Veintidós años de evolución de las desigualdades socioeconómicas en la mortalidad en la ciudad de Barcelona

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Ir J Med Sci DOI 10.1007/s11845-014-1189-x


Trends in socio-economic inequalities in mortality by sex in Ireland from the 1980s to the 2000s R. Layte • J. Banks • C. Walsh • G. McKnight

Received: 6 May 2014 / Accepted: 19 August 2014  Royal Academy of Medicine in Ireland 2014

Abstract Background It has been recognised for some time that mortality rates vary across social class groups, with lower rates in the higher social classes. Internationally, but particularly in Ireland, many studies on the topic of inequalities in mortality have been confined to men, partly because the most frequently used socioeconomic classification, that based on occupation, can less easily be applied to women. Where research does exist, studies indicate that health inequalities are greater for men than for women. Given the issues around classification, there remains however, little knowledge of the socio-economic inequalities in female mortality in Ireland. Aims Using annual mortality data from the Irish Central Statistics Office over the period 1984–2008 this paper calculates crude and standardised mortality rates per 100,000 population for men and women in different socioeconomic groups (SEG) and examines trends in these over time. This means that for the first time, longitudinal comparisons can be made between men and women across an important period of recent Irish history. Results There is a significant gradient in mortality rates across SEG for both men and women with the absolute and relative differential between professional and manual

R. Layte (&)  J. Banks Department of Sociology, Trinity College Dublin, Dublin, Ireland e-mail: [email protected] R. Layte  J. Banks Economic and Social Research Institute, Dublin, Ireland C. Walsh  G. McKnight School of Computer Science and Statistics, Trinity College Dublin, Dublin, Ireland

occupational groups increasing between the 1980s and 2000s even though the mortality rates were falling over time for all SEG groups for both sexes. Conclusions The results confirm international findings that women generally have smaller gradients than men across SEG with the ratio of male/female differentials (i.e. the ratio of the male SEG rate ratio to the female SEG rate ratio) decreasing between the 1980s and 2000s from 1.25 to 1.07. Keywords

Mortality  Social class  Gender  Time trends

Introduction Research from Ireland has confirmed the international finding that individuals from lower occupational class positions have higher standardised mortality rates than more advantaged individuals [1–4]. Analyses suggest that mortality rates among unskilled manual men may be three times higher than those of professional men but estimates of the rate ratio vary from 1.8 to 3 depending on the period observed and methodological approach. With one notable exception [3], analysis of socio-economic variation in women’s mortality in Ireland has been largely absent. The scarcity of studies of socio-economic differentials in women’s mortality is largely because they rely upon socioeconomic classifications based on occupation that are harder to apply to women. Women are more likely than men to be outside paid employment and often cannot be classified according to their own occupational class. This can mean that occupational details are missing, or that they are classified according to the occupation of others (usually the male partner) in the household. Even where women are classified according to their own occupation, this may not


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be a good indicator of the socio-economic status of their household or their living standards [5, 6]. Research internationally has tended to find socio-economic inequalities in mortality for women but also suggests that these inequalities are smaller among women than men [6, 7]. This pattern may stem from the use of occupational class rather than other measures such as education or income but research suggests that differentials are lower for those variables too. [5, 8, 9] Analyses of trends in socio-economic group (SEG) differentials for women and comparisons of these differentials by sex for Ireland are almost non-existent to date1 due to methodological problems with the measurement of socio-economic group in Irish death records. Although these methodological issues are still problematic, in this paper we rely upon previous work [10] which provides a method for adjusting for these issues and thus allows us to examine trends in mortality rates over time by SEG and make comparisons between men and women.

