Accounting for the dead in the longitudinal analysis of income-related health inequalities

Abstract

This paper develops an accounting framework to consider the effect of deaths on the longitudinal analysis of income-related health inequalities. Ignoring deaths or using Inverse Probability Weights (IPWs) to re-weight the sample for mortality-related attrition can produce misleading results. Incorporating deaths into the longitudinal analysis of income-related health inequalities provides a more complete picture in terms of the evaluation of health changes in respect to socioeconomic status. We illustrate our work by investigating health mobility from 1999 till 2004 using the British Household Panel Survey (BHPS). We show that for Scottish males explicitly accounting for the dead rather than using IPWs to account for mortality-related attrition changes the direction of the relationship between relative health changes and initial income position, from negative to positive, while for other groups it significantly increases the strength of the positive relationship. Incorporating the dead may be vital in the longitudinal analysis of health inequalities.

1. Introduction

A strong cross-sectional relationship between individuals’ socioeconomic status and health has been documented in numerous studies (Benzeval and Judge, 2001; Deaton, 2003). Significant income-related inequalities in health have persisted, and even increased, in some western countries over the last decade in spite of considerable improvements in average health status (Van Doorslaer and Koolman, 2004; Kunst et al., 2005). Thus, reducing socioeconomic inequalities in health has become a key policy objective for many European governments (Mackenbach and Bakker, 2002; Strategic Review of Health Inequalities in England Post 2010, 2010). As with any policy objective, it is important to be able to evaluate progress and understand reasons for progress in order to inform future policy (Exworthy et al., 2006).

Often the longitudinal analysis of income-related health inequalities focuses on how the cross-sectional relationship, between income (or some other socioeconomic status indicator) and the morbidity of those currently alive, evolves over time (Lahelma et al., 2002; Gravelle and Sutton, 2003; Kunst et al., 2005). However, in order to evaluate the performance of policies in reducing income-related health inequalities, a measurement framework is needed which simultaneously examines changes in inequality associated with both morbidity changes and mortality (Khang et al., 2004).

The main measure of income-related health inequality within the health economics literature is the concentration index (Wagstaff and Van Doorslaer, 2000). This captures the extent to which good health in any period is concentrated among the rich compared to the poor and is equal to twice the covariance between health and income rank normalised by average health.

Changes in the concentration index (CI) over time have been analysed in the manner of Gravelle and Sutton (2003) using repeated cross-sections, but this does not consider the impact of individuals dying and dropping out of the population between cross-sectional surveys. The changes in cross-sectional income-related health inequality are usually calculated based only on a sample of those in the population at each point in time. Holding all else equal, if the poor are more likely to die than the rich then this will result in an improvement in the cross-sectional CI of those alive in the final period, given that the health of the poor is usually worse on average than the rich, even though such an outcome is likely to be viewed as a policy failure rather than a success.

The longitudinal analyses of the CI have also been conducted using both balanced and unbalanced panel data on individuals where the dead are either excluded from the analysis in all periods or included only in periods where they are alive.¹ One recent longitudinal study, Allanson et al. (2010), tracks the performance of individuals over time by decomposing the change in the CI into “income-related health mobility”, which measures the effect of the relationship between health changes and the initial income rank of the individuals on the change in the CI, and “health-related income mobility”, which measures the effect of the relationship between income rank changes and the final health of the individuals on the change in the CI.² While this allows one to follow the performance of individuals over the period it again does not capture the impact of individuals who are alive in the initial period but dead by the final period, as it uses a balanced sample of only those alive in both periods. Taking mortality into account is important for the evaluation of policies which tackle health inequalities since a failure to do so would ignore perhaps the most important of all health outcomes. In our empirical example, we find that between 1999 and 2004 health changes due to mortality made up over one-third of all absolute health changes in Great Britain.

One option used to deal with attrition in analysing the dynamics of health is to re-weight the sample using inverse probability weights (IPWs) (Contoyannis et al., 2004; Jones et al., 2006; Lorgelly and Lindley, 2008; Van Kippersluis et al., 2009). This involves placing extra weight on those individuals within the final sample who appear to have the same initial characteristics as those who drop out of the sample. However, in the current context, it seems unreasonable to assume that there are some individuals who stay within the sample (stay alive) who could represent the longitudinal experience of those that die, given that death is the most extreme health outcome possible.³ In particular, if those that die between the initial and final period were in general sicker in the initial period, then by construction the sick in the initial period that survive obviously had a better longitudinal experience in terms of their health. Therefore, simply placing more weight on the performance of these individuals would bias the result. In our empirical example we show that for Scottish males explicitly accounting for the dead rather than using IPWs to account for mortality-related attrition changes the direction of the relationship between relative health changes and initial income position, from negative to positive, while for other population groups it significantly increases the strength of the positive relationship.

This paper aims to provide a unified framework for the longitudinal analysis of changes in income-related health inequality due to both morbidity changes and mortality, based on the assumption that the dead are assigned a health state of zero.⁴ First, we provide an overview of the longitudinal methods employed by Allanson et al. (2010). Second, we extend these methods to explicitly account for the impacts of mortality on income-related health inequalities. The paper then uses data from the BHPS (British Household Panel Survey) to perform a forward looking evaluation of the extent to which relative health changes from 1999 to 2004 in England & Wales and in Scotland were progressive in the sense that they have favoured the initially poor. It compares the results when mortality is assumed to be just another form of attrition and adjusted for using IPWs to when mortality is explicitly taken account of in the decomposition analysis. Finally, the paper compares the performance of England & Wales versus Scotland in tackling income-related health inequalities over this period.

2. Decomposition methodology

2.1. Review of Allanson et al. (2010)

The approach is based on the simple observation that any change in income-related health inequality over time must arise from some combination of changes in health outcomes and income ranks. By decomposing the change in CI between two periods, an index of income-related health mobility is provided that captures the effect on short run income-related health inequality of differences in relative morbidity changes between individuals with different levels of initial income. Thus, the measure addresses the question of whether the pattern of morbidity changes is biased in favour of those with initially high or low incomes, providing a natural counterpart to measures of income-related health inequality that address the issue of whether those with better health tend to be the rich or poor. In addition, a health-related income mobility index that captures the effect of the reshuffling of individuals within the income distribution on cross-sectional income-related health inequalities is obtained.

The change in the short run CI between any initial (or start) period s and any final period f of only those alive in both periods is decomposed into two parts⁵:

$$C{I}_{ff}^A-C{I}_{ss}^A=\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{if}^A)-\frac{2}{{\overline{h}}_s^A}\text{cov}(h_{is}^A,R_{is}^A)=\left(\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{if}^A)-\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{is}^A)\right)+\left(\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{is}^A)-\frac{2}{{\overline{h}}_s^A}\text{cov}(h_{is}^A,R_{is}^A)\right)=(C{I}_{ff}^A-C{I}_{fs}^A)+(C{I}_{fs}^A-C{I}_{ss}^A)=M_R^A-M_H^A\text{,}$$ (1)

where $C{I}_{ss}^A$ and $C{I}_{ff}^A$ are the CI's in periods s and f respectively of those individuals who are alive (A) in the final period, and $C{I}_{fs}^A$ is the CI obtained when health outcomes in the final period are ranked by income in the initial period; ${\overline{h}}_f^A$ is the average final health of all those who survive to the final period; ${\overline{h}}_s^A$ is the average initial health of all those who survive to the final period; $h_{if}^A$ is the final health of individual i who survives to the final period; $h_{is}^A$ is the initial health of individual i who survives to the final period; $R_{if}^A$ is the relative income rank⁶ of individual i in the final income distribution of all those alive in the final period, and $R_{is}^A$ is the relative income rank of individual i in the initial income distribution of all those alive in the final period.

In (1), the index $M_H^A=(C{I}_{ss}^A-C{I}_{fs}^A)$ provides a measure of income-related health mobility, which captures the effect of differences in relative morbidity changes between individuals with different initial levels of income. $M_H^A$ is positive (negative) if morbidity changes are progressive (regressive) in the sense that the poorest individuals either enjoy a larger (smaller) share of total morbidity gains or suffer a smaller (larger) share of total morbidity losses compared to their initial share of health, and equals zero if relative morbidity changes are independent of income. $M_H^A$ in turn depends on the level of progressivity and scale of morbidity changes:

$$M_H^A=(C{I}_{ss}^A-C{I}_{fs}^A)=\left(\frac{2}{{\overline{h}}_s^A}\text{cov}(h_{is}^A,R_{is}^A)-\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{is}^A)\right)=\left(\frac{2}{{\overline{h}}_s^A}\text{cov}(h_{is}^A,R_{is}^A)-\frac{2}{{\overline{\Delta h}}^A}\text{cov}(h_{if}^A-h_{is}^A,R_{is}^A)\right)\left(\frac{{\overline{\Delta h}}^A}{{{\overline{h}}_f}^A}\right)=(C{I}_{ss}^A-C{I}_{\Delta s}^A)\left(\frac{\overline{\Delta h^A}}{{{\overline{h}}_f}^A}\right)=P^A{q}^A$$ (2)

where $C{I}_{\Delta s}^A$ is the concentration coefficient of morbidity changes ranked by initial income⁷ and $\overline{\Delta h^A}={\overline{h}}_f^A-{\overline{h}}_s^A$ is the average morbidity change between the two periods of those who are still alive in the final period. Progressivity is captured by the disproportionality index $P^A=(C{I}_{ss}^A-C{I}_{\Delta s}^A)$ and measures the concentration of relative morbidity changes within the poor. Note that if the average morbidity change is negative, then P^A will be negative if health depreciation is progressive (such that relative morbidity losses tend to be larger for rich individuals than poor ones). For any given P^A, the gross redistributive effect is proportional to the scale of morbidity changes $q^A=\overline{\Delta h^A}/{\overline{h}}_f^A$, measured as the ratio of average morbidity changes to average final period health.

The income-related health mobility index $M_H^A$ will not exactly be equal to the change in income-related health inequality because it does not allow for the effect of changes in the ranking of individuals in the income distribution between the initial and final periods. This effect is captured by the health-related income mobility index $M_R^A=C{I}_{ff}^A-C{I}_{fs}^A$ which measures the extent to which the re-ranking of income is related to the final health status of individuals.

While this analysis does examine the performance of individuals over time it is only applicable to a balanced sample and thus cannot take into account those that die between the two periods. We next extend this analysis to explicitly consider the impact of mortality on the change in the CI.

2.2. Accounting for the dead

We now decompose the change in the concentration index across two periods explicitly taking into account that some of the initial population may die and therefore will not be included in the final period evaluation of income-related health inequalities. In this extended decomposition the income-related health mobility index is now defined over the whole population alive in the initial period, and therefore also includes health changes due to mortality. And the health-related income mobility index now captures not only the effect of income re-ranking among survivors but also the effect of the dead not being included in the final period concentration index.⁸

Let $C{I}_{ff}^A$ again denote the final period CI among all those individuals who are alive in the final period whereas $C{I}_{ss}$ is the initial period CI among all individuals, including those who die between the two periods. We decompose the difference between these two cross-sectional CIs;

$$C{I}_{ff}^A-C{I}_{ss}=\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{if}^A)-\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})=\left(\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{if}^A)-\frac{2}{{\overline{h}}_f}\text{cov}(h_{if},R_{is})\right)+\left(\frac{2}{{\overline{h}}_f}\mathrm{cov}(h_{if},R_{is})-\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})\right)=(C{I}_{ff}^A-C{I}_{fs})+(C{I}_{fs}-C{I}_{ss})=M_R-M_H$$ (3)

where ${\overline{h}}_s$ is the average initial period health of all individuals regardless of whether they are alive or dead in the final period; ${\overline{h}}_f$ is the average final period health of all individuals including the dead who are assumed to have a health of zero; $R_{is}$ is the relative income rank of an individual in the initial period (regardless of whether they are alive or dead in the final period); $h_{is}$ is the health of an individual in the initial period regardless of whether they are alive or dead in the final period; $h_{if}$ is the health of an individual in the final period where if the individual is dead they are assumed to have zero health; and $C{I}_{fs}$ is the concentration index of final health ranked by initial income where the dead are also included in the calculation.

The income-related health mobility index $(M_H=C{I}_{fs}-C{I}_{ss})$ captures the effect of differences in relative health changes (including both morbidity changes and mortality) between individuals with different initial levels of income, which depends upon both the level of progressivity (P) of the health changes and the scale of health changes (q).

$$M_H=\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{{\overline{h}}_f}\text{cov}(h_{if},R_{is})\right)=\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{\overline{\Delta h}}\mathrm{cov}(h_{if}-h_{is},R_{is})\right)\left(\frac{\Delta h}{{\overline{h}}_f}\right)=\left(C{I}_{ss}-C{I}_{\Delta s}\right)\left(\frac{\Delta h}{{\overline{h}}_f}\right)=Pq$$ (4)

where $\overline{\Delta h}$ is the average change in health (including both morbidity changes and mortality), and $C{I}_{\Delta s}$ is the concentration index of the change in health (included both morbidity changes and mortality) by initial income rank.

