Decomposition guide Technical report on decomposition

Transcription

1 June 2013 Decomposton gude Techncal report on decomposton Erasmus MC Start date of project: 20 Aprl 2012 Duraton: 36 months 1

2 Table of contents Abstract... 4 Acknowledgements... 5 Introducton... 6 Part 1: The attrbuton method Background of the decomposton method Ratonale of the attrbuton method General prncple of the decomposton method Sullvan and Arraga methods as core of the decomposton method Sullvan method Arraga method Decomposton method Decomposton of lfe expectancy wth dsablty nto mortalty vs. dsablty effect Decomposton of lfe expectancy wthout dsablty nto mortalty vs. dsablty effect Decomposton of mortalty effect by cause Decomposton dsablty effect by cause Decomposton of total effect by cause Dscusson of the decomposton method Dscusson of the decomposton method Part 2: The decomposton software tool Introducton of the software tool Features of the tool General opton 1: Famly of decompostons General opton 2: Dfferent types and formats of nput data Mortalty data: lfe table by sngle-year of age Mortalty data: abbrevated lfe table Dsablty prevalence (proporton) by cause, age and populaton Dsablty prevalence (proporton) by age and populaton Dsablty prevalence (proporton) by age and populaton Dsablty prevalence (proporton) by age and populaton General opton 2: Decomposton of lfe and health expectancy from dfferent startng ages General opton 3: Opton to calculate and decompose partal lfe expectances General opton 3: Opton to calculate and decompose partal lfe expectances How to use the tool Input preparatons and runnng the model Input dataset The Excel nput fle Runnng R Output of the model Part 3: Example Input Input dataset (ASCII or POR-format) Input specfcaton fle (.csv) R syntax fle (.R) Output Illustraton of features of the tool Illustraton of dfferent startng ages Illustraton of partal lfe expectances Illustraton of partal lfe expectances

3 Appendces References

4 Abstract Ths report focuses on ths decomposton tool to decompose dfferences n health expectancy nto the addtve contrbuton of the mortalty vs. dsablty effect, of dfferent age groups and of dfferent causes. The frst part of the report s devoted to the method, whch was prevously publshed n Demography (Nusselder and Looman 2004). The second part focuses on the tool; t descrbes ts man features, explans how to use the tool and provdes some llustratons. Ths techncal report s an updated verson of the techncal report of July The man addtons as compared to the pror verson are: 1) opton to calculate confdence ntervals based on bootstrappng and 2) possblty to start the analyses also from death and populaton numbers n 5-year age groups. The extended tool s avalable on request from the authors (w.nusselder@erasmusmc.nl). 4

5 Acknowledgements Ths document s delvered as part WP9 of the JA EHLEIS. More nformaton on JA-EHLEIS can be found on the webste ( The current work n the JA-EHLEIS bulds upon the work n the EHEMU and EHLEIS project. In the EHEMU project ( ) the decomposton method to decompose dfferences n health expectancy nto the addtve contrbuton of the mortalty vs. dsablty effect, of dfferent age groups and of dfferent causes, was developed. In the EHEMU project ( ) a tool was developed to decompose dfferences n health expectancy. In the current JA EHLEIS ( ) the possbltes to derve confdence ntervals and to start the analyses from death and populaton numbers n 5-year age groups were added. Ths report was prepared by Wlma Nusselder and Caspar Looman. It reflects only ts authors vews; the European Commsson and those who provded nformaton are therefore not lable for any use that may be made. 5

6 Introducton Health expectancy s ncreasngly used to montor populaton health. To explan dfferences n HE between populatons (men vs. women, member states) and over tme, dfferences n HE can be decomposed nto the addtve contrbuton of (1) dfferences n total mortalty vs. dfferences n dsablty, (2) dfferent age groups, and (3) dfferent causes (dseases) (Nusselder and Looman 2004). Ths s the frst of two techncal reports prepared wthn WP9 of the JA EHLEIS, focussng on the decomposton tool. The decomposton tool allows decomposng dfferences n health expectancy nto the addtve contrbuton of the mortalty vs. dsablty effect, of dfferent age groups and of dfferent causes. But the tool can also be used to decompose dfferences n total lfe expectancy by age and/or cause. Dependng on avalable data, dfferent decompostons can be made ( famly of decompostons ). Applcaton of the tool to decompose dfferences n health expectancy requres standard data to calculate health expectancy,.e. a lfe table or populaton and death data to buld a lfe table, and agespecfc prevalence of dsablty. Apart from ths requrement, the tool s flexble. It allows the user to work wth dfferent types and formats of nput data (txt and xls) and has the opton to nclude causes of death and dsablty. The user s free to select dseases and age categores n the analyses. The user also has the opton to obtan addtonal output on the lfe table or on the lfe table decomposton. A new feature s that confdence ntervals based on bootstrappng can be obtaned. The tool s programmed n R, but the user does not need to have any R knowledge to run the program. The decomposton and attrbuton tool are each descrbed n a separate techncal report, whch can be read ndependently. The tools are freely avalable from the author. The current document on the decomposton tool s organsed as follows. In part 1, we gve the background, ratonale and the general prncple of the decomposton method, publshed n Demography (Nusselder and Looman 2004). In Part 2 we descrbe the tool that s based on ths method, ts man features, and explan how to use t. In Part 3 we llustrate the dfferent types of decompostons that are possble wth the tool. To allow ndependent readng of the dfferent parts, some nformaton s gven n more than one part of the report. 6

7 Part 1: The decomposton method 1. Background of the decomposton method Health expectancy ndcators, that combne mortalty and morbdty data nto a sngle composte ndcator, are ncreasngly used to montor the health of populatons and to compare health over tme or between populatons or populaton groups. Health expectancy ndcators share mportant attractve propertes wth lfe expectancy, such as ther measurement n expected years of lfe and ther ndependence from the age structure of the populaton, f small age ntervals are used. An addtonal attractve feature s that health expectancy takes nto account both mortalty and the health status of the survvng populaton and thus provdes nformaton on the length of lfe (addng years to lfe), and the healthfulness of lfe (addng lfe to years). A well-known example s the dsablty-free lfe expectancy (DFLE). DFLE ndcates how many years of the total lfe expectancy a person of a gven age can expect to lve wthout dsablty, and the dfference between the total lfe expectancy and the DFLE s the lfe expectancy wth dsablty. Dfferent varants of DFLE exst, dependng on how dsablty s measured. Next to descrbng dfferences n health expectancy, t s mportant to understand how and why the health of a populaton changes over tme and why dfferences n health exst between populaton groups. Knowng whch age groups and dseases contrbute most to descrbed dfferences n populaton health can pont at potental determnants and can assst n the evaluaton of past trends and health nequaltes. Ths may facltate the defnton of prortes n the feld of publc health, and may mprove the assessment of targeted health prortes. In mortalty research, decomposton (.e. parttonng) technques were developed n the 1980s to assess the contrbuton that age groups make to dfferences n lfe expectancy by Andreev (Andreev, Shkolnkov et al. 2002), Arraga (Arraga 1984) and Pressat (Pressat 1985). A contnuous verson of the method for decomposton of dfferences between lfe expectances by age was developed by Pollard n 1982 and n 1988 compared wth the dscrete approach (Pollard 1988). A general algorthm for the decomposton of dfferences between two values of an aggregate demographc measure, ncludng lfe expectances, was developed by Andreev and colleagues (Andreev, Shkolnkov et al. 2002). Decomposton tools have been wdely used to explan dfferences n the length of lfe between sexes, soco-economc groups and tme. 7

