Sullivan Method

Sullivan Method for Health Expectancy and Quality-Adjusted Life Expectancy

The Sullivan method splits the years in a period life table into years lived in good health and years lived in poorer health, using the share of people in each state at each age. The Office for National Statistics (ONS) uses it to produce UK healthy life expectancy, and health economists use the same arithmetic with utility norms to estimate the quality-adjusted life expectancy of the general population. That last use matters in England because NICE judges the severity of a condition against the QALYs the general population would be expected to have. The method needs only cross-sectional survey data and routine mortality statistics, and its main weakness is that current prevalence stands in for the health experience of a cohort that no one has followed.

A prevalence-based way to divide life expectancy

Jagger, Van Oyen and Robine, in a practical guide updated for the European Health Expectancy Monitoring Unit, describe life expectancy as made up of lengths of time spent in different states of health until death, and call those lengths health expectancies. They trace the idea of health expectancies as indicators to Sanders in 1964 and the first example to a 1971 report by Sullivan for the US Department of Health, Education and Welfare, which gave preliminary estimates of disability-free life expectancy. Sullivan's approach applies to any definition of the healthy state, which is why one calculation sits behind disability-free, healthy and active life expectancy alike.

Strictly, years lived in a health state from a given age depend on future incidence of that state, and the guide describes health expectancies in theory as longitudinal measures. Computing them directly needs transition rates between states, the approach of the multi-state life table. Sullivan's shortcut replaces those transitions with age-specific prevalence from a cross-sectional survey. Imai and Soneji note that Sullivan gave no formal justification for the method, and they prove that, under stationarity assumptions, the Sullivan estimator is unbiased and consistent.

The calculation in an abridged life table

The guide states that the method is not very sensitive to the width of age groups, so an abridged life table with five-year bands is usual, closing with an open interval such as 85 and over because survey numbers at the oldest ages are small. Each band's person-years are multiplied by the proportion of people in the healthy state, and the products are summed and divided by the survivors at the starting age.

$$HE_x = \frac{1}{l_x} \sum_{i=x}^{\omega} L_i \, (1 - \pi_i)$$

where $HE_x$ is health expectancy at age $x$, $l_x$ is the number of life-table survivors at exact age $x$, $L_i$ is the person-years lived in age band $i$, $\pi_i$ is the proportion of people in band $i$ who are in the unhealthy state, and $\omega$ is the open-ended final band. Setting every $\pi_i$ to zero gives ordinary life expectancy at age $x$, so the unhealthy remainder is life expectancy minus $HE_x$.

ONS describes the same final step in its healthy life expectancy quality and methods guide, after modelling the prevalence of "good" health by age, sex and area with regression to cope with small samples. Where a survey has a complex design, Jagger and colleagues use weighted prevalence. Surveys that leave out people in institutions can bias results for older populations, and the guide gives a worked case that adds separate data for institutionalised people.

Replacing the yes or no state with utility weights

The same structure accepts a fraction in place of the healthy share. McNamara, Schneider, Love-Koh, Doran and Gutacker pooled EQ-5D-5L data for 14,412 Health Survey for England participants, calculated health-related quality of life norms, and combined them with ONS life tables for 2017 to 2019 using the Sullivan method to derive quality-adjusted life expectancy by age and sex.

$$QALE_x = \frac{1}{l_x} \sum_{i=x}^{\omega} L_i \, \bar{u}_i$$

where $QALE_x$ is quality-adjusted life expectancy at age $x$ in QALYs, $\bar{u}_i$ is the mean health state utility value of the general population in age band $i$, and $l_x$ and $L_i$ are as above. McNamara and colleagues reported values discounted at 0%, 1.5% and 3.5%. Measures that weight ill health by severity follow the same pattern, and the HALE calculation page sets out those steps.

Precision and formal comparisons

Survey prevalence is subject to sampling error, so a Sullivan estimate carries a standard error that is simple to compute. The guide gives the variance formula attributed to Mathers (1991) and notes that, when the survey sample is small relative to the population behind the mortality data, the mortality term is negligible and can be ignored.

$$S^2(HE_x) \approx \frac{1}{l_x^2} \sum_{i=x}^{\omega} L_i^2 \, \frac{\pi_i (1 - \pi_i)}{N_i}$$

where $S^2(HE_x)$ is the approximate variance of $HE_x$, $N_i$ is the number of survey respondents in age band $i$, and $l_x$, $L_i$ and $\pi_i$ are as above. An approximate 95% confidence interval is $HE_x$ plus or minus 1.96 standard errors, and ONS publishes its healthy life expectancy figures with intervals of this form after adjusting for survey design.

For testing whether two health expectancies differ, the guide forms a z statistic by dividing the difference by the sum of the two standard errors, which it describes as a conservative approximation. It adds that a wide open-ended final band biases each estimate, because prevalence of disability rises steeply with age, yet the same bias applies to both populations being compared, so the estimated difference stays unbiased.

Worked example with five bands at age 65

All numbers in this example are illustrative. A period life table starts with 100,000 people alive at exact age 65. A health survey gives the share of each band with disability, the number of respondents, and mean EQ-5D utility.

1. Life expectancy. Total person-years divided by survivors gives 1,730,000 / 100,000 = 17.3 years at age 65.

2. Disability-free life expectancy. Each band's person-years are multiplied by the share without disability, for example 470,000 × 0.75 = 352,500. The five products sum to 1,058,500, so disability-free life expectancy at 65 is 1,058,500 / 100,000 = 10.585 years, or 61.2% of remaining life (10.585 / 17.3 = 0.612). Life expectancy with disability is 17.3 minus 10.585, or 6.715 years.

3. Standard error. For the first band, $L_i^2 \pi_i (1 - \pi_i) / N_i$ is 470,000 × 470,000 × 0.25 × 0.75 / 1,200 = 34,515,625. The five terms sum to 169,526,282, and dividing by 100,000² gives a variance of 0.01695 and a standard error of 0.130 years. The 95% interval is 10.585 plus or minus 1.96 × 0.130, or about 10.33 to 10.84 years.

4. Comparison with a second area. Suppose a second area has disability-free life expectancy at 65 of 9.90 years with a standard error of 0.150. The difference is 0.685 years, the conservative standard error is 0.130 + 0.150 = 0.280, and z = 0.685 / 0.280 = 2.45, with a two-sided p value of about 0.014.

5. Quality-adjusted life expectancy. Weighting by mean utility instead, for example 470,000 × 0.82 = 385,400, gives 1,300,800 quality-adjusted person-years and an undiscounted QALE at 65 of 13.008 QALYs. In this example the figure lies between disability-free and total life expectancy because a year with disability still carries some value, and a year without it carries less than full health.

6. Interpretation. If, purely for illustration, people of this age and sex with a condition could expect 6.5 QALYs on current care, the absolute shortfall is 13.008 minus 6.5, or 6.508 QALYs, and the proportional shortfall is 6.508 / 13.008 = 0.500, both below the lowest cut-offs in Table 6.1 (12 and 0.85), so no severity weight would apply. A real severity assessment would discount both figures and match the age and sex mix of the patient population, as described below.

Uses in economic evaluation and severity

The NICE manual (PMG36), NICE technology appraisal and highly specialised technologies guidance, defines absolute QALY shortfall in section 6.2.14 as the total QALYs the general population with the same age and sex distribution would be expected to have, minus the QALYs people with the condition would be expected to have with current treatment. Section 6.2.17 asks that the population EQ-5D data and survival data come from recent and reliable sources and that shortfall calculations be discounted at the reference-case rate. Under Table 6.1, a QALY weight of 1.2 applies at a proportional shortfall of 0.85 to 0.95 or an absolute shortfall of 12 to 18, and 1.7 applies at 0.95 or more or 18 or more. The general-population term is a Sullivan-type quality-adjusted life expectancy, and McNamara and colleagues present their norms for exactly this purpose, reporting QALE at birth of 68.24 QALYs for men and 68.21 for women. Details of the rule itself are on the QALY shortfall page.

Quality-adjusted life expectancy also serves equity analysis. Love-Koh, Asaria, Cookson and Griffin combined Health Survey for England quality-of-life data with ONS mortality rates to estimate QALE by socioeconomic group and found an inequality at birth of 11.87 QALYs. They present the approach as a refinement of binary measures such as disability-free life expectancy and suited to evaluating the health inequality impact of interventions within cost-effectiveness analysis, the use developed in distributional cost-effectiveness analysis.

A Sullivan estimate describes a population under current period rates and is not a model of a treatment. A Markov cohort model in cost-utility work follows a defined cohort through transitions, which makes it the decision-modelling relative of the multi-state life table, not of the Sullivan method.

Assumptions and where the approximation breaks down

The guide reports that the Sullivan and multi-state methods give similar results when transition rates are smooth and regular over time. Prevalence at a given age reflects past onset at younger ages, so Sullivan estimates may understate or overstate health expectancy when incidence changes rapidly while prevalence stays the same. Mathers and Robine compared the two methods in simulations based on French data and found that the Sullivan method could not detect a sudden change in disability transition rates, while it gave a good estimate of the multi-state value when disability prevalence changed smoothly. Under smoothly rising or falling incidence, the absolute bias was relatively constant with age, so the relative bias grew at older ages. They judged the method generally acceptable for monitoring smooth long-term trends. Imai and Soneji show that the stationarity assumption can be relaxed when a cohort life table and consecutive cross-sectional surveys or a longitudinal survey are available.

Comparability rests on the health measure. The Jagger guide requires the same definitions of health states and age intervals for every population or period compared, and warns that prevalence estimates are very sensitive to how the data are collected.

Several misreadings recur. ONS states that a healthy life expectancy figure does not imply that the first part of life is spent in good health followed by poorer health. The figure is an average total spread across the lifespan. The guide adds that, even where it is biased against a cohort's true experience, a Sullivan figure remains a meaningful indicator of a population's current health, not a prediction for an individual. A QALE norm also depends on the instrument and survey behind its utilities, and McNamara and colleagues report values significantly lower than earlier norms based on the 3-level EQ-5D.

Sources

• Imai K, Soneji S. On the estimation of disability-free life expectancy: Sullivan's method and its extension. Journal of the American Statistical Association. 2007;102(480):1199-1211. https://doi.org/10.1198/016214507000000040
• Jagger C, Van Oyen H, Robine JM. Health Expectancy Calculation by the Sullivan Method: A Practical Guide. 4th ed. October 2014. https://ined-legacy.reves-network.org/fichier/s_rubrique/20182/sullivan.guide.pre.final.oct2014.en.pdf
• Love-Koh J, Asaria M, Cookson R, Griffin S. The social distribution of health: estimating quality-adjusted life expectancy in England. Value in Health. 2015;18(5):655-662. https://doi.org/10.1016/j.jval.2015.03.1784
• Mathers CD, Robine JM. How good is Sullivan's method for monitoring changes in population health expectancies? Journal of Epidemiology and Community Health. 1997;51(1):80-86. https://doi.org/10.1136/jech.51.1.80
• McNamara S, Schneider PP, Love-Koh J, Doran T, Gutacker N. Quality-adjusted life expectancy norms for the English population. Value in Health. 2023;26(2):163-169. https://doi.org/10.1016/j.jval.2022.07.005
• 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. Sections 6.2.14 and 6.2.17 and Table 6.1. https://www.nice.org.uk/process/pmg36/chapter/committee-recommendations-2
• Office for National Statistics. Healthy life expectancy quality and methods guide. Last revised 15 April 2026. https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/healthandlifeexpectancies/methodologies/healthylifeexpectancyqualityandmethodsguide
• Sullivan DF. A single index of mortality and morbidity. HSMHA Health Reports. 1971;86(4):347-354. https://pubmed.ncbi.nlm.nih.gov/5554262/