0.90 + 0.65 = 1.55 life years, a within-trial gain of 1.55 − 1.25 = 0.30, less than half the lifetime gain of 0.65.

The cost per life year gained looks favourable because every added year counts as a full year, while the cost per QALY is higher because those years are lived at a utility of 0.6. Step 6 shows why extrapolation matters, since more than half of the survival gain in this example lies beyond two years.

What a cost per life year gained can and cannot support

A cost per life year gained is an incremental cost-effectiveness ratio with survival as the outcome, so it can compare options whose main effect is on mortality. Drummond and colleagues note that such a ratio can only compare programmes that produce the same kind of effect, and life years record nothing about treatments whose benefit is relief of symptoms or better function.

Quality of life during the added years is ignored. A year alive in severe disability and a year alive in full health count the same, which is why, for a treatment that acts only on survival, a cost per life year looks better than the cost per QALY whenever utilities are below one, as in the worked example. Comparing a life year ratio with a cost-effectiveness threshold set per QALY mixes two units and overstates value. A treatment that improves quality of life without extending life has no life years gained at all, and a ratio built on them cannot be calculated.

How life years gained differ from neighbouring measures

Several outcomes count years of life, and they answer different questions. Some describe the effect of an intervention on a cohort, while others describe the burden of premature death in a population.

Common misreadings of life years gained

Most errors with life years gained come from reading a mean as something it is not. Others come from mixing estimates made over different horizons or on different discounting bases.

• Median survival gain is not life years gained. A difference in medians describes the middle patient, while the cost-effectiveness calculation needs the mean, which TSD 14 ties to the area under the curve.
• A mean gain is not a gain for each patient. In the worked example 0.65 life years is an average across the cohort, which can combine large gains for some patients with none for others.
• Within-trial and lifetime gains differ. A restricted mean difference understates the lifetime gain whenever patients remain alive at the end of follow-up, as step 6 shows.
• Discounted and undiscounted figures get mixed. A ratio should use discounted life years and discounted costs together, and the undiscounted figures are reported alongside for transparency.
• Extrapolated gains carry model uncertainty. Latimer and Adler show that the choice of parametric model can change the estimated benefit widely, so scenario analysis over plausible extrapolations belongs beside the base case.

Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press; 2015.
• Latimer N. NICE DSU Technical Support Document 14: Survival analysis for economic evaluations alongside clinical trials, extrapolation with patient-level data. Decision Support Unit, University of Sheffield; June 2011, updated March 2013. https://www.sheffield.ac.uk/nice-dsu/tsds
• Latimer NR, Adler AI. Extrapolation beyond the end of trials to estimate long term survival and cost effectiveness. BMJ Medicine. 2022;1(1):e000094. doi:10.1136/bmjmed-2021-000094
• Royston P, Parmar MKB. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Medical Research Methodology. 2013;13:152. doi:10.1186/1471-2288-13-152
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Chapter 4. https://www.nice.org.uk/process/pmg36/chapter/economic-evaluation-2
• National Institute for Health and Care Excellence. Single technology appraisal and highly specialised technologies evaluation: user guide for company evidence submission template (PMG24). Section 3, base-case results. Accessed 17 October 2026. https://www.nice.org.uk/process/pmg24/chapter/cost-effectiveness
• Institute for Clinical and Economic Review. ICER's Reference Case for Economic Evaluations. Boston: ICER; 2025. https://icer.org/wp-content/uploads/2024/02/ICER_Reference-Case_For-Publication_070126.pdf
• Institute for Clinical and Economic Review. 2023 Value Assessment Framework. Boston: ICER; 2023. https://icer.org/wp-content/uploads/2023/09/ICER_2023_VAF_For-Publication_092523.pdf
• Inflation Reduction Act of 2022, Public Law 117-169, 16 August 2022. https://www.congress.gov/117/plaws/publ169/PLAW-117publ169.pdf
• Social Security Act, section 1182 (Limitations on certain uses of comparative clinical effectiveness research), subsection (e), added by the Affordable Care Act 2010. https://www.ssa.gov/OP_Home/ssact/title11/1182.htm
• Centers for Medicare and Medicaid Services. Medicare Drug Price Negotiation Program: revised guidance. June 2023. https://www.cms.gov/files/document/revised-medicare-drug-price-negotiation-program-guidance-june-2023.pdf