Previous literature The study by Nolan [11] was the first to examine Irish male mortality differentials using national data from 1981. The results revealed substantial differences in mortality across SEGs. For example, men in the unskilled manual category had a standardised mortality rate (SMR) that was almost three times higher than men in the professional group. The analysis was confined to males aged 15–64 years of age and did not differentiate between different causes of death. O’Shea [2] extended Nolan’s work by combining mortality data from a number of years (1986–1991) and analysing mortality by cause of death. He found similar patterns of mortality by SEG and that there were gradients in mortality by SEG for all of the five major causes of death for males (for example, the ratio of SMRs for cancer between the unskilled manual category and the higher professional group was 2.2:1). Unfortunately, trend analyses by O’Shea [2] between 1981 and 1986–1991 were hampered by the fact that the proportion of death certificates with missing or ‘unknown’ SEG had increased between the periods. International experience [12] and recent Irish work (see below) suggests that deaths with missing or unknown SEG are more likely to be from groups with higher mortality rates. The exclusion of these cases from analysis is likely to lead to bias in the estimation of SEG mortality differentials. The most recent year for which information on socio-economic inequalities in mortality in Ireland have been presented is 2006 [3]. 1 The sole exception to this is CSO’s report on mortality differentials in 2006 using matched data from the Census (CSO 2010).


Taking a different approach the Central Statistics Office analysed all those who died in the 12 month period following the census date in 2006 following a matching process to link death records to census information collected in 2006.2 The overall match rate was 85 %, i.e., 85 % of the death records over the period were matched to a census record. Analyses showed pronounced socio-economic differentials in mortality rates across a variety of indicators such as social class, area deprivation3 and education. For example, males in the unskilled social class had an SMR of 798 per 100,000 population, in comparison to 449 per 100,000 population for professional males. Comparisons between men and women showed that socioeconomic inequalities were higher for men but the differential (rate ratio of 1.77 vs. 1.69) was smaller than that typically found outside Ireland. It is unclear whether the smaller differential by sex stems from the matching process used, the measure of social class used, or actually reflects smaller differentials for Ireland so comparisons using a different methodological approach are warranted. The analysis was also confined to a single year and so no conclusions about trends over time could be inferred. In the following section, we outline the data obtained to examine trends in mortality rates by SEG and sex and an approach for dealing with the methodological issues that this data presents.

Data and methods Population denominators Unlike CSO (2010) where linked death record/census data were used, this paper uses unlinked information from death records and census records. Whilst linked data would provide the best basis for the comparison of death rates between groups such data are only available for 2006 at the moment and it is unlikely that data for previous census years will become available. The available linked data also suffers from missing data problems and this means that there is value in analysing other methodological approaches including the ‘unlinked’ approach adopted here. Calculation of crude mortality rates (CMR) and SMRs in unlinked analysis requires data on the numerator (deaths) and denominator (population) that can then be used to calculate mortality rates by group. Analyses using this approach are aggregate analyses. Denominator 2 CSO. Mortality Differentials in Ireland. Analysis based on the census characteristics of persons who died in the 12 month period after Census Day 23 April 2006. Dublin: CSO, 2010. 3 Each electoral division (ED) in Ireland is assigned a deprivation score, with EDs then grouped into quintiles.

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information, i.e., population counts, is taken from the 1986, 1991, 1996, 2002 and 2006 census of population. As the Irish census occurs every 5 years,4 we replace population counts for non-census years with those of the nearest census year (for example, the relevant population count for 1988 is 1986, while for 1989 it is 1991).5 Population numerators Information on the numerator, i.e., death counts, is available from the death certificate records administered by the CSO. Information on date of death, age (in years), sex, principal economic status (i.e., at work, retired, etc.) and SEG for every death that occurred in Ireland over the period 1 January 1984–31 December 2008 were made available to the authors. SEG refers to the 12-category 1996 SEG schema employed by the CSO. SEG is derived from information on occupation. Children under 15 years of age are classified under the occupation of their parent or guardian, retired individuals are classified under their former occupation and married or widowed women may be classified under their husband’s occupation (if their own occupation is missing). Denominator information on socioeconomic group was coded to a different coding scheme from 1996 onward. In response, a collapsed socio-economic schema was developed using a translation table supplied by the Central Statistics Office which harmonised denominator information across the observation period. The collapsed SEG groups were professionals, employers and managers, clerical and administrative, manual and last, farming. More information on this approach is available elsewhere [10]. To aid comparison of death rates across time periods, year of death was grouped into three categories 1980s (1984–1989), 1990s (1990–1999) and 2000s (2000–2008). Another complication with the numerator data is variation in the proportion of deaths that are classified as having an ‘unknown’ or missing SEG across years. For men the proportion of missing SEG’s varies from 16 to 25 %, for women from 30 to 49 %. For both males and females, the proportion of missing observations was relatively steady up to 1996, and then increased to a peak in 2002 before declining thereafter. The proportion of missing cases is higher among younger age groups and among those not 4 The exception was 2001, in which the census was delayed for a year due to the outbreak of foot and mouth disease in 2001. 5