Furthermore $M_H$ can be expanded to consider the separate vertical redistributive effects of health changes due to morbidity changes (health changes for those still alive in the final period) and those health changes due to mortality (the health status of non-survivors dropping to zero):

$$M_H=(C{I}_{ss}-C{I}_{\Delta s})\left(\frac{\overline{\Delta h}}{{\overline{h}}_f}\right)=Pq=\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{\overline{\Delta h}}\text{cov}(\Delta h_i,R_{is})\right)\left(\frac{\overline{\Delta h}}{{\overline{h}}_f}\right)=\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{\overline{\Delta h}}\text{cov}(\Delta h_i^{MB}+\Delta h_i^{MT},R_{is})\right)\left(\frac{\overline{\Delta h^{MB}}+\overline{\Delta h^{MT}}}{{\overline{h}}_f}\right)=\left(\left(\frac{\overline{\Delta h^{MB}}+\overline{\Delta h^{MT}}}{{\overline{h}}_f}\right)\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\left(\frac{\overline{\Delta h^{MB}}}{{\overline{h}}_f}\frac{2}{\overline{\Delta h^{MB}}}\text{cov}(\Delta h_i^{MB},R_{is})+\frac{\overline{\Delta h^{MT}}}{{\overline{h}}_f}\frac{2}{\overline{\Delta h^{MT}}}\text{cov}(\Delta h_i^{MT},R_{is})\right)\right)=\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{\overline{\Delta h^{MB}}}\text{cov}(\Delta h_i^{MB},R_{is})\right)\frac{\overline{\Delta h^{MB}}}{{\overline{h}}_f}+\left(\frac{2}{{\overline{h}}_s}\text{cov}(h_{is},R_{is})-\frac{2}{\overline{\Delta h^{MT}}}\text{cov}(\Delta h_i^{MT},R_{is})\right)\frac{\overline{\Delta h^{MT}}}{{\overline{h}}_f}=(C{I}_{ss}-C{I}_{\Delta s}^{MB})\left(\frac{\overline{\Delta h^{MB}}}{{\overline{h}}_f}\right)+(C{I}_{ss}-C{I}_{\Delta s}^{MT})\left(\frac{\overline{\Delta h^{MT}}}{{\overline{h}}_f}\right)=P^{MB}{q}^{MB}+P^{MT}{q}^{MT}=M_H^{MB}+M_H^{MT}$$ (5)

where $\Delta h_i^{MB}$ and $\Delta h_i^{MT}$, are health changes due to morbidity changes and mortality respectively and are defined so that only one of the measures can be non-zero for any individual.⁹ $\overline{\Delta h^{MB}}$ is the average morbidity change for the whole sample including the dead whom by construction have no change in morbidity and $\overline{\Delta h^{MT}}$ is the average mortality related change for the whole sample including those still alive in the final period who have no change in health related to mortality. The overall redistributive effect can thus be decomposed into the effects of the two sources of health changes, where each component can in turn be expressed in terms of the progressivity and scale of that type of health change relative to the initial distribution of health and income. By definition, $q=q^{MB}+q^{MT}$ where the scaling factor due to mortality will be higher than might be expected since the averages are determined by net rather than gross health changes. This is because health changes due to mortality are all negative while health changes due to morbidity are both positive and negative and will therefore to some extent cancel each other out. It is also easily shown that the overall progressivity index is simply the weighted average of the component progressivity indices, $P=(q^{MB}/q)P^{MB}+(q^{MT}/q)P^{MT}$, with weights determined by the net health change shares.

We now expand the income re-ranking term $M_R$ into two key components. Some of the income re-ranking is due to the dead dropping out of the income distribution (and the remaining being re-ranked as a result) while some income re-ranking still reflects the shuffling of those alive in both periods.

$$M_R=\left(\frac{2}{{\overline{h}}_f^A}\text{cov}(h_{if}^A,R_{if}^A)-\frac{2}{{\overline{h}}_f}\text{cov}(h_{if},R_{is})\right)=\left(\frac{2}{N^A{\overline{h}}_f^A}\sum _i^A(h_{if}^A)\left(R_{if}^A-\frac{1}{2}\right)-\frac{2}{N{\overline{h}}_f}\sum _i^N(h_{if})\left(R_{is}-\frac{1}{2}\right)\right)$$ (6)

Noting that $N^A{\overline{h}}_f^A=N{\overline{h}}_f$ given that those dead in the final period are given a health status of zero, (5) may be re-written as:

$$M_R=\left(\frac{2}{N{\overline{h}}_f}\sum _i^A(h_{if}^A)\left(R_{if}^A-\frac{1}{2}\right)-\frac{2}{N{\overline{h}}_f}\sum _i^A(h_{if}^A)\left(R_{is}-\frac{1}{2}\right)-\frac{2}{N{\overline{h}}_f}\sum _{i=A+1}^N(h_{if}^D)\left(R_{is}-\frac{1}{2}\right)\right)$$ (7)

where $h_{if}^D$ is the final health state of non-survivors which by assumption will be equal to zero. Thus, (7) becomes;

$$M_R=\left(\frac{2}{N{\overline{h}}_f}\sum _i^A(h_{if}^A)(R_{if}^A-R_{is})\right)$$ (8)

We then use the relative income rank for the initial period income, excluding those dead in the final period, $R_{is}^A$, to separate the re-ranking effect due to reshuffling of those still alive compared to the re-ranking effect due to the dead dropping out of the sample.

$$\begin{array}{l}{M}_R=\frac{2}{N{\overline{h}}_f}\sum _i^A(h_{if}^A)(R_{if}^A-R_{is}^A)+\frac{2}{N{\overline{h}}_f}\sum _i^A(h_{if}^A)(R_{is}^A-R_{is})\\ M_R=M_R^{MB}+M_R^{MT}\end{array}$$ (9)

The term $M_R^{MB}=(2/N{\overline{h}}_f){\sum }_i^A(h_{if}^A)(R_{if}^A-R_{is}^A)$ measures the relationship between the change in the relative income rank based on final health, only considering those living in both periods,¹⁰ and the term $M_R^{MT}=(2/N{\overline{h}}_f){\sum }_i^A(h_{if}^A)(R_{is}^A-R_{is})$ reflects the change in the final concentration index due to the dead dropping out of the index.

For $M_R^{MT}$ if those who died were, in general, poorer in the initial period then $(R_{is}^A-R_{is})$ is likely to be negative as those who survive are likely to have been ranked higher in the initial period when those who died were included in the ranking rather than when they were excluded (e.g. if we remove the poorest person from the income distribution then all individual income ranks will fall as they become closer to being the poorest person). And thus, given that the final health of all those still alive $(h_{if}^A)$ must be positive then if those who survived were on average richer in the initial period, then this second term will be negative. As a result the change in concentration indices between the two periods would be less positive or more negative and the final distribution of health, excluding non-survivors would seem less pro-rich than otherwise. If deaths were not related to initial income and instead random then $(R_{is}^A-R_{is})$ and thus $M_R^{MT}$ would be expected to be zero and there would be no effect on the final CI.

3. Empirical analysis

We use both the original decomposition (Allanson et al., 2010) on the balanced sample of those alive in both periods and the new decomposition outlined above that accounts for the dead to evaluate the extent to which relative health changes from 1999 to 2004 of residents in Scotland and in England & Wales¹¹ were biased in favour of the poor or the rich and to explore the other reasons for the observed changes in income-related health inequalities.

We apply the measures separately for males and females and provide a comparative analysis between Scotland and the rest of Great Britain to explore their performances in tackling health inequalities following the devolution of health policy to Scotland in 1999.¹²

3.1. Data

This paper employs data from the annual British Household Panel Survey (BHPS). The BHPS is a longitudinal survey of private households in Great Britain, based on an original, nationally representative sample of 5500 households and 10,300 individuals in 1991. A further 1500 households were added to the survey in both Scotland and Wales in 1999, and 2000 households from Northern Ireland in 2001. In addition from 1994 the BHPS included the UK component of the European Community Household Panel (ECHP) but this sub-sample stopped after 2001. The BHPS is a multi-purpose survey providing information on, inter alia, health, income and wealth, education, employment, housing, household composition, smoking, leisure activities and individual demographics. The current analysis considers all those who answered a full questionnaire in 1999 and then follows these individuals until 2004. The causes of sample attrition between waves, including deaths, are recorded where known.

3.1.1. Health measure

The health measure used is Quality Adjusted Life Years (QALYs) derived from the SF6D instrument (Brazier et al., 2002), which is available for 1999 and 2004 in the BHPS (i.e. Waves 9 and 14). Those who had been reported deceased by friends, family members or other contacts in or before 2004 were given a QALY weight of zero in 2004.

3.1.2. Income measure

The income measure (y) used is equivalised household income, which takes into account the number of adults and children in the household using the McClements equivalence scale (Taylor, 1995). Because the analysis only involves the relative income rank at each point in time there is no need to convert incomes into real terms.

3.1.3. Sample definition

Our initial sample includes all those who answered a full questionnaire in 1999.¹³ Those who were resident in Northern Ireland are excluded from the sample because they are all from the ECHP sub-sample which stopped in 2001 (before our final period). The BHPS provides cross-sectional weights (W) for respondents who answered the full questionnaire in 1999 which are based on the BHPS sample including those from the ECHP.

3.2. Adjusting sample weights for missing data and sample attrition

Some individuals in the sample do not have health reported in the initial period and others do not have reported health and/or income in the final period. A proportion of the latter are because individuals die between the two periods, but deaths are not the only cause of sample attrition and therefore to provide a more accurate picture of the forward looking evaluation of changes in income-related health inequalities we also consider other reasons for sample attrition. We report the differences in initial health, income and age for all those that drop out of the sample in the final period against those who remain in the sample.

To control for missing data and sample attrition we use Inverse Probability Weights (IPWs) (as in Jones et al., 2006 and Wooldridge, 2002). This is done by using probit models to derive the probability with regards to the likelihood of non-response for each individual in the initial sample. These are then used to adjust the initial sample weights such that those who had a higher probability of non-response are given a greater weight, as they are underrepresented in the observed sample. We derive two different alternative final weightings, one which considers death as just another source of sample attrition and one which excludes deaths as a form of sample attrition. Note that while re-weighting the sample to take account of death-related attrition is likely to produce misleading results, re-weighting the sample for other attrition will have no effect on the progressivity and vertical redistribution indices if those that leave the sample have, on average, the same longitudinal profiles as those individuals with similar initial characteristics who remain in the sample.¹⁴ In all calculations we provide weighted indices where the weights are derived from a combination of the cross-sectional sample weights from 1999 and our adjustment due to missing data and sample attrition.

Some individuals who receive a full interview in 1999 have data missing on the required health variables in 1999.¹⁵ In order to correct the sample weightings for this we use IPWs to re-weight the sample based on initial income (y₀), gender, age in 1999 (Age₀) and whether the individual was resident in Scotland (Sco₀) as opposed to England or Wales in 1999. The dependent variable Full_i is equal to 1 if the individual has data on health in 1999 and ${\epsilon }_{1i}$ is assumed to be normally distributed.

$$\begin{array}{ll}Ful{l}_i\hfill & =1\text{if}{\beta }_0+{\beta }_1{y}_{0i}+{\beta }_{2}Gende{r}_i+{\beta }_{3}Ag{e}_{0i}+{\beta }_{4}Sc{o}_{0i}+{\epsilon }_{1i}>0\hfill \\ \hfill & =0\text{otherwise}\hfill \end{array}$$

The predicted probability for each individual $\hat{P}(Ful{l}_i)$ is then used to adjust the original cross-sectional weights W_i to derive the new weights (WN_1i)¹⁶;

$$W{N}_{1i}=\frac{W_i}{\hat{P}(Ful{l}_i)}$$

As mentioned earlier, the BHPS cross-sectional weights provided for 1999 are derived from the BHPS sample including those from the ECHP. The ECHP sample, however, are excluded from the full BHPS after 2001. This combined with the fact that the ECHP sample within the BHPS was oversampled from low-income households (Taylor et al., 2010) means there is a need to correct the 1999 cross-sectional weights for the non-inclusion of the ECHP households in our longitudinal sample. In order to adjust the cross-sectional weights we use another set of IPWs to re-weight the sample based on initial income (y₀), initial health (QALY₀), gender, age in 1999 and whether the individual was resident in Scotland (Sco₀) in 1999, where $NECH{P}_i$ is equal to 1 if an individual was not in the ECHP sub-sample and ${\epsilon }_{2i}$ is assumed to be normally distributed.

$$\begin{array}{ll}NECH{P}_i\hfill & =1\text{if}{\alpha }_0+{\alpha }_1{y}_{0i}+{\alpha }_{2}QAL{Y}_{0i}+{\alpha }_{3}Gende{r}_i+{\alpha }_{4}Ag{e}_{0i}+{\alpha }_{5}Sc{o}_{0i}+{\epsilon }_{2i}>0\hfill \\ \hfill & =0\text{otherwise}\hfill \end{array}$$

The predicted probability for each individual $\hat{P}(NECH{P}_i)$ is then used to adjust the current cross-sectional weights WN_1i to derive the new weights (WN_2i):

$$W{N}_{2i}=\frac{W{N}_{1i}}{\hat{P}(NECH{P}_i)}$$

Next we address the problem of non-random attrition between the initial and final periods. We apply the same IPW procedure as above to take into account those individuals who did not receive a full interview or had missing data on health in the final period 2004. Here we derive two different possible weightings. First, one weighting assumes reported deaths are not attrition, such that, $NMiss{f}_i$ is equal to 1 if the individual had data on health in the final period or had been recorded as having died before the final period.

$$\begin{array}{ll}NMiss{f}_i\hfill & =1\text{if}{\varphi }_0+{\varphi }_1{y}_{i0}+{\varphi }_{2}QAL{Y}_{i0}+{\varphi }_{3}Gende{r}_i+{\varphi }_{4}Ag{e}_{i0}+{\varphi }_{5}Sc{o}_{0i}+{\epsilon }_{3i}>0\hfill \\ \hfill & =0\text{otherwise}\hfill \end{array}$$

The random error term ${\epsilon }_{3i}$ is again assumed to be normally distributed. The predicted probability for each individual $\hat{P}(NMiss{f}_i)$ is then used to adjust the current cross-sectional weights (WN_2i) to derive the new weights (WN_3i):

$$W{N}_{3i}=\frac{W{N}_{2i}}{\hat{P}(NMiss{f}_i)}$$

And the alternate final weightings which assumes death as just another form of attrition, such that, $NMissD{f}_i$ is equal to 1 if the individual had data on health in the final period but had not been recorded as having died before the final period.

$$\begin{array}{ll}NMissD{f}_i\hfill & =1\text{if}{\gamma }_0+{\gamma }_1{y}_{0i}+{\gamma }_{2}QAL{Y}_{0i}+{\gamma }_{3}Gende{r}_i+{\gamma }_{4}Ag{e}_{0i}+{\gamma }_{5}Sc{o}_{0i}+{\epsilon }_{4i}>0\hfill \\ \hfill & =0\text{otherwise}\hfill \end{array}$$

The predicted probability for each individual $\hat{P}(NMissD{f}_i)$ is then used to adjust the current cross-sectional weights (WN_2i) to derive the new weights (WN_4i):

$$W{N}_{4i}=\frac{W{N}_{2i}}{\hat{P}(NMissD{f}_i)}$$

The decomposition of Allanson et al. (2010), which considers only those alive in both periods, is applied using sample weights assuming reported death as just another form of attrition. While, the new decomposition described in this paper, which considers both those alive and dead in the final period, is applied using the sample weights derived assuming reported death is not a form of attrition.

3.3. Robustness

In order to explore the statistical significance of the results and whether or not the results differ across genders and countries we apply a bootstrap sampling procedure 2000 times, where the re-sampling occurs at the clustered level (Primary Sampling Unit) within each major Strata¹⁷ (see Biewen (2002) regarding bootstrap inference for inequality and mobility measures). The mobility calculations are re-estimated for each bootstrapped sample to provide 95% confidence intervals around the concentration and mobility indices and provide significance levels.

To further illustrate that explicitly taking mortality into account in the decomposition rather than just using IPWs is important we also take a very conservative approach and estimate the income-related health mobility assuming death has an implied weight of 0.319 rather than zero, where 0.319 is the lowest QALY weight of anyone still alive in our population in the final period.¹⁸ However, the detailed results provided in the paper assume death is equivalent to a zero QALY weight as this is more consistent with the current health economics literature.

4. Results

4.1. Deaths and sample attrition

Table 1 provides the frequency of reasons for sample attrition for both England & Wales and Scotland, plus some descriptive statistics relating to the initial mean health, mean income and mean age of each group. In England & Wales, 29.5% and 26.4% of the males and females respectively who had answered the full BHPS questionnaire in 1999 failed to answer the full questionnaire in 2004. These included, 4.9% and 4.3% of males and females respectively who were alive in England & Wales in the initial period but who had been reported deceased by the final period. This is compared to Scotland where 35.1% and 35.0% of males and females respectively failed to answer the full questionnaire in 2004 which included 5.0% and 4.9% of males and females respectively whom had died between the two periods. Between 1999 and 2004 health changes related to mortality made up 37% and 29% of all absolute health changes for English & Welsh males and females respectively. While for Scotland, mortality contributed 39% and 34% to all the absolute health changes for males and females respectively.¹⁹

Table 1.

Reasons for sample attrition in 2004 and descriptive statistics for each group in 1999.

Interview status in 2004	Number in each category		Mean health 1999		Mean income 1999 (£,000s)		Mean age 1999
	Scotland	England & Wales	Scotland	England & Wales	Scotland	England & Wales	Scotland	England & Wales
Males
Full interview in 2004	892 (64.9%)	3391 (70.5%)	0.83 (0.12)	0.83 (0.11)	23.8 (24.1)	24.5 (20.5)	44.4 (16.6)	44.6 (16.9)
Dead	69 (5.0%)	234 (4.9%)	0.71 (0.17)	0.70 (0.16)	15.3 (11.2)	16.4 (10.6)	71.3 (12.5)	71.0 (14.0)
Full interview in 2004 (no health data)	12 (0.9%)	44 (0.9%)	0.81 (0.12)	0.80 (0.15)	29.9 (25.0)	23.8 (18.6)	47.3 (16.8)	57.5 (19.7)
Proxy interview	10 (0.7%)	62 (1.3%)	0.86 (0.12)	0.79 (0.16)	28.7 (17.7)	22.3 (21.3)	40.8 (11.6)	44.6 (19.3)
Telephone interview	74 (5.4%)	169 (3.5%)	0.81 (0.14)	0.84 (0.11)	23.3 (13.7)	23.8 (14.6)	43.7 (14.4)	42.0 (17.1)
Refusal	86 (6.3%)	212 (4.4%)	0.84 (0.11)	0.82 (0.13)	21.4 (13.7)	20.0 (12.5)	43.0 (18.5)	41.0 (17.9)
Other non-interview	12 (0.9%)	41 (0.9%)	0.87 (0.06)	0.84 (0.13)	24.4 (16.6)	16.7 (9.1)	28.8 (15.2)	31.8 (13.6)
Age, infirmity or disability	5 (0.4%)	13 (0.3%)	0.61 (0.19)	0.67 (0.13)	13.4 (4.1)	13.2 (10.8)	69.4 (9.9)	72.0 (15.4)
Non-contact	100 (7.3%)	242 (5.0%)	0.81 (0.13)	0.82 (0.14)	17.2 (13.3)	21.0 (17.2)	31.1 (13.2)	32.7 (12.9)
Out-of-scope	34 (2.5%)	83 (1.7%)	0.84 (0.10)	0.86 (0.10)	25.3 (16.8)	26.8 (16.2)	35.8 (13.6)	35.9 (13.4)
Institutionalised	3 (0.2%)	10 (0.2%)	0.77 (0.19)	0.67 (0.11)	14.5 (5.0)	14.3 (12.3)	57.0 (31.2)	73.2 (8.2)
Isolated temporary sample member	14 (1.0%)	155 (3.2%)	0.84 (0.11)	0.82 (0.12)	20.4 (19.8)	31.2 (39.4)	34.6 (10.6)	34.3 (13.9)
Adamant refusal at previous wave	61 (4.4%)	145 (3.0%)	0.85 (0.11)	0.81 (0.15)	24.1 (13.4)	23.6 (18.1)	44.7 (16.5)	43.9 (18.6)
Long-term untraced or withdrawn	3 (0.2%)	8 (0.2%)	0.88 (0.08)	0.86 (0.03)	12.9 (9.5)	29.6 (15.7)	42.0 (12.5)	31.6 (7.3)
Total with health data in 1999	1375	4809
Females
Full interview in 2004	1129 (65.0%)	4122 (73.6%)	0.80 (0.13)	0.79 (0.13)	22.1 (23.9)	22.5 (21.8)	44.7 (17.1)	45.5 (17.4)
Dead	85 (4.9%)	241 (4.3%)	0.63 (0.16)	0.64 (0.16)	14.0 (12.0)	14.1 (9.8)	74.2 (12.5)	75.5 (12.4)
Full interview in 2004 (no health data)	6 (0.3%)	49 (0.9%)	0.82 (0.09)	0.75 (0.16)	16.2 (13.0)	22.4 (12.5)	61.3 (13.0)	52.1 (15.9)
Proxy interview	4 (0.2%)	26 (0.5%)	0.77 (0.10)	0.77 (0.16)	24.7 (12.2)	17.6 (11.3)	41.8 (26.0)	53.1 (22.9)
Telephone interview	79 (4.6%)	211 (3.8%)	0.79 (0.13)	0.81 (0.12)	20.0 (12.3)	22.9 (21.5)	46.8 (15.2)	42.5 (15.6)
Refusal	110 (6.3%)	215 (3.8%)	0.80 (0.14)	0.79 (0.14)	19.3 (12.3)	19.2 (13.8)	44.1 (18.8)	42.1 (19.6)
Other non-interview	23 (1.3%)	39 (0.7%)	0.79 (0.13)	0.78 (0.13)	23.9 (21.2)	18.6 (13.1)	38.0 (19.7)	43.1 (20.8)
Age, infirmity or disability	8 (0.5%)	40 (0.7%)	0.67 (0.18)	0.66 (0.16)	8.4 (4.4)	12.1 (8.2)	70.6 (12.0)	79.4 (9.4)
Non-contact	154 (8.9%)	189 (3.4%)	0.79 (0.13)	0.79 (0.14)	17.0 (13.6)	17.8 (15.8)	29.5 (10.8)	33.0 (14.8)
Out-of-scope	39 (2.2%)	107 (1.9%)	0.84 (0.14)	0.83 (0.11)	22.5 (15.4)	26.4 (16.8)	36.4 (15.2)	34.8 (15.0)
Institutionalised	2 (0.1%)	10 (0.2%)	0.75 (0.12)	0.72 (0.13)	9.2 (0.25)	15.0 (13.3)	77.5 (3.5)	73.8 (19.7)
Isolated temporary sample member	10 (0.6%)	159 (2.8%)	0.78 (0.13)	0.79 (0.12)	15.9 (9.3)	24.3 (23.1)	32.5 (12.8)	33.8 (16.2)
Adamant refusal at previous wave	84 (4.8%)	183 (3.3%)	0.82 (0.13)	0.80 (0.14)	24.6 (16.1)	22.8 (21.0)	44.2 (17.4)	48.4 (19.3)
Long-term untraced or withdrawn	3 (0.2%)	7 (0.1%)	0.88 (0.02)	0.73 (0.14)	11.4 (10.9)	24.4 (20.8)	39.3 (8.4)	33 (14.7)
Total with health data in 1999	1736	5598