8 Decomposton tools are now avalable to partton dfferences n health expectancy. A method for decomposton of a dfference between two health expectances was ndependently developed n the early 2000s by Andreev (Andreev, Shkolnkov et al. 2002) and Nusselder (Nusselder and Looman 2004). Both methods are based on the Sullvan method and decompose health expectancy nto the addtve contrbutons of mortalty vs. dsablty dfferences and of age groups. The method of Nusselder addtonally decomposes dfferences n health expectancy nto the addtve contrbuton of causes of death and causes of dsablty. The tool presented n ths report s based on the publcaton of Nusselder and Looman n Demography (Nusselder and Looman 2004). 2. Ratonale of the decomposton method The technque to decompose dfferences (or changes) n health expectancy earler publshed n Demography (Nusselder and Looman 2004) s based on the Sullvan method (Sullvan 1971) and s an extenson of the decomposton method for lfe expectancy developed by Arraga (Arraga 1984; Arraga 1989). The Sullvan method s the standard method to calculate health expectancy on a routne bass as t uses data from cross-sectonal survey n combnaton wth mortalty data or lfe tables that are wdely avalable. The Arraga method s frequently used to decompose dfferences n lfe expectancy. Whle Arraga s formula s wrtten n a slghtly dfferent form, t s essentally equvalent to the formulae by Andreev and Pressat (Shkolnkov, Andreev et al. 2006). 3. General prncple of the decomposton method The general prncple s frst to decompose dfferences n years wth (or wthout) dsablty nto the contrbuton of mortalty dfferences (mortalty effect) vs. dsablty dfferences (dsablty effect). The mortalty effect s then further decomposed by age and cause of death usng a modfcaton of the Arraga method. Ths methods assumes that wthn each age group, the contrbuton that a cause of death makes to the change n lfe expectancy between tme t and t+n s proportonal to the contrbuton that ths cause makes to the change n the central mortalty rate n that age group. The dsablty effect s further decomposed by cause of dsablty by usng dsablty prevalence by cause (attrbutons), whch can be obtaned from cross-sectonal data usng the attrbuton tool. For more detals on ths tool and assumptons, see the techncal report on the attrbuton tool (Nusselder and Looman 2010) 8

9 4. Sullvan and Arraga methods as core of the decomposton method 4.1 Sullvan method The Sullvan method s a prevalence-based lfe table technque to calculate health expectancy(sullvan 1971). Accordng to ths technque, the number of person years n the age nterval x, x+ ( L x ) s subdvded nto years wth and wthout dsablty, by multplyng L x by the observed age-specfc dsablty prevalence (.e., the proporton wth dsablty between age x and x+, x ). Summaton of the number of person years wth(out) dsablty across age gves the number of person years-lved beyond age a (T a ) wth(out) dsablty. Dvdng T a wth(out) dsablty by the exact number of survvors at age a (l a ) gves lfe expectancy wth(out) dsablty at age a. The last step can be omtted n a lfe table wth radx 1 (l a =1). For more detals on the Sullvan method to calculate health expectancy, see the Sullvan calculaton gude: Arraga method The Arraga method frst decomposes the dfference or change n lfe expectancy by age. For the sake of transparency, we explan the method n terms of change, hence a dfference between tme ponts, but the user can also read a dfference between populatons or subpopulatons. Arraga dstngushes three dfferent effects of mortalty changes on lfe expectancy: a drect effect (DE), an ndrect effect (IE) and an nteracton effect (I). The drect effect s the change n the number of person years lved wthn a partcular age group ( L x ) as a consequence of a mortalty change n that age group. The ndrect effect s the number of years added to (or removed from) a gven lfe expectancy, because a mortalty change wthn a specfc age group produces a change n the number of survvors at the end of that age nterval. In the presence of unchanged mortalty rates at older ages than the age group under consderaton, the ncrease (or decrease) n the number of survvors at the end of the age nterval results n an ncrease (or decrease) n the number of years lved. Both the drect and ndrect effect take nto account mortalty change n a specfc age group, ndependent of the changes n other ages. Snce n general mortalty changes occur smultaneously n all ages, n addton a small part of the change n lfe expectancy s due to the fact that the addtonal (or fewer) survvors (those responsble for the ndrect effect) do not experence unchanged mortalty at older ages. The effect resultng from the combnaton of the changed number of survvors at the end of the age nterval and the lower (or hgher) mortalty rates at older ages s termed the nteracton effect (I) (Arraga 1984). Addng the drect, ndrect and nteracton effect gves the total contrbuton of each age group to the change n lfe expectancy, or n other words, the decomposton of a change n lfe expectancy by age. In the second step, the contrbuton of each age group s further decomposed by cause of death, 9

10 assumng that wthn each age group, the contrbuton that a cause of death makes to the change n lfe expectancy between tme t and t+n s proportonal to the contrbuton that ths cause makes to the change n the central mortalty rate n that age group. The equatons of the Arraga method are gven the publcaton of Nusselder and Looman (Nusselder and Looman 2004), appendx A. 4.3 Arraga decomposton method appled to Sullvan lfe table Whle the decomposton method to decompose dfferences n health expectancy s based on the Arraga method, to apply the Arraga method to a Sullvan lfe table nstead of a standard (sngledecrement) lfe table for the calculaton of lfe expectancy, addtonal steps are needed. Whereas changes n lfe expectancy are caused by changes n mortalty rates only, changes n health expectancy (calculated wth the Sullvan method) reflect changes n mortalty rates and/or changes n the prevalence of dsablty. The frst extra step s the decomposton nto the contrbuton made by each of these components (.e. the mortalty and dsablty change), whch we refer to as decomposton by type of effect. Next, smlar to the Arraga method, mortalty changes are decomposed by age, and fnally causes of death and causes of dsablty are ncorporated. Whereas the Arraga method decomposes the change n lfe expectancy by age (Arraga 1984) and further by cause (Arraga 1989), here we decompose the change n the number of person years lved n each age nterval by age and cause. Ths modfcaton s needed, because n the Sullvan method the proporton wth dsablty n each age group s multpled wth the number of person years n that age group. For ths reason, we re-expressed the Arraga method. Frst, we made a dstncton between the age group where the mortalty change occurs ( age at orgn labeled as y, y+) and the age group where the person years are added to, or removed from ( age at destnaton, labeled as x, x+). Second, we re-expressed the number of person years lved after age x (T x,) n terms of L x (.e., age-specfc contrbuton to T x ), usng that summaton of L x over age gves T x 5. Decomposton of health expectancy nto mortalty vs. dsablty effect Core of the Sullvan lfe table s the number of person years wth dsablty ( x L x), n age group, x, x+, (where s the length of the age nterval). Ths s the product of the number of person years lved ( L x ) and the proporton wth dsablty ( x ). A change n the number of person years wth dsablty s: x( t) x( tn) Lx( t) Lx( tn) x Lx Lx x (1)

11 The change n the number of person years wth dsablty s the sum of two components: MOR x x( t) x( tn) 2 L x (2) DIS x L x( t) 2 L x( tn) x (3) The frst component, the mortalty effect MOR x s the change n the number of person years wth dsablty due to a change n the number of person years lved. The mortalty effect s the change n the number of person years wth dsablty that would occur f only mortalty rates would change. A negatve MOR x, for nstance, reflects a declne n the number of person years lved wth dsablty n the age group x, x+ due to an ncrease n the mortalty n that age group, or n younger age groups. The second component, the dsablty effect ( DIS x ), s the change n the number of person years wth dsablty due to a change n the proporton wth dsablty (ceters parbus). The dsablty effect n one age group s the change n the number of person years wth dsablty that would occur f only the proporton wth dsablty would change. A negatve DIS x reflects a declne n the number of person years lved wth dsablty n the age group x, x+ due to a declne n the proporton wth dsablty n that age group. For the decomposton of the change n the number of years wthout dsablty (DFLE), the approach s smlar. The only dfference s that the proporton wthout dsablty (.e., 1- x ) rather than the proporton wth dsablty ( x ) s used n the equatons. 6. Further decomposton of mortalty and dsablty effect by age and cause To decompose the mortalty effect ( MOR x, see equaton 2) by age and cause, the change n the number of person years lved ( L x ), s frst decomposed nto the contrbuton made by age and next by specfc causes of death. The dsablty effect s (equaton 3) s already by age. Age-specfc dfferences n prevalence of dsablty orgnate from dfferences n ncdence, recovery and mortalty rates at younger ages, however, based on cross-sectonal prevalence data, these underlyng dynamcs cannot be further assessed. Agan we explan the decomposton for the lfe expectancy wth dsablty. For the lfe expectancy wthout dsablty (DFLE), the proporton wthout dsablty (.e., 1- x ) rather than the proporton wth dsablty ( x ) s used n the equatons. 11

12 6.1 Decomposton of mortalty effect by age Smlar to the Arraga method, we defne the drect, ndrect, nteracton and total effect, though we dstngush between age groups of orgn y, y+ and the age groups of destnaton x, x+. The drect effect ( DE xy ) of a mortalty change n the age group y, y+ between tme t and t+n on the number of person years lved between age x, x+ s expressed as follows: t tn t l y Lx Lx DE xy t tn t (x=y) (4a) la l y l y DE 0 (x >y) (4b) xy The formula for the last open-ended age group s as follows: t tn t l y Tx Tx DE xy t tn t (y=x, open ended age group) (5) la l y l y A mortalty change n the open-ended age group causes only a drect effect. For the other age groups n addton to the drect effect also the ndrect and nteracton effect have to be calculated. The ndrect effect conssts of the number of person years added (or removed) because the mortalty change wthn a specfc age group of orgn produces a change n the number of survvors at the end of that age nterval. The ndrect effect s the effect that would arse f the changed number of survvors would contnue lvng after age y+ as many years as the rest of the populaton before the change n mortalty (.e. the lfe expectancy at age y+ before the change n mortalty). The formula for the ndrect effect IE xy s: t t tn L ly l x y IE xy 1 t tn (x>y) (6) t la ly ly The nteracton effect ( I xy ) s calculated as the dfference between two components: (1) the number of person years added (removed) f the addtonal survvors at age y+ would contnue lvng as many years as the rest of the populaton after the change n mortalty (.e. the lfe expectancy at age y+ after the change n mortalty) and (2) the ndrect effect, beng the number of years added (removed) f the addtonal survvors would contnue lvng under the old mortalty regme. The frst component labeled OE xy s calculated as follows: 12

13 tn t t L l y l x y OE xy t tn tn (x>y) (7) la l y l y Usng equaton (6) and (7), the nteracton effect ( I xy ) s: I xy OE IE (x>y) (8) xy xy The total contrbuton of a mortalty change n each age group of orgn y, y+, to the change n the number of person years lved between age x and x+ ( L x ) s calculated as follows: TOT xy DE IE I (x>y) (9) xy xy xy The total effect by age of orgn y, y+ gves ths nformaton the decomposton by age. 6.2 Decomposton of mortalty effect by cause For the decomposton of the total effect ( TOT xy ) by cause of death k, we follow the Arraga method for the decomposton by cause of death (Arraga 1989). It s assumed that the contrbuton of the change n mortalty from each cause n age group y, y+ to the change n the number of person years n age group x,x+ (or: total lfe expectancy n the Arraga method), s proportonal to the contrbuton of ths cause to the change n the central mortalty rate n the age group y, y+. We multply TOT xy wth the contrbuton of the mortalty change n the age group y, y+ attrbutable to cause k, C yk, to obtan the decomposton by cause: TOT xyk TOT C (x >y) (10) xy yk where TOT xyk s the contrbuton of a mortalty change due to cause k n age group y, y+ to the number of person years lved between age x, x+ (where y x). C yk s calculated usng: tn tn t t R yk M y Ryk M y C yk tn t (11) M y M y where M t y s the central mortalty rate at age y, y+ at tme t, R t yk s the proporton of deaths from cause k n the total number of deaths n the age group y, y+ at tme t and n s the dfference between the frst year of observaton and the second. The contrbuton of cause k to the change n the number of person years lved between age x, x+ ( TOT xk ) s obtaned as follows: TOT xk y a, x TOT xyk (12) 13

14 The mortalty effect by cause ( MOR xk ) s obtaned as follows: MOR xk x( t) x( tn) x( t) x( tn) Lxk 2 2 TOT xk (13) Summaton of MOR xk over age x gves the total mortalty effect by cause,.e. the change n health expectancy that would occur f only mortalty from that specfc cause k would have changed. In order to avod that the results of the decomposton depend on whether the frst or second tme pont s used as reference, we averaged the components of the dfference between tme t and t+n (wth t+n as baselne) wth the respectve components of the dfference between populaton t+n and t (wth t as baselne). Ths addtonal step was proposed by Andreev and Pressat (Shkolnkov et al. 2001); the orgnal Arraga method dd not nclude ths step. 6.3 Decomposton dsablty effect by cause For each age group, n order to decompose the dsablty effect ( DIS x ) by cause of dsablty, the change n the proporton wth dsablty ( x ) needs to be attrbuted to dfferent causes of dsablty k. Dsablty by cause can ether be obtaned from dsablty surveys, or can be estmated usng ndvdual-level data on chronc dseases and dsablty from health surveys usng the attrbuton tool (Nusselder and Looman 2010). Smlar to causes of death, causes of dsablty (attrbutons) should be addtve, that s, the sum of all causes should equal total dsablty. The change n the proporton wth dsablty decomposed by cause can be obtaned by subtracton of the proporton of dsablty for each cause k at tme t from that at tme t+n, or: xk tn xk t xk (14) where t+n xk s the proporton wth dsablty from cause k n age group x, x+ at tme t+n, and t xk s the proporton wth dsablty from cause k n age group x, x+ at tme t. And where: (15) x k xk Substtuton of the change n the proporton wth dsablty by cause n equaton 5 gves the dsablty effect by cause ( DIS xk ): DIS xk L x(1) 2 L x(2) xk (16) Summaton of DIS xk over x gves the total dsablty effect by cause,.e. the change n health expectancy that would occur f only dsablty from that specfc cause k would have changed. 14

15 6.4 Decomposton of total effect by cause Summaton of the mortalty and dsablty effect by cause gves the decomposton of the total change n health expectancy by cause. 7. Calculaton of confdence ntervals Parametrc bootstrappng was used to obtan confdence ntervals (Efron and Tbshran 1994). Bootstrappng, sometmes called re-samplng, constructs a new dataset ( replca ) whch contans a random sample of the orgnal observatons wth replacement. Ths mmcs the stuaton where you would have repeated the collecton of your data. Ths leads to dfferent estmates of the parameters. If ths s repeated for nstance 1000 tmes t gves an mpresson of the uncertanty of the parameters. Non-parametrc bootstrap makes no assumptons about the dstrbutonal form of the populaton or probablty (parent) dstrbuton. However, when t s known from whch famly of dstrbutons the parent dstrbuton belongs to, parametrc bootstrappng can be used. For the parametrc bootstrap, one selects the dstrbuton type one beleves the data to come from and then fnd the parameters for that dstrbuton. In case of parametrc bootstrappng, each observaton s replaced wth a sample taken at random from the ftted populaton dstrbuton. In ths way a bootstrap sample replca s generated, whch has the same (sample) sze as the orgnal data. Then the outcomes (parameters) for whch confdence ntervals are needed are calculated from the bootstrap sample. Ths samplng process s repeated many tmes, yeldng a dstrbuton of each outcome. In the decomposton analyss, mortalty rates (derved from number of deaths and md-year populaton, total or by cause) and the prevalence of dsablty (number of dsabled as fracton of total populaton are used. The number of deaths s generally consdered to be Posson dstrbuted and the prevalence bnomally dstrbuted. 8. Dscusson of the decomposton method A few ssues may mert extra explanaton or dscusson. The decomposton method s based on the Sullvan method, because ths s the standard method to calculate health expectancy on a routne bass. Health expectancy derved from the Sullvan method reflects the current health composton of a real populaton adjusted for mortalty. The major dsadvantage of the Sullvan method s that t ntegrates observed prevalence data on dsablty (.e. 15

16 stock data) n a lfe table whch s based on ncdent data on mortalty (.e. flow data). As a result the Sullvan method generally does not produce a pure perod ndcator such as (perod) lfe expectancy (Barendregt, Bonneux et al. 1994; Van de Water, Boshuzen et al. 1995; Mathers and Robne 1997) The devaton from a pure perod ndcator can ntroduce bas. A change n health expectancy may have been caused by prevalence reachng ts equlbrum values, nstead of a real change n populaton health. Consensus seems to exst that serous bases are only expected to occur when sudden, large changes (Barendregt, Bonneux et al. 1994; Van de Water, Boshuzen et al. 1995; Mathers and Robne 1997). Nonetheless, conclusons about changes n health expectancy assessed wth the Sullvan method requre some cauton. Less concern s warranted for comparsons between populaton groups (such as men and women) n a perod wthout large changes (such as n the Netherlands n the 1990s). That the decomposton method s based on the Sullvan method has two consequences for the nterpretaton of the outcomes. Frst, the decomposton method quantfes to what extent dfferences n dsablty prevalence and total mortalty (n each age group) contrbute to health expectancy dfferences, but does not ndcate to what extend these dfferences are due to dfferences n agespecfc transton rates nto and out the dsabled state and mortalty rates from the nondsabled and dsabled state. Second, the dsablty effect by age shows to what extend dfferences n the prevalence of dsablty n specfc age groups contrbute to the dfference n health expectancy. Prevalence of dsablty n each age group s the net result of transtons n and out of dsablty and nto death from brth up to that and ncludng that age group. These underlyng dynamcs cannot be further assessed, and the dsablty effects by age ponts where age-specfc dfferences n prevalence occur, but not at whch age or age group they orgnate. 16

17 Part 2: The decomposton software tool 1. Introducton of the software tool The decomposton tool allows the user to decompose dfferences n health expectancy dfferences nto the addtve contrbuton of mortalty vs. dsablty effects, of dfferent age groups and of dfferent causes. The software tool mplements the decomposton method as publshed by Nusselder and Looman n Demography (Nusselder and Looman 2004). Ths decomposton method s based on the Sullvan method to calculate health expectancy and s an extenson of the Arraga method (Arraga 1984) to decompose dfferences n total lfe expectancy. The decomposton tool frst decomposes the dfference (or change) n health expectancy at certan age nto mortalty and dsablty effects. Ths s called decomposton by type of effect. The mortalty effect s the dfference n health expectancy due to a dfference n the number of person years lved caused by a dfference n total mortalty up to and ncludng that age. The dsablty effect s the dfference n health expectancy due to a change n the proporton wth dsablty. The mortalty effect s further decomposed by age of orgn usng an adjustment of the Arraga method. If data on dsablty and mortalty by cause are ncluded, the tool allows further decomposton by cause of death and dsablty. The decomposton s developed to decompose dfferences n health expectancy by type of effect, age and cause, but the tool allows dfferent decompostons. These range from decomposton of lfe expectancy by age, usng only mortalty data by age and sex, to the full decomposton of health expectancy by type of effect, age and causes, usng mortalty and dsablty data by age, sex and cause. The tool decomposes dfferences n health or lfe expectancy between two populatons. Two populatons can refer to dfferent populatons (e.g. member states), dfferent subpopulatons (e.g. gender, soco-economc groups) but also to dfferent tme perods. The decomposton tool s flexble as t allows the user to work wth dfferent types and formats of nput data, both for the mortalty and the dsablty data. The user can obtan detaled outcomes on the lfe table calculatons and the Arraga decomposton method. The decomposton software s programmed n R, but all the user-specfed nput s communcated to the R program though an Excelfle (saved as csv-fle ), therefore user does not need to have any R knowledge to use the program. Before we explan n more detal how the tool works, we frst explan the features of the tool. 17

18 2. Features of the tool The decomposton tool has the followng features. Frst, the tool allows makng dfferent decompostons. Second, the tool offers the possblty to use dfferent types of nput data, both for the mortalty data and the dsablty data, allowng usng exstng databases maxmally. Thrd, the tool offers the possblty to decompose lfe and health expectancy from dfferent startng ages. Fourth, t allows the decomposton of partal lfe and health expectances. 2.1 General opton 1: Famly of decompostons The tool allows dfferent decompostons. Table 1 presents the possble decompostons, dependng on whether or not data are avalable on causes of death, on prevalence of dsablty, and on prevalence of dsablty by cause (attrbutons). Table 1 Famly of decompostons LIFETABLE data: Always Causes of death Dsablty No Yes No nformaton 1. LE dfference by age 2.LE dfference by cause Also - LE dfference by age Prevalence by age Prevalence by cause (attrbutons) 3.HE dfference by type of effect Also: - LE dfference by age - Dsablty effect by age - Mortalty effect by age 5.HE dfference: dsablty effect by cause of dsablty Also: - LE dfference by age - HE dfference by type of effect - Dsablty effect by age - Mortalty effect by age LE wth dsablty by cause (of dsablty) 4.HE dfference: mortalty effect by cause of death Also: - LE dfference by age - LE dfference by cause - HE dfference by type of effect - Dsablty effect by age - Mortalty effect by age 6.HE dfference by cause (death and dsablty) Also - LE dfference by age - LE dfference by cause - HE dfference by type of effect - Dsablty effect by age - Mortalty effect by age - Dsablty effect by cause - Mortalty effect by cause - Total effect by cause - LE wth dsablty by cause of dsablty 18

19 2.2 General opton 2: Dfferent types and formats of nput data The tool offers the possblty to use dfferent types of nput data. For the lfe table data four optons exst: 1. Number of deaths and populaton at rsk by sngle-year of age and populaton (varant DPs) 2. Number of deaths and populaton at rsk by fve-year of age and populaton (varant DPa 3. Lfe table by sngle year of age and populaton (varant LTs) 4. Abrdged lfe table (5 year or larger groups) by populaton (varant LTa) For dsablty data, the followng optons exst: 1. Dsablty prevalence by age, populaton and causes (attrbutons) 2. Dsablty prevalence (proporton) by age (sngle year of age, as or age groups, ag ) and populaton 3. No dsablty data (only decomposton of total lfe expectances) For mortalty data, the followng optons exst: 1. Causes of death (numbers) by age groups and populaton 2. Wthout causes of death The famly of decompostons, n combnaton wth dfferent data choces, yeld a large number of varants for whch the decomposton tool can be used. Table 2 presents the names we use for each varant n ths techncal report. The tool can read lfe table data and dsablty prevalence by age n txt format (easy to obtan from the Human Mortalty Database) and Excel format (easy to obtan from the EUROHEX Database). Attrbutons must be a text fle; all other fles must be n Excel format. 19

20 Table 2 Namng of decompostons (jobs) Varant DPa DPs LTs 1 nput decomposton 1-DPa.csv nput decomposton 1-DPs.csv nput decomposton 1-LTs.csv 2 nput decomposton 2-DPa.csv nput decomposton 2-DPs.csv nput decomposton 2-LTs.csv 3 nput decomposton 3-DPa-as.csv nput decomposton 3-DPa-ag.csv 4 nput decomposton 4-DPa-as.csv nput decomposton 4-DPa-ag.csv nput decomposton 3-DPs-as.csv nput decomposton 3-DPs-ag.csv nput decomposton 4-DPs-as.csv nput decomposton 4-DPs-ag.csv nput decomposton 3-LTs as.csv nput decomposton 3-LTs ag.csv nput decomposton 4-LTs as.csv nput decomposton 4-LTs ag.csv 5 nput decomposton 5-DPa-cause Input decomposton 5-DPs-cause nput decomposton 5-LTs cause.csv 6 nput decomposton 6-DPa-cause Input decomposton 6-DPs-cause nput decomposton 6-LTs cause.csv DPs=deaths or person years by sngle year of age DPa=deaths or person years by age group LTs=lfe table by sngle year of age LTa=lfe table by age groups: abbrevated or abrdged lfe table ag=dsablty by age group as = dsablty by sngle year of age cause= dsablty by cause 20

21 2.2.1 Lfe table data: Number of deaths and populaton at rsk The frst varant of data to construct the lfe table s based on the number of deaths and populaton at rsk, by sngle year of age of fve year age groups. For the populaton at rsks the md-year populaton can be used, or the exposure to rsk populaton. The md-year populaton s smply obtaned by takng the average of the populaton (at a gven age) n two adjacent years (e.g. n combnaton wth deaths 2006, the md-year populaton s the average of the populaton per January 1 st 2006 and per January 1 st 2007). Informaton on the number of deaths and populaton per January 1 st by sex and sngle year of age s avalable from EUROHEX ( or the Human Mortalty database ( We use n ths document and n the fle names the abbrevaton DP for ths varant, where D stands for deaths and P for populaton. Based on the number of deaths and populaton at rsk, a lfe table s bult accordng to the Sullvan calculaton gude A smplfcaton n the varant startng from the number of deaths and populaton at rsk s that deaths are assumed to occur n the mddle of the age nterval, also n the age group 0-1 years. Lfe and health expectances at brth based on ths varant may therefore be slghtly dfferent from the Eurostat method, that also uses nformaton on the number of brths). To avod ths, the user can start from an exstng lfe table (see next secton) or specfy ax the fracton of the year alve. If no ax s provded t s set to Lfe table data: lfe table by sngle year of age The tool can also start from a publshed sngle-year lfe table. Ths assures that the decomposed lfe or health expectancy s dentcal to a publshed one, and hence avods slghtly dfferent outcomes because of dfferent assumptons n the lfe table. Also ths s practcal for users who made already a (Sullvan) lfe table themselves and want to decompose health or lfe expectancy based on ths lfe table. However, wth ths varant bootstrappng to obtan confdence ntervals s not possble. To start from the lfe table, the user should provde nformaton on age, lx (number of survvors at age x) and dx (number of death between age x and x+1) and the populaton Lfe table data: abrdged lfe table The tool can also start from a publshed abrdged lfe table. An abrdged lfe table ncludes age groups, n stead of sngle year ages. Smlar to the varant startng from a lfe table by sngle year of age, ths assures that the decomposed lfe or health expectancy s dentcal to an already publshed lfe or health expectancy or a lfe table already made n Excel. To start from the abrdged lfe table, the user should 21

22 provde nformaton on age, lx (number of survvors at age x) and dx (number of death between age x and x+1). The tool requres that the age classes n the abrdged lfe table are the same as those used n the fle wth mortalty data by age and cause and n the fle wth the dsablty prevalence data. We advse to use 5-year age groups. Larger age groups can be used, but decrease the accurateness of the lfe table. If the user wants to use larger age ntervals, mortalty by cause of death should be classfed nto these larger age ntervals as well. If no nformaton on causes of death s used, the user should provde n the nput specfcaton fle the cut-levels of the age categores, also for the stuaton of 5- year age groups. The reason that the user has to specfy age groups also n the stuaton of 5-year age groups s that age ntervals may be dfferent for the last age group, for nstance 85+ vs and Dsablty prevalence (proporton) by age, populaton and cause Dsablty prevalence by cause can be derved wth the attrbuton tool (Nusselder and Looman 2010). The attrbuton tool generates a fle (wth extenson mrc, or n case of bootstrappng wth mrcxx) that can serve as nput to the decomposton tool Dsablty prevalence (proporton) by age and populaton In case dsablty prevalence by cause s not avalable, the tool can be used wth dsablty prevalence by age to decompose health expectancy nto the addtve contrbuton of the mortalty vs. dsablty effect and of ages. In combnaton wth sngle year lfe table, dsablty prevalence by sngle year of age (referred to as S ) or by age group (referred to as A ) can be used. In combnaton wth an abrdged lfe table only prevalence of dsablty by age groups can be used No nformaton on dsablty In case no nformaton on dsablty s avalable, the tool can stll be used to decompose total lfe expectancy by age, and f nformaton on mortalty by cause s present, by cause of death Causes of death by age and populaton Data on causes of death are generally avalable, for nstance from the WHO mortalty database ( Causes of death can be entered as numbers or as proportons. 2.3 General opton 3: Decomposton of lfe and health expectancy from dfferent startng ages The tool can calculate and decompose health and lfe expectances from any startng age, as long as ths startng age s a cut-off pont n the lfe table and all data are avalable for the ncluded ages. Thus for a lfe table wth age classes, 5-9, 10-14, the lfe table can start at age 5, 10, etc. but not 12. When 22

23 nformaton for causes of death and/or dsablty, f ncluded n the analyss, s avalable only above a certan age, the user should select ths or a hgher age to start the lfe table. 2.4 General opton 4: Partal lfe expectances The tool can calculate and decompose partal health and/or lfe expectances. A partal lfe expectancy s a lfe expectancy wthn a specfed age range, for nstance, lfe expectancy between age 15 and 80 years of age. 2.5 General opton 4: Confdence ntervals usng bootstrappng The tool can calculate confdence ntervals usng bootstrappng for the varants that start from number of deaths and the populaton at rsk. For varants ncludng dsablty prevalence (ag or as n varant 3 or 4), the number of cases n the survey should be provded by the user. In case nformaton on dsablty by cause s used (cause n varant 5 or 6) the attrbuton tool should also be run wth bootstrappng wth the same number of bootstraps so that an mrcxx fle s made wth all the attrbuton tables for all the bootstrap samples. 3. How to use the tool The decomposton tool s programmed n R. All the user-specfed nput s communcated to the R program though the nput specfcaton Excel-fle (saved as csv-fle ). Hence, the user does not need to have any R knowledge to use the program. To use the decomposton tool n R you need: I. Input datasets wth lfe table or mortalty data, dsablty data (optonal) and cause of death data (optonal) II. Input specfcaton fle (csv format or txt format) III. R syntax: decomposton.r If R s not already nstalled, do frst the followng: Go to Choose the system you are usng, probably Wndows(95 and later) Clck base Choose: Other bulds Choose prevous releases Choose verson R

24 Further follow the nstructons. Havng R nstalled on the computer, do the followng: Put the scrpt and data fles n one folder. Check that the separator s a comma (check the computer), va start\settngs\control panel\regonal optons. 3.1 Input preparatons and runnng the model The user only has to specfy n the R syntax the path and name of the Excel nput specfcaton fle (csv-fle). As an alteratve to the Excel nput specfcaton fle, a text nput specfcaton fle can be used, though ths s not the preferred opton. The nput specfcaton fle has to nclude the name and locaton of the data fles wth the lfe table data, dsablty data (optonal) and cause of death data (optonal). Addtonally ths nput specfcaton fle ncludes all the user choces for the optons provded. Runnng a specfc nput specfcaton fle results n an analyss and output-fle. Ths wll be further named as job. The output s wrtten to fles (text format), whch can be read by e.g., TextPad, Notepad, or MS-Word. Users can opt for addtonal output Input datasets Here follows a descrpton of the nput datasets for each varant of the decomposton tool (Table 3). All data need to be provded by populaton, as the decomposton tool always decomposes dfferences between two populatons. A populaton can be a country, but also one gender, or populaton for specfc calendar year or perod. 24

25 Table 3 Overvew of data needed for each varant All varants Addtonal nformaton INFORMATION TO CONSTRUCT THE LIFE TABLE INFORMATION TO CONSTRUCT THE LIFE TABLE Populaton and deaths by sngle year (DPs) or age groups (DPa), or lfe table by sngle year (LTs) or by age groups (LTa) DISABILITY CAUSE OF DEATH Varant Varant 2 - Number of deaths by cause, age and populaton Varant 3 ag Varant 3 as Varant 4 ag Varant 4 as Proporton dsabled by age (age group) and populaton Proporton dsabled by age (sngle-year) and populaton Proporton dsabled by age (age group) and populaton Proporton dsabled by age (sngle-year) and populaton Proporton dsabled by age - - Number of deaths by cause, age and populaton Number of deaths by cause, age and populaton Varant 5 Attrbutons by age and populaton - A pont of specal attenton s the consstency of age groups f dfferent nput data sets n one analyss (job) are used. The mnmum requrements for each varant are specfed below. Varants usng more data also provde the results or the less data demandng varants. The name of each job s gven n brackets. All nput data should be provded by age and populaton. Age should be ncluded n the nput fle as a number (e.g. 70) and not a label, such as or 70+. Varant 1: Only lfe table data for decomposton of total lfe expectancy - number of deaths and populaton at rsk by sngle of age and populaton (1-DPs) OR - number of deaths and populaton at rsk by fve year age groups and populaton (1-DPa) OR - lfe table by sngle year of age (1-LTs) OR - lfe table by age group(1-lta) It s noteworthy that the output of ths varant becomes also avalable when varants 2-6 are analysed. 25

26 Varant 2: Lfe table and mortalty data by cause for decomposton of lfe expectancy by age and cause of death - number of deaths and populaton at rsk by sngle of age and populaton (2-DPs) OR - number of deaths and populaton at rsk by fve year age groups and populaton (2-DPa) OR - lfe table by sngle year of age (2-LTs) OR - abrdged lfe table (2-LTa) AND - number of deaths by cause of death and age (age group) and populaton The age classes n the cause of death fle determne the age classes n the abbrevated lfe tables that wll be constructed f the tool starts from number of deaths and populaton by sngle year of age, or from a sngle year lfe table. It s noteworthy that the output of ths varant becomes also avalable when varants 4 and 6 are analysed. Varant 3: Lfe table and dsablty data by age for decomposton of health expectancy by type of effect - number of deaths and populaton at rsk by sngle of age and populaton (3-DPs-as) OR - number of deaths and populaton at rsk by fve year age groups and populaton (3-DPa-ag) OR - lfe table by sngle year of age (3-LTs-as; 3-LTs-ag) OR - abrdged lfe table (3-LTa-ag) AND - prevalence of dsablty by sngle year of age (3-PDs-as, 3-LTs-as) or age group (3DPa-ag, 3-LTaag, 3-LTs-ag) and populaton If prevalences by sngle year of age are avalable, but the lfe table s abrdged (LTa), no nformaton on the populaton szes by sngle year of age s avalable. Therefore prevalences cannot be aggregated nto age groups. For ths reason the combnaton of abrdged lfe table (LTa) or deaths and populaton by age groups (DPa) and prevalence of dsabled by sngle year of age (as) s not possble. 26

27 The user has to specfy the age groups n the abbrevated lfe table for varants startng from sngle year lfe table data. These should be the same as the ones used n the fle wth data on dsablty prevalence by age group. Also the age groups n the abrdged lfe tables have to match wth the prevalence data. It s noteworthy that the output of ths varant becomes also avalable when varant 6 s analysed. Varant 4: Lfe table and dsablty data by age and mortalty data by cause for decomposton of mortalty effect by cause - number of deaths and populaton at rsk by sngle year of age and populaton (4-DPa-as, 4-DPa-ag) OR - number of deaths and populaton at rsk by fve year of age and populaton (4-PDa-ag) OR - lfe table by sngle year of age (4-LTs-as; 4-LTs-ag) OR - abrdged lfe table (4-LTa-ag) AND - prevalence of dsablty by age (sngle year ( as or age group ag ) and populaton AND - number of deaths by cause of death, age and populaton The age classes n the cause of death fle determne the age classes n the abbrevated lfe tables that wll be constructed f the tool starts from the number of deaths and populaton by sngle year of age, or from a sngle year lfe table. The age classes n the fle wth dsablty prevalence by age group should be dentcal to these age groups. Also the age groups n the abrdged lfe tables have to match wth the prevalence data. It s noteworthy that the output of ths varant becomes also avalable when varant 6 s analysed. Varant 5: Lfe table data and dsablty prevalence by cause for decomposton of dsablty effect by cause - number of deaths and populaton at rsk by sngle year of age and populaton (5-PDs-cause) OR - number of deaths and populaton at rsk by fve year of age and populaton (5-PDa-cause) OR - lfe table by sngle year of age (5-LTs-cause) OR - abrdged lfe table (5-LTa-cause) AND 27

28 - prevalence of dsablty by cause (and age group) and populaton The user has to specfy the age groups n the abbrevated lfe table for varants startng from sngle year lfe table or deaths and populaton data (5-DPs-cause; 5-LTs-cause). These should be the same age groups as used n the prevalence by cause data. It s noteworthy that the output of ths varant becomes also avalable when varant 6 s analysed. Varant 6: All nput data for full decomposton of health expectancy - number of deaths and populaton at rsk by sngle year of age and populaton (6-DPs-cause) OR - number of deaths and populaton at rsk by fve year of age and populaton (6-DPa-cause) OR - lfe table by sngle year of age (6-LTs-cause) OR - abrdged lfe table (6-LTa- cause) AND - prevalence of dsablty by cause (and age group) and populaton AND - number of deaths by cause of death and age (age group) and populaton The age classes n the cause of death fle determne the age classes n the abbrevated lfe tables that wll be constructed f the tool starts from the number of deaths and populaton by sngle year of age, or from a sngle year lfe table. The age classes n the dsablty prevalence by cause, should be dentcal to these age groups. Sequences of causes of death and causes of dsablty should be the same (not necessarly the labels). The tool s delvered wth example datasets. The dataset wth the lfe table nformaton preferably should contan the names of the populatons. These names are used n the output fle. The datasets can nclude more nformaton than actually used n the decomposton analyses, as the user should specfy whch columns are used. Ths allows one dataset to be used for more analyses. The only excepton s the fle wth dsablty data by cause (attrbuton n mrc fle), where all nformaton s used. A dataset can have more rows before the real data start, but f more than one ttle row s used, a # should be gven to all except one ttle lne. The program expects the data to start at the second row wthout #. We recommend un-experenced users to follow the format of the examples. 28

29 3.1.2 The Excel nput specfcaton fle The Excel nput fle s n a csv (comma separate varables) format, that can be saved n excel, choosng save as, csv comma delmted. If questons pop up your screen (startng wth nput fle already exsts and nput fle may contan features that are not compatble wth csv format, the user answers two tmes yes ). As alternatve an nput specfcaton fle n txt format can be used. It should be organsed n two columns, separated by An example of the txt nput fle s gven below: The user may only change the content of the frst column. Except for the oblgatory questons, the frst column may be left empty or NA (not applcable) may be entered. The second column, and more mportantly, the rows should never be changed. The nput fle the user specfes: Q1: Enter the name of your default drectory. End always wth a \ (back slash) Q2: Enter the name for output fle. You may end ths fle wth ".out" Q3: Enter type of nput: 1 for populaton and number of deaths; 2 for sngle year lfe table; 3 for abrdged lfe table Q3a: enter "t" f ths nput s gven n txt fles, "c" f ths nput s gven n csv-fles. Use same format for both populatons Q4-1: Enter the name of the fles wth data specfed n Q3 for the FIRST populaton Q4-2: Enter the name of the fles wth data specfed n Q3 for the SECOND populaton Q5-1: Enter column numbers dependng on fle type, specfed n Q3 for fle type =1 n Q3 for the FIRST populaton (see also row 23 to row 25) Q5-2: Enter column numbers dependng on fle type, specfed n Q3 for fle type =1 n Q3 for the SECOND populaton (see also row 23 to row 25) 29

30 Enter for fle type =1 n Q3 the column numbers for: populaton, age n sngle years, md-year populaton, deaths, and f applcable ax Enter for fle type =2 or 3 n Q3 the numbers of the columns wth the: populaton, age, lx, dx, and LX. Where: ax s the fracton of the year alve. If no ax s provded t s set to 0.5. lx s the number alve at the begnnng of the age nterval dx s the number of deaths n the age nterval Lx s the number of person years lved wthn the age nterval Q6-1: Enter the fle name wth cause-specfc deaths for the FIRST populaton (f no causes of death, enter "NA") Q6-2: Enter the fle name wth cause-specfc deaths for the SECOND populaton (f no causes of death, enter "NA") Q7: Enter the numbers of the columns wth deaths per cause n the fles specfed n Q8 and Q9 Q8: If no fles wth causes of death are ncluded n Q6-1 and Q6-2: enter cut-levels for frst year of age classes for the abrdged lfe tables. These should match wth prevalence age classes f avalable. Q9: enter CAUSE f you have dsablty data by cause (attrbutons), AGE f you only have dsablty data by age or NA f you have nether Q10: f you have prevalences of dsablty by age only (Q9=AGE): enter "S" for sngle-year prevalences or "G" for prevalence by age group. If you have no prevalences, enter "NA" Q11-1: enter the flename wth dsablty by cause (mrc fle from attrbuton tool) or dsablty by age (proporton) for the FIRST populaton. If ths s a text fle, use ".txt" Q11-2: enter the flename wth dsablty by cause (mrc fle from attrbuton tool) or dsablty by age (proporton) for the SECOND populaton. If ths s a text fle, use ".txt" Q12-1: If you have proporton of dsablty by age: enter column numbers for age (sngle years or age group) and for proporton of dsablty for the FIRST populaton IF BOOTSTRAP ALSO NUMBERS OF RESPONDENTS (UNWEIGHTED). Q12-2: If you have proporton of dsablty by age: enter column numbers for age (sngle years or age group) and for proporton of dsablty for the SECOND populaton. IF BOOTSTRAP ALSO NUMBERS OF RESPONDENTS (UNWEIGHTED). Q13: Enter age to start lfe table. For partal lfe expectances also enter after "," the last age group to be ncluded (age group specfed n fles wth cause-specfc deaths or Q8), e.g. "50,70" Q14: Enter 0, 1, or 2 to specfy the level of detal n the output. IF BOOTSTRAP GIVE NUMBER OF REPLICAS Q15: Enter T for results n E-notaton (for nstance e-02) or F for roundng to 4 decmals (0.0705) 30

31 For partal lfe expectances you have to enter n Q-13 both the lowest age of the startng age group and last age group. Please be aware that the age groups here are the ones used n the cause-of death fles, or, f these fles are not used, those specfed n Q-8. And be aware that snce you work here wth age groups, 0,70 means from 0-4 up to and ncludng Runnng R The R-syntax decomposton fle s ready to use. Users only need to specfy the path and name of the nput specfcaton fle. Frst open t. Ths can be done n two ways: 1. In Tnn-R: fle / open /, (or double clck on name) 2. In R: fle/ open scrpt/ open Then the path and name of the nput specfcaton fle should be entered or adapted n the lne that starts wth flen. E.g. flen <- "d:\\decomman\\decom 1 DP.csv" Be careful wth the double \\ The user can nclude more nput fles for dfferent runs. Always the last one wll be used by the program. The user can also put # before the lnes wth nput fles not to be used n the specfc run. The program then reads ths lne as comment. When runnng several jobs, we suggest clearng the R console (n Tnn-R: controllng R/clear Console). 3.2 Output of the model The output depends on the varant of the decomposton tool used and on the selecton of optonal output on the lfe table or on the Arraga method. We descrbe here the output of the full decomposton,.e. both by cause of death and by cause of dsablty, referred to as varant 6. Ths varant ncludes also the results of all decompostons that need fewer data. Other varants that provde the descrbed output are gven between brackets. The output of varant 1-5 conssts of parts of the output on varant 6. Part I of the output serves for data nspecton and documentaton so the user can easly see whch data fles, populaton, varables and specfcatons were used. The user should check ths n case an error occurs whch s recognzed by a blue error message n the console wndow after runnng R, but also to assess whether the analyss s correctly specfed. It provdes: 31

32 Path and name of output fle and of nput specfcaton fle (csv fle). Path and names of datasets used to construct the lfe tables (.e. fle wth death and populaton (DPs, DPa), or fle wth lfe tables (LTs or LTa), and frst rows of these fles. In the output, populaton s here referred to as t and t+n, as n the orgnal publcaton of Nusselder and Looman (Nusselder and Looman 2004), but populaton can refer to any type of populaton, as long as there are two populatons specfed. We recommend the user to put the name of the populaton n the fle wth the lfe table data, by ncludng a column wth n the column headng populaton and n the rows (at least n the frst row wth data) the name of the populaton (e.g. Italan males). Path and names of datasets wth cause-specfc deaths for each populaton (varant 2, 4, and 6 only), and names of the selected causes of death. Specfcaton of addtonal output. Specfcaton of age where the lfe table calculatons have to start, and f partal lfe expectances, where the lfe table calculaton ends. Table wth dsablty by cause (attrbutons) n each populaton (varant 5 and 6). As varant 6 ncludes both causes of death and dsablty t s mportant to check that the causes are the same and n the same order. For ths reason both are lsted. 32

33 Part II of the output gves the followng results of combnng nput data and descrptve calculatons. Lstng of the combned nformaton from the dfferent nput fles by age and populaton. Ths ncludes: - deaths by causes and total deaths - lfe table nformaton: lx. Lx. Tx, dx and mx - proporton dsabled (p) Descrptve calculatons of lfe expectancy, total (all varants), wth and wthout dsablty (varant 3-6) and dfferences. Part III gves supplementary output for the decomposton of lfe expectancy by cause. It gves: Proporton dsablty by cause Lfe expectancy wth dsablty by cause In contrast wth the other decompostons, whch are decompostons of dfferences or changes and based on a comparson of two populatons, ths s the number of years wth dsablty wthn each populaton. Ths output could be easly generated wth the tool and s useful as such, but s not part of the decomposton tool that focuses on dfferences or changes n health expectancy. Part IV of the output presents the outcomes of the decomposton analyss, startng wth: Total lfe expectancy (also varants 1-5) and lfe expectancy wthout and wth dsablty (also varant 3-5) n each populaton Dfferences n total lfe expectancy (also varants 1-5) and lfe expectancy wthout and wth dsablty (also varant 3-5) between the two populatons. These dfferences are the values for the second populaton mnus those for the frst populaton (reference populaton). Thus, f lfe expectancy n the frst (reference) populaton s 80 years and n the second populaton 82, the dfference s +2. If the user prefers the other populaton to be the reference, the user should n the nput change the nformaton provded for the frst and second populaton. Next are the core outcomes from the decomposton analyses gven: Frst the decomposton of total lfe expectancy by age s gven (also varant 1-5). Ths shows whch age groups contrbute most to the dfference n lfe expectancy. The sum of these age specfc contrbutons s the total lfe expectancy. Next s gven the contrbuton of the dsablty and mortalty effect (also varant 3-5). The mortalty effect s the dfference n health expectancy due to a dfference n the number of person years lved, caused by a dfference n total mortalty up to and ncludng that age. The dsablty effect s the dfference n health expectancy due to a dfference n the proporton wth dsablty. 33

34 Then the dsablty and the mortalty effect by age are gven (also varant 3-5). The dsablty effect s provded by age. It s mportant to realze that whle age-specfc dfferences n prevalence of dsablty orgnate from dfferences n ncdence, recovery and mortalty rates at younger ages, based on cross-sectonal prevalence data, these underlyng dynamcs cannot be further assessed, and the dsablty effects by age pont where age-specfc dfferences n prevalence occur, but not where they orgnate. Fnally the dsablty effect decomposed by cause (also varant 5) and mortalty effect decomposed by cause (also varant 2 and 4) are presented. As varant 6 yelds both the decomposton of the dsablty effect by cause and of the mortalty effect by cause, the sum s also gven. The yelds the contrbuton of specfc causes, both as cause of death and cause of dsablty to the dfference n years wth and wthout dsablty. For ths applcaton s t crucal that the dsease enttes of the causes of death and causes of dsablty are comparable. The output ends wth gvng the same nformaton on decomposton by cause n another sequence. Instead of provdng separate tables for the moralty, dsablty and total effect, separate tables are provded for lfe expectancy wthout dsablty, lfe expectancy wth dsablty and total lfe expectancy. If bootstrap s chosen, at the end the bootstrap results wll be presented. The followng nformaton s gven: o Number of replca s o Table: short name of the varable o Row: row labels of the orgnal output o Column: column labels of the orgnal output o Value: value from the analyses wthout bootstrappng o Bmean: mean from the analyss wth bootstrappng o Blow: lower lmt of 95% confdence nterval o Bhg: hgher lmt of 95% confdence nterval 34

35 Part 3: Example The llustraton focuses on dfferences n lfe expectancy wth and wthout dsablty between Dutch and Italan women. As dsablty measure n the example s used the Global Actvty Lmtaton Index (GALI) based on the queston For the past sx months at least, to what extent have you been lmted because of a health problem n actvtes people usually do? As dsabled s consdered severely lmted and lmted, but not severely. The example llustrates the full decomposton of dfferences n lfe expectancy wth and wthout dsablty by causes of death and dsablty and age, usng data on populaton and deaths to construct the lfe table (decom-6_pd_cause). Ths varant ncludes also the results of all varants that need fewer data. Varants startng from lfe tables (LTs or LTa)) nstead of the number of deaths and populaton (DPs or DPa) have smlar output. Example fles are avalable from the authors on request, see Appendx 1. Smlar data fles can be easly derved from databases avalable on the nternet, ncludng the EUROHEX ( Human Mortalty database ( and WHO database ( Only dsablty data by cause are not generally avalable and were be derved wth the attrbuton tool based on the SHARE survey ( For more detals on dsablty by cause, see the techncal report on the attrbuton tool (Nusselder and Looman 2012). 1. Input 1.1 Input datasets (ASCII or POR-format) Table 4 shows the names of the datasets for the full decomposton of health expectancy (by age, mortalty vs. dsablty effect and cause), usng the number of deaths and populaton to construct the lfe table (decom6_pd_cause). The tool always uses two populatons, here Dutch and Italan women. 35

36 Table 4 Datasets used n the example of decom6_pd_cause Netherlands Italy Populaton and deaths NL-DP-F-2004.csv IT-DP-F-2004.csv Prevalence of dsablty by cause (and age group) NL-F-attrb.mrc IT-F-arrtb.mrc and populaton Number of deaths by cause, age and populaton NL-CoD-F csv IT-CoD-F csv The mrc fle s output of the attrbuton tool. The frst rows of each fle are gven below. For IT-DP-F-2004.csv: Age Year populaton-2 Deaths PY at rsk twomen twomen twomen twomen twomen twomen twomen Includng the populaton name, here as example twomen, s recommended as ths name s prnted n the output fle. For IT-F-attrb.mrc: nn dsab backgrnd heart stroke cancer copd dabetes muskulo other The mrc fle s made wth the attrbuton tool and can be opened n Notepad or TextPad. 36

37 For IT-CoD csv: Age Heart Stroke cancer COPD dabetes muskul other All Input specfcaton fle (.csv) The nput specfcaton fle of varant 6 (nput decomposton 6-DPa-cause.csv) s gven n Table 1. Appendx 2 shows the names of the nput specfcaton fