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National Institute of Economic and Social Research Healthy Life Expectancy in the EU Member States Calculations from the ECHP Ehsan Khoman and Martin Weale

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Measuring HLE The ECHP contains two types of data on health status 1. Self-Assessed Health (SAH). Individuals reporting their health condition over the last 12 months by replying: (i) very good; (ii) good; (iii) fair or (iv) bad/very bad. 2. Hampering Health (HH) condition. Individuals reporting any chronic physical or mental health problems, illnesses or disabilities by replying: (i) none/slight; (ii) some; (iii) severe. Note that for both of these measures, individuals have to be in one of these states at time, t.

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The model - multistate method Most existing work is done using Sullivans method (prevalence based, i.e. dependent on past history) as opposed to the multistate method (incidence based which can adjust to represent current health outcomes). Here we set out an incidence-based method and consider the problem of aligning healthy life estimates with known mortality data.

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The model - multistate method We denote by the transition matrix for an individual aged i. Each element shows the probability that an individual in health state k in year i will be in health state j in year i+1. So [1] where is the probability that an individual is state j conditional on him or her being in state k at birth. In order to calculate expected time spent in each of the health states denoted by,, we have [2]

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The model - alignment (adjusted) method We use probit equations to estimate transition probabilities between different states, with death as a final absorbing state. The EHCP records death very badly in most countries- not distinguishing death from dropping out of the sample. We focus on aligning the transition matrices generated by the probit equations with known mortality rates.

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The model - alignment (adjusted) method We use a least-squares solution to the problem of adjusting the transition matrices. We denote by, n k, the vector constructed from the four columns (for SAH) and three columns (for HH) of the transition matrix,, stacked in order and further consider the vector [3] The vector of survival proportions generated by the vector n can be written as s(n) and the observed survival proportions as s*.

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The model - alignment (adjusted) method We then aim to find as the solution to [4] where is a weighting matrix which we set and (i j). By applying the Taylor expansion we have [5] We then set and. Therefore [6]

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The model - alignment (adjusted) method A recursive algorithm can therefore be constructed so that [7] Since the minimand is evaluated afresh at each value of, an optimum is reached as falls towards zero and the iterations can be stopped when it is close to zero as defined by an appropriate tolerance level. The adjusted vector provides the transition matrices at the jth iteration and when these are consistent with observed survival rates, so too will be the healthy and unhealthy life expectancies derived from them.

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Results - HLE after adjustment Table 1. LE and HLE estimates at age 65 using SAH for men in each EU member state: averages Member State LE (unadj.) HLE (unadj.)LE (adj.)HLE (adj.)Eurostat estimate Years % of LE in ill- health Years % of LE in ill- health Years Belgium Den (30%) Den (40%) Finland n/a Germany Ireland Italy U.K

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Results - HLE after adjustment Table 2. LE and HLE estimates at age 65 using SAH for women in each EU member state: averages Member State LE (unadj.) HLE (unadj.)LE (adj.)HLE (adj.)Eurostat estimate Years % of LE in ill- health Years % of LE in ill- health Years Belgium Den (30%) Den (40%) Finland n/a Germany Ireland Italy U.K

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Results - HLE after adjustment Table 3. LE and HLE estimates at age 65 using HH for men in each EU member state: averages Member State LE (unadj.) HLE (unadj.)LE (adj.)HLE (adj.)Eurostat estimate Years % of LE in ill- health Years % of LE in ill- health Years Belgium Den (30%) Den (40%) Finland n/a Germany Ireland Italy U.K

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Results - HLE after adjustment Table 4. LE and HLE estimates at age 65 using HH for women in each EU member state: averages Member State LE (unadj.) HLE (unadj.)LE (adj.)HLE (adj.)Eurostat estimate Years % of LE in ill- health Years % of LE in ill- health Years Belgium Den (30%) Den (40%) Finland n/a Germany Ireland Italy U.K

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Summary and conclusions In sum, our estimation methods has meant that we have the unique advantage of being able to produce a multistate method of using the ECHP longitudinal survey to predict precise estimates of HLE for the EU member states. Future areas of development could include multistate breakdowns of region, social class and ethnic group.

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