Un-weighted statistics. Standard deviations in brackets for health, income and age.

In general, for both countries it can be seen that those who died between the two periods were sicker, poorer and older in 1999 compared to those who survived. Those who did not respond in 2004 due to age, infirmary, disability or because they were institutionalised were also sicker, poorer and older in 1999 but these accounted for only a very small percentage of the total sample (<1%). Compared to England & Wales, those in Scotland who answered the full questionnaire in 1999 were less likely to answer the full questionnaire again in 2004 mainly due to a higher refusal rate (including adamant refusals at previous waves), more people not being contactable and more telephone interviews taking place in Scotland for 2004.

4.2. Sample weights and inverse probability weightings (IPWs)

Appendix A, Table A1, provides the results for each of the probit models which are used to derive the inverse probability weightings (IPW) and thus re-weight the sample for missing initial health data in 1999, ECHP sub-sample exclusion, sample attrition and missing health data in 2004 including death and the sample attrition and missing health data in 2004 excluding death. The results suggest that older individuals who answered the full questionnaire in 1999 were significantly less likely to have their health variable available in 2004 than younger individuals. As expected, those in the ECHP sample were more likely to be poorer, older and sicker in 1999 than those in the regular BHPS sample.²⁰

In both cases, when deaths were either accounted for explicitly or treated simply as another form of attrition, non-response was significantly related to among other things initial health and income. Those who did not give a full interview (apart from those recorded as dead) or did not answer the necessary health questions in 2004 were significantly more likely to be male, younger, poorer, sicker and from Scotland in 1999 than those who either answered the health questions in the full interview for 2004 or were recorded as dead by 2004.

4.3. Decomposition results by treatment of death

Table 2 shows, for Scottish males, that when mortality is treated as just another form of attrition using IPWs, income-related health mobility is positive, which would imply that relative health changes from 1999 to 2004 were progressive such that those with initially low incomes experienced a larger share of the total net health gains compared to their initial share of health (although not significantly so at conventional levels). However, if deaths are explicitly incorporated in the decomposition the result completely reverses with health changes now shown to have been significantly regressive with the poor experiencing a greater relative share of what are now total net health losses compared to their initial share of health. This bias in the income-related health mobility related to the IPWs treatment of deaths is also evident in Tables 2 and 3 for Scottish females, English & Welsh males and English & Welsh females. Thus, income-related health mobility in these cases goes from having a mildly regressive effect when mortality is treated using IPWs to be being 14.5, 6.7 and 4.9 times larger respectively when mortality is explicitly accounted for in the decomposition analysis.

Table 2.

Males: concentration and mobility indices for Scotland and England & Wales.

		Mortality treated as a form of attrition using IPWs		Mortality explicitly accounted for in the decomposition
		Scotland	England & Wales	Scotland	England & Wales	Scotland-E&W differences
Mean health 1999	${\overline{h}}_s^A/{\overline{h}}_s$	0.816***	0.825***	0.817***	0.822***	−0.00559
Mean health 2004 (including the dead)	${\overline{h}}_f$	–	–	0.778***	0.767***	0.0105
Mean health 2004 (excluding the dead)	${\overline{h}}_f^A$	0.823***	0.815***	0.829***	0.820***	0.00882*
Mean income 1999	${\overline{y}}_s^A/{\overline{y}}_s$	22.6***	23.9***	22.6***	23.8***	−1.19
Mean income 2004 (excluding the dead)	${\overline{y}}_f^A$	27.7***	28.3***	28.3***	28.8***	−0.513
Concentration index 1999	$C{I}_{ss}^A/C{I}_{ss}$	0.0198***	0.0153***	0.0198***	0.0175***	0.00237
Concentration index 2004	$C{I}_{ff}^A$	0.0243***	0.0232***	0.0227***	0.0216***	0.00011
Change in concentration index	$\Delta CI$	0.00445	0.00792***	0.00284	0.00413***	−0.00129
Income-related health mobility	$M_H^A/M_H$	0.00155	−0.00382***	−0.0179***	−0.0257***	0.00784
Income-related morbidity mobility	$M_H^{MB}$	–	–	0.000833	−0.00325***	0.00408
Income-related mortality mobility	$M_H^{MT}$	–	–	−0.0187***	−0.0225***	0.00376
Progressivity index	P	0.192	0.310***	0.355***	0.357***	0.00178
Morbidity progressivity	PMB	–	–	0.173	0.249***	−0.0763
Mortality progressivity	PMT	–	–	0.339***	0.381***	−0.0415
Scale factor	q	0.00807	−0.0123***	−0.0504***	−0.0721***	0.0217*
Morbidity scale factor	qMB	–	–	0.00458	−0.0121***	0.0167***
Mortality scale factor	qMT	–	–	−0.0525***	−0.0551***	0.00254
Health-related income mobility	$M_R^A/M_R$	0.00600***	0.00410***	−0.0151**	−0.0216***	0.00655
Due to income re-ranking of those still alive	$M_R^{MB}$	–	–	0.00687***	0.00442***	0.00244
Due to income re-ranking as the dead drop-out	$M_R^{MT}$	–	–	−0.0219***	−0.0260***	0.00410

The “Mortality treated as a form of attrition using IPWs” statistics use sample weights that are derived on the basis that death is just another form of attrition whereas “Mortality accounted for explicitly in the decomposition “statistics use sample weights where death is not treated as a form of attrition and instead explicitly accounted for in the decomposition. The lower and upper 95% bootstrapped percentile confidence intervals from 2000 replications can be found in the working paper version (Petrie et al., 2010). Income is measured in thousands of pounds. Note that when the deaths are excluded and just treated as attrition this places greater weight on those remaining individuals who were poor and sick in 1999 compared to when deaths are explicitly included in the analysis. Death is assumed to have a QALY weight of zero.

^*Significant at 10% level.

^**Significant at 5% level.

^***Significant at 1% level.

Table 3.

Females concentration and mobility indices for Scotland and England & Wales.

		Mortality treated as a form of attrition using IPWs		Mortality explicitly accounted for in the decomposition
		Scotland	England & Wales	Scotland	England & Wales	Scotland-E&W differences
Mean health 1999	${\overline{h}}_s^A/{\overline{h}}_s$	0.786***	0.782***	0.785***	0.780***	0.00440
Mean health 2004 (including the dead)	${\overline{h}}_f$	–	–	0.730***	0.732***	−0.00231
Mean health 2004 (excluding the dead)	${\overline{h}}_f^A$	0.774***	0.774***	0.782***	0.780***	0.00183
Mean income 1999	${\overline{y}}_s^A/{\overline{y}}_s$	21.3***	22.1***	21.3***	22.0***	−0.685
Mean income 2004 (excluding the dead)	${\overline{y}}_f^A$	24.8***	26.0***	25.3***	26.5***	−1.23*
Concentration index 1999	$C{I}_{ss}^A/C{I}_{ss}$	0.0181***	0.0185***	0.0186***	0.0205***	−0.00186
Concentration index 2004	$C{I}_{ff}^A$	0.0240***	0.0276***	0.0220***	0.0261***	−0.00417
Change in concentration index	$\Delta CI$	0.00594*	0.00908***	0.00336	0.00568***	−0.0230
Income-related health mobility	$M_H^A/M_H$	−0.00137	−0.00558***	−0.0198***	−0.0273***	0.00756*
Income-related morbidity mobility	$M_H^{MB}$	–	–	−0.000444	−0.00534***	0.00490
Income-related mortality mobility	$M_H^{MT}$	–	–	−0.0193***	−0.0220***	0.00266
Progressivity index	P	0.0897	0.547***	0.265***	0.419***	−0.154**
Morbidity progressivity	PMB	–	–	0.0271	0.480***	−0.453*
Mortality progressivity	PMT	–	–	0.332***	0.406***	−0.0745
Scale factor	q	−0.0153***	−0.0102***	−0.0747***	−0.0653***	−0.00940
Morbidity scale factor	qMB	–	–	−0.0152***	−0.0104***	−0.00480
Mortality scale factor	qMT	–	–	−0.0543***	−0.0508***	−0.00341
Health-related income mobility	$M_R^A/M_R$	0.00457	0.00351**	−0.0164***	−0.0217***	0.00525
Due to income re-ranking of those still alive	$M_R^{MB}$	–	–	0.00516*	0.00395***	0.00122
Due to income re-ranking as the dead drop-out	$M_R^{MT}$	–	–	−0.0216**	−0.0256***	0.00403

The “Mortality treated as a form of attrition using IPWs” statistics use sample weights that are derived on the basis that death is just another form of attrition whereas “Mortality accounted for explicitly in the decomposition “statistics use sample weights where death is not treated as a form of attrition and instead explicitly accounted for in the decomposition. The lower and upper 95% bootstrapped percentile confidence intervals from 2000 replications can be found in the working paper version (Petrie et al., 2010). Income is measured in thousands of pounds. Note that when the deaths are excluded and just treated as attrition this places greater weight on those remaining individuals who were poor and sick in 1999 compared to when deaths are explicitly included in the analysis. Death is assumed to have a QALY weight of zero.

^*Significant at 10% level.

^**Significant at 5% level.

^***Significant at 1% level.

The further decomposition of income-related health mobility in terms of mortality and morbidity contributions are also provided in Tables 2 and 3. The results show mortality-related health changes as the dominant factor of income-related health mobility. This dominance was in part due to the large contribution that deaths make to the overall scale of net health changes q.²¹ Additionally, the distribution of mortality-related health changes had higher regressivity than morbidity-related changes for males in both regions and for females in Scotland.²²

For all cases, when mortality is treated as a form of attrition using IPWs, health-related income mobility ($M_R^A$) is positive, resulting in a larger final CI. This is because those with lower final health are more likely to have moved down the income rank between 1999 and 2004. When deaths are explicitly accounted for in the decomposition, the effect of income re-ranking among the survivors $M_R^{MB}$ is virtually the same as $M_R^A$. However, this positive effect on the final CI is more than offset by the effect of income re-ranking resulting from the dead dropping out of the population $M_R^{MT}$. This negative effect is because the dead, who were mostly the initially poor, drop out of the income distribution resulting in a lower income rank for the survivors. This produces a smaller final CI compared to if the dead had remained in the final concentration index with their initial income rank. Thus, overall health-related income mobility $M_R$ gives rise to an improvement in the CI of the population alive in the final period even though it is a consequence of the undesirable situation where the initially poor are more likely to die.

From these results we can see that mortality plays a large role in explaining the evolution of income-related health inequalities over time, and the small changes in cross-sectional CI's between 1994 and 2004 hide large underlying changes in health and income at the individual level.

4.4. Sensitivity to mortality assumption

Even when we take a conservative approach and assume mortality equal to the lowest health level achieved of those still living in the final period (0.319) instead of zero, we find large differences in income-related health mobility compared to the estimates obtained by treating deaths as just another form of attrition using IPWs. Given this conservative assumption, Scottish males’ income-related health mobility is still regressive (M_H = −0.00873) when deaths are accounted for explicitly in the decomposition compared to being progressive in the IPW case. While for Scottish females, English & Welsh males and English & Welsh females, income-related health mobility goes from having a mild regressive effect when mortality is treated using IPWs to being 7.4, 3.9 and 2.8 times larger respectively when mortality is explicitly incorporated into the decomposition analysis with the dead given a QALY weight of 0.319.

4.5. Comparing the results across regions

After explicitly accounting for mortality in the decomposition, both males and females in England & Wales have more regressive levels of income-related health mobility than in Scotland, though the differences are only significant at the 10% level for females. Examining the progressivity index and the scale factors for the two regions allows us to explore the extent to which this is a result of differences in the concentration of relative health changes among the poor or in the size of the net health changes, respectively. For males, the relative health losses in England & Wales are significantly larger (10% level) than for Scotland and this appears to drive the higher income-related health mobility. While for females the opposite appears true with the higher progressivity index in England & Wales, which is significantly different at the 5% level, driving the differences and suggesting that the relative health losses in English & Welsh females were more concentrated within the poor than in Scotland.

5. Conclusion

This paper extends Allanson et al. (2010) by outlining a decomposition method in order to explicitly account for mortality in the longitudinal analysis of income-related health inequalities. Excluding deaths from the decomposition analysis may give a misleading picture of the performance in tackling income-related health inequalities. For example, a constant or even increasing cross-sectional concentration index of the population over time may not be a bad outcome if it is a result of efforts to keep the poor and sick alive for longer than previously may have been the case. Moreover, simply re-weighting the sample to account for mortality-related attrition does not solve the problem as those who die between the initial and final periods experience the most extreme health changes possible and are thus significantly different from those with similar initial characteristics whom stay alive.

The decomposition method outlined in the current paper provides a comprehensive picture of the extent to which both morbidity changes and mortality are related to socioeconomic status and how these impact on income-related health inequalities. Using the performance in reducing income-related health inequalities of England & Wales and Scotland from 1999 till 2004 as an example it was found that explicitly accounting for the dead is important and can lead to very different results compared to when mortality is treated as just another form of attrition.

Accounting for deaths in the decomposition analysis shows that the relative health changes for both regions and genders between 1999 and 2004 were significantly regressive such that the initially poor experienced a greater share of the health losses compared to their initial share of health. This was mostly because those who were initially poor were more likely to die between the two periods than the rich. However, as the dead drop out of the population this also contributes to a lower final cross-sectional CI of those still alive in 2004 compared to if those who had died between 1999 and 2004 were included in the final CI but given their initial income rank. If the health system in these regions had done a better job at keeping the poor and sick alive then this would be revealed in our new decompositions as a positive development, by making income-related health mobility less regressive, even though it would have made the 2004 CI appear more pro-rich.

When deaths are explicitly taken into account all of the mobility indices are significant for each region and gender, however, there are few significant differences between regions. For females the significant differences suggest that the relative health losses are more concentrated among the poor in England & Wales compared to Scotland and this led to more regressive levels of income-related health mobility in England & Wales. While for males there is some evidence to suggest that those in England & Wales experienced a larger total relative health loss over the period than their Scottish counterparts, but there was very little difference in terms of how concentrated these relative health losses were among the poor.

While the current methods are a significant improvement on previous work, there are still a number of caveats worth mentioning. In the current analysis we have only considered the longitudinal analysis of those that reported their health and income levels in the initial period and thus have excluded from the analysis some individuals who were alive in the initial period but for some reason may not have completed the full questionnaire.²³ As such the analysis may not be representative of the population as a whole if those that did not answer the initial questionnaire experienced different longitudinal outcomes than those that did. Also by using IPWs for non-mortality related attrition we have assumed that those who did not provide responses to the questionnaire in the final period due to reasons other than mortality experienced similar patterns in terms of health and income rank changes between the initial and final periods as their counterparts with similar characteristics in the initial period. While this assumption is unlikely to hold, we may only expect small differences in the results given that only a small percentage of the sample are in non-mortality related attrition categories that also suggest a poor longitudinal health experience. However, further research could explore the extent to which this assumption impacts on the results.²⁴

It is also worth noting that the comparison of mobility indices across countries and genders may be misleading to the extent that socioeconomic health differentials may be expected to have changed over the period simply due to both the ageing of the sample (Kiula and Mieszkowski, 2007) and changes in other determinants of health which may differ across populations groups and countries. Further research is needed to develop standardized measures of mobility to account for those factors which are outside the control of policy.

While the decomposition in this paper has been applied to the change in the CI over time and therefore measures changes in relative income-related health inequalities it can be easily extended to consider the decomposition of changes in absolute measures or absolute measures adjusted for the bounds of the health variable (Erreygers, 2009) plus other income-related health inequality measurement tools (see Allanson, 2010).

Appendix A.

See Table A1

Table A1.

Probit models used to adjust sample weights.

Dependent variable	Health Data available for 1999	Not in ECHP sample	Health data available for 2004 and not reported dead	Health data available for 2004 or reported dead
Explanatory variable	Coefficient (std error)	Coefficient (std error)	Coefficient (std error)	Coefficient (std error)
Constant	2.89*** (0.112)	0.656*** (0.105)	−0.127 (0.0858)	0.00882 (0.0903)
Age	−0.0113*** (0.00168)	−0.0021** (0.00081)	0.000809 (0.000641)	0.0116*** (0.000687)
Income (1999)	0.000240 (0.00154)	0.0106*** (0.00098)	0.00369*** (0.000663)	0.00231*** (0.000645)
Health (1999)	–	0.649*** (0.110)	0.811*** (0.0901)	0.232** (0.0953)
Male	0.0351 (0.0645)	−0.0011 (0.0300)	−0.106*** (0.0232)	−0.0624*** (0.0240)
Scotland	0.0705 (0.0806)	0.361*** (0.040)	−0.207*** (0.0267)	−0.201*** (0.0275)
Sample size	14,986	14,845	13,516	13,516
Pseudo R2	0.0313	0.0343	0.0123	0.0244

All dependent variables are equal to 1 when they are still included in the sample and 0 when they are to be excluded from the sample. Age refers to the age in 1999. Scotland refers to the fact that the individual was recorded as resident in Scotland in 1999 and are given a value of zero if they are resident in England or Wales in 1999. Note that two individuals do not report their age and therefore these are individual were given their original cross-sectional weights with no adjustments. Income is equivalised annual income measured in thousands of pounds.

^*Significant at 10% level.

^**Significant at 5% level.

^***Significant at 1% level.

.