An alternative approach would be to estimate population counts for non-census years (e.g., by assuming a constant rate of population growth between Census years). See for example, 13. Williams G, Najman J, Clavarino A. Correcting for numerator/denominator bias when assessing changing inequalities in occupational class mortality, Australia 1981–2002. Bulletin of the World Health Organization 2006;84(3):198–203.

currently in paid work.6 This problem is not unique to Ireland; many international analyses have discussed the problem of how to incorporate those with missing information on socio-economic status (in most cases, women are excluded from the analysis for this reason) [2, 12, 14– 16]. However, as those with missing information on SEG are more likely to have higher mortality rates, their exclusion from the analysis results in the underestimation of mortality rates. In this paper, we employ three methods in an attempt to incorporate those with missing information on SEG into the analysis: • • •

Direct adjustment of the observed mortality rates within SEGs to account for differential levels of missing SEGs Imputation of missing SEGs A Baysian approach to imputation producing five different estimates

Full details on the approach to missing data are provided in the appendix to this paper. Each of the methods for dealing with missing data produces a different estimate of the population numerator. We have no a priori reason for choosing any one of the estimates over the others and so we adopt the standard approach taken in multiple imputations [17] and combine the estimates with equal weighting and calculate the mean and standard errors. The combined data allow us to produce estimates of the true crude and standardised mortality rates plus confidence intervals taking account of variation across methods. Methods to deal with the different levels of missing SEGs among men and women improve our ability to compare death rates between SEGs across sexes. As discussed above, one reason for the higher proportion of missing SEGs for women compared to men is the lower level of paid employment among female deaths compared to male. In the CSO data for death registrations inactive or unemployed women should be allocated the SEG of their partner, if married and if the partner has a valid SEG but the proportion of missing cases suggests that this does not happen in all cases. In this paper, we deal with this issue by comparing SEG differentials among men to those among women, but crucially, we differentiate women according to whether they were employed at the time of death. This means that we can examine the sensitivity of the estimates to the definition of the group. Ideally, we would have nonmissing information on the individual’s SEG and that of their partner but this is only available from 2006 onward. However, even where women are classified according to their own occupation, this may not be a good indicator of the socio-economic status of their household or their living standards which are known to contribute to SEG 6 For more detail on the pattern of missings in these data see Layte and Nolan (2014).


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differentials in mortality rates [5, 6]. Nonetheless, given the limitations of the data available to us we suggest that it is better to provide some, perhaps limited analysis rather than no analysis. For our analyses we compare SEG differentials across the following groups: • • • • •

Men aged 15–64 Men aged 65? All women aged 15–64 Employed women aged 15–64 All women aged 65?

This will allow us to examine the sensitivity of the estimate to the coding of women’s SEG. Our expectations about variation in gradients using the different measures will depend upon the distribution of employed women across SEG groups and the extent to which an employed woman’s SEG position is an accurate measure of her living standards and mortality risk. Men are more likely to be found in manual occupations so the adoption of partners SEG for women (i.e. the inclusion of non-employed women in the ‘all women’ analysis) will increase the proportion of manual women. On the other hand, since women with higher SEG jobs are more likely to be in employment this will increase the proportion in higher SEG groups in the analysis of employed women. However, many employed women in lower SEG positions are likely to have better living standards (and thus lower death rates) than their occupation would suggest because they are married to partners in higher SEG positions, with the effect that measured inequalities will be reduced. The main objective of this paper is to compare SEG differentials in Ireland over time from the 1980s to 2000s. There are a number of ways in which mortality may be analysed empirically. The standard approach is to calculate mortality rates. The CMR is simply the number of deaths divided by the population, and is typically expressed per 100,000 population. However, mortality rates are strongly age-related, so it is necessary to adjust mortality rates for the age distribution of the group in question. We therefore, calculate an age-adjusted standardised mortality rate (SMR) for each group, using the direct standardisation approach:

Results Crude mortality rates Crude mortality rates (i.e. not standardised for the distribution of age across groups) and the rate ratios between the professional and other SEG groups by sex are provided in Table 1. This shows that for both men and women there is a gradient in death rate across SEGs with professionals generally having the lowest rate and farmers the highest rate but the pattern is complex. Professionals have lower mortality rates than employers and managers among both men and women but only in the 1980s as shown by the rate ratio larger than unity. In the 1990s and 2000s, employers and managers have lower mortality rates than professionals except among men under 65 and women over 65 where the reversal in position does not occur until the 2000s. Among the intermediate groups, clerical and manual SEGs have higher mortality rates than professionals and employers and managers among men whereas the clerical SEG for women has the lowest mortality rates. These CMRs give us a preliminary view of whether the SEG gradient is steeper for women compared to men, albeit without adjusting for the distribution of age groups. If we confine ourselves to a comparison of the rate ratio of the manual SEG to the professional SEG and compare men and (all) women aged less than 15–64, it does appear that the inequality is lower for women across all years: in the 1980s the rate ratio is 1.46 for women compared to 1.96 for men (a 35 % higher gradient for men—1.96/1.46) and although the difference falls to 15 % by the 2000s, a larger gradient remains for men. As hypothesised earlier, confining the sample of women’s deaths to those of employed women appears to increase the female SEG gradient, but only for the 1990s and 2000s. However, the increase in the rate ratio for women in the 2000s leads to the gradient for women being higher than that for men. However, if we compare men aged 65? to women 65?, it appears that the relationship is reversed. Here gradients are 10 % lower for men in the 1980s and the pattern remains relatively stable into the 2000s.

SMRi ¼ Ri wsi  mi

Standardised mortality rates

Where the SMR for each group i is the sum of the mortality rate in each age group weighted by the proportion of the reference population in each age group. We initially compare CMR between all the SEG groups and provide unstandardised rate ratios before standardising the data to account of variation in the age composition of the different SEG groups and comparing the absolute rate difference and rate ratio, between the professional SEG and the manual SEG.

Table 2 gives the standardised rate difference (SRD) (i.e. the absolute difference in standardised mortality rates) and the standardised rate ratio (SRR) (i.e. the ratio of the standardised mortality rate for manual groups relative to professional) for manual SEG groups relative to the professional SEG group for men and women aged 15–64 with results provided for ‘all’ women and those who were employed. These analyses use a direct standardisation


Ir J Med Sci Table 1 CMR trends by sex, year and age band

Table 2 SRD and SRR by sex and time period (aged 15–64)

Crude mortality rates (per 100,000)

Rate ratio (to professional)






Standardised rate difference (per 100,000) 90s




Men age 15–64





95 % CI











(All) women



Employers and managers







95 % CI



(Active) women











95 % CI





















95 % CI







Men age 65?

100.3** 98.9–01.7

Standardised rate ratio 2.41**








(All) women

Employers and managers







95 % CI




Employed women











95 % CI


















** Difference between professional and manual groups significant at \0.01 Table 3 SRD and SRR by sex and time period (aged 65?)

All women aged 15–64 Professional







Employers and managers
































95 % CI




Employed women aged 15–64




Standardised rate difference (per 100,000)





95 % CI











Employers and managers














Men 95 % CI

1.22** 1.21–1.23

1.34** 1.33–1.34

1.51** 1.50–1.52



















95 % CI











Employers and managers




























Women aged 65?

procedure to adjust for the distribution of age groups across SEGs. Table 2 shows that whilst the absolute rate difference between male SEGs falls across time periods, the comparable figures for women increase as shown by the nonoverlapping confidence intervals. The pattern for women emerges whether we use the figures for all women or just employed women. The lower panel of Table 2 shows that the irrespective of whether we use ‘all’ women or

Standardised rate ratio

** Difference between professional and manual groups significant at \0.01

employed women, women have lower standardised morality rates than men in all time periods. As suggested in Table 1, the standardised rates show that if we examine deaths among active women alone we tend to find higher SEG differentials among women themselves and thus lower male/female rate ratio differentials. The faster growth in SEG gradients among women across periods, however, means that the ratio of male to female SEG gradients falls from the 1980s to the 2000s. For active women for instance, the ratio of male/female rate ratios falls from 1.25 in the 1980s to 1.07 in the 2000s. Table 3 provides standardised rate differences and rate ratios for men and women aged 65?. The findings here are quite different to those found in Table 2 as women have


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higher SEG rate ratios than men in all time periods. The male SEG rate ratio remains between 81 and 83 % of the female ratio from the 1980s to the 2000s even though the differential between SEG groups increases throughout the observation period for both men and women.

Discussion In the period covered by the data analysed for this paper, Ireland experienced rapid economic and social change which may well have had a profound impact on socioeconomic differentials in mortality rates yet there are no analyses of mortality trends since the publication of a group of research papers and reports using deaths up to 1996 [2, 4, 18] and a single analysis of mortality differentials by SEG among women [3]. The primary reasons for the absence of research in this area are the limitations of the data on the SEG of deaths occurring in Ireland. This paper applied a suite of approaches which were discussed in detail in a previous paper [10] to deal with these data issues and produced estimates of both crude and age standardised mortality rates across SEGs for both men and women for the 1980s, 1990s and 2000s. The primary objective of this paper was to provide estimates of SEG differentials for men and women and to examine trends in these over time. Research outside Ireland has found that SEG differentials are, in general, lower among women compared to men but research is still ongoing as to whether the difference in gradients between socio-economic groups are real or an artefact of the manner in which SEG is measured among men and women. Women are more likely than men to be outside paid employment and often cannot be classified according to their own occupational class. This can mean that occupational details are missing, or that they are classified according to the occupation of others (usually the male partner) in the household. Even where women are classified according to their own occupation, this may not be a good indicator of the socio-economic status of their household or their living standards. [5] The fact that smaller differentials are found for women when analyses are based on socio-economic indicators other than occupational group (such as education) suggests that pattern reflects a real differential in the impact of SEG between the sexes [5, 7]. Indeed, research has indicated that the difference in mortality rates by sex may reflect differences in the distribution of cause of death between men and women [6, 19]. Our results showed significant SEG gradients in mortality for both men and women with the absolute and relative differential between professional and manual occupational groups increasing between the 1980s and 2000s even though the mortality rates were falling over time


for all SEG groups for both sexes. This finding confirms a previous finding for male mortality that SEG differentials increased between the 1980s and 2000s [2, 10] and extends this finding to female mortality. The results also confirmed international findings that women generally have smaller gradients than men with the ratio of male/female differentials (i.e. the ratio of the male SEG rate ratio to the female SEG rate ratio) decreasing between the 1980s and 2000s from 1.25 to 1.07. Interestingly, this differential would be reasonably consistent with the finding from analysis carried out using linked census/death registration data for 2006 which found male differentials to be 2 % larger than female differentials [3] for comparisons of the professional/ unskilled manual SEGs (all manual groups other than farmers were combined in our analyses). The decreasing male/female differential would suggest that there has been some convergence in the factors explaining the sex differential in the impact of SEG on mortality risk. These patterns were found for comparisons based both on a measure using all women and one only using those who were employed. However, analyses also found that the differential between the sexes was reversed for those aged 65? where the SEG rate ratios for women were 20 % higher than those found for men. As far as we know, this switch in the pattern among older age groups is novel and requires more analysis. Study limitations These results need to be carefully evaluated in the light of the data problems with the measurement of SEG outlined in an earlier section. The comparability of data on mortality and SEG group across time and between the sexes is clearly an issue given the extent of missing data, its variability across the observation period and the unlinked nature of the numerators and denominators. In response, a suite of different imputation and adjustment methods were developed, each of which provided an estimate that were combined for analysis. We believe that this approach provides a method for dealing with the data issues. Sensitivity analyses showed that though the size of SEG and sex differentials varied when different adjustment methods were applied individually, the overall pattern remained the same giving us some confidence that the results are valid. Study implications The findings from this paper suggest the need for further research to explain why the socioeconomic differential in total mortality is lower for women than men. Research internationally has discounted choice of socioeconomic indicator as the primary source of this differential [6, 20], thus research has begun to focus on male/female differences in the causes of death.

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Studies have shown that inequalities between socioeconomic groups are smaller among women than men for cancer mortality [6, 21] and external-cause mortality [21]. In France for example, the contribution of cancer mortality to male/female differentials by education sharply increased over the period 1968–1996 [22] largely because of the development of a positive association between level of education and breast cancer mortality among women [23]. Socioeconomic inequalities in cardiovascular disease mortality on the other hand have been found to be larger among women than men [6, 21], which, as a leading cause of mortality, tempers male/female differences in socioeconomic inequalities in mortality. However, the contribution of cardiovascular disease to all-cause mortality across European countries (including Ireland) has fallen over time and this could mean that male/female differentials will increase. Findings suggest that sex differences in the social patterning of health behaviours can explain some of the difference in patterns of disease and mortality between the sexes. In particular, the social patterning of the main risk factors for neoplasms (such as smoking and excessive alcohol consumption) is less strong among women than men. This pattern may, however, be changing over time with men shown to be reducing smoking faster than women [24]. Women’s mortality advantage over men continues, however, to increase for causes of death unrelated to smoking such as external causes, suicide or homicide. On the other hand, for heart disease, the social patterning of risk factors such as diet, lack of physical activity and obesity are found to be stronger among women than among men [25]. Further research on the distribution of causes of death between men and women could address this socioeconomic mortality differential. Acknowledgments This research was carried out as part of the research programme ‘trends in socio-economic inequalities in mortality differentials in Ireland 1985–2006’ (2012–2015), HRA-PHS/ 2011/4 funded by the Health Research Board. The authors would like to thank the CSO for access to the data. Conflict of interest The authors have no conflict of interest in the production and publication of this paper. This work was funded using a grant from the Health Research Board (HRB_PHS/2011/4).

Appendix: incorporating observations with missing socio-economic group into the analysis Rubin [17] has identified three potential patterns of missing data: • • •

Missing completely at random (MCAR) Missing at random (MAR) Missing not at random (MNAR)

Data are said to be MCAR if the probability that the case is missing is unrelated to its value or that of any other of the variables in the analysis. Here, MCAR would entail that the value of missing SEGs do not depend on the true value of the SEG (i.e. unskilled manual SEGs are no more likely to be missing than professional SEGs) or other variables such as the year of death. If MCAR could be assumed we would be able to delete the missing cases from the analysis and the results would not be biassed. This assumption does not seem tenable since the extent of missing varies by sex and year at least. MAR defines a situation where the probability of ‘missingness’ does not depend on the true value of the missing variable but may depend on the values of other variables in the model. For example, MAR in our data would imply that the probability of missing does not depend on the true value of SEG but may depend on the value of other variables such as age and year. If the assumption held, we would be able to correct for this missing information using several possible methods. One approach is the reweighting of the observed distribution of SEGs to match a distribution in the true population. A second approach would be to use an indirect adjustment approach where distribution of observed independent variables is used to adjust the mortality rates of the nonmissing SEGs. Kunst et al. [16] have described such a process based on the proportion of unemployed or inactive individuals (see below). A third approach would be the imputation of missing SEGs based upon the observed relationship between non-missing SEG groups and other variables in the data. A model of these relationships would provide a set of parameters from which the true value of missing SEGs could be estimated. Examination of the incidence of missing male SEGs by year suggests that there is an increase in the proportion of deaths among some SEG groups after 2002 that may be related to the fall in the proportion of ‘unknown’ or missing SEGs (this is particularly pronounced among the skilled manual) but the relationship is unclear and statistical tests suggest that it is weak. Given this it is not possible to reject MAR. MNAR occurs where neither MCAR nor MAR holds, that is, that the true value of the missing value itself may be associated with the probability of being missing. In this situation it is not possible to use other information in the data to predict the value of the missing SEG and thus the missing data mechanism itself becomes informative and must be modelled. This can be achieved using a ‘fullyBaysian’ approach to modelling the missing data process. Our inability to reject the MAR assumption means that any of the three approaches above could be used. However, no data are available on the true distribution of SEGs for Irish death records which rules out a simple reweighting


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approach. Given this, we adopt the indirect adjustment approach of Kunst et al. [16] and a multiple imputation approach. The likely possibility of MNAR means that we also adopt a fully Baysian approach. Detail on all three approaches is given below. The direct adjustment of mortality rates First, following Kunst et al. [16], we calculate adjustment factors for the SMRs of those with complete information on SEG to take account of differential missing information. Analysis of the pattern of missing SEGs shows that those records with a missing SEG are significantly more likely to be economically inactive or unemployed and that these groups also tend to have higher SMRs. Kunst et al. [16] developed a method which combines information on the proportion of each group unemployed or inactive from external sources with information from within the data on SMRs among the unemployed or inactive (henceforth referred to simply as ‘inactive’) to create an adjustment factor. The adjustment factor for SEG x is calculated thus:   ¼ 1 þ Pinactive  RRxinactive=active  1 x represents the proportion of the population in where Pinactive x represents each SEG who are inactive and RRinactive=active x the mortality rate ratio of active and inactive groups   =rateactive rateinactive . x x Multiple imputation of missing SEGs Second, using regression analysis, we directly impute SEG for those that are missing such information (see Williams et al. [13], for example). In other words, we re-allocate those with missing information on SEG to one of the six SEGs (later collapsed to five), using the information within the death registration data to carry out the imputation. To impute the missing SEG information we model the relationship between a polytomous-dependent variable with categories q and a set of k predictor variables (x1, x2,…xk), which are either categorical or continuous:   k X Probðcat jÞ ðjÞ ðjÞ log b i Xi ; ¼ b0 þ Probðcat qÞ i¼1 j ¼ 1; . . .; q  1 Here, the logit of q-1 categories of SEG is estimated as a linear function of an intercept, b0 plus a set of predictor variables, Xi. The model is estimated using maximum likelihood and produces a set of predicted probabilities for q-1 categories for each case, the highest of which represents the most probable value of SEG given the other observed characteristics of the case.


A fully Baysian approach Bayesian methodology naturally provides a framework for dealing with a missing data problem where the probability of being missing is associated with the true value of the variable. In analysis of data with missing values, a joint model is built comprising a model of interest and one or more models to describe the ‘missingness’ mechanism. Estimation of the joint model is made through use of Markov-Chain Monte-Carlo (MCMC) methods to sample from the posterior distribution. If the data is partitioned into observed and missing data the joint model can be represented as follows: f ðzðobsÞ; zðmisÞ; mj b; hÞ ¼ f ðmj zðobsÞ; zðmisÞ; hÞ f ðzðobsÞ; zðmisÞjbÞ

• • •

Here f (m| z(obs), z(mis), h) is the model of the missing data mechanism. While f (z(obs), z(mis)| b) is the analysis model. b and h are vectors of unknown parameters for which priors are provided.

With this approach, realistic (informed) assumptions about the mechanism of missingness (or equivalently mislabelling) can be incorporated into the model and the sensitivity of the results of the analysis on assumptions made can be examined. Also uncertainty about imputed values is fully propagated through the model and is reflected in estimates for parameters, whereas results from other approaches fail to reflect this inherent uncertainty. We estimate five different Baysian models, each of which represents an assumption about the nature of the missing data mechanism. Each combines a multinomial logit model which estimates parameters for the effect of year, sex and age group on the probability of the case being in one of five SEGs (one being the reference category) with a different model of the missingness mechanism. An initial model assuming that discrepancies between the numbers of deaths in each group and the population counts proved a poor fit. Given this, four models assumed that the distribution of deaths should approximate that of the census data (conditional on year, sex, age group and SEG). The model then reallocated different proportions (0.9, 0.7, 0.5, 0.3) of the ‘unknown’ SEGs across the 6 known SEGs using the estimated probabilities of the underlying model. These models are referred to as reclassification models. A fifth model assumed that the pattern of ‘unknown’ SEGs was a function of time. Here the model for the missingness mechanism assumed that the pronounced fall in known cases after 2004 means that this period has little or no mislabeling problem. Based on this assumption a

Ir J Med Sci

probability of reallocation of 0.4 using the parameter estimates from the model is used prior to 2005 and 0 thereafter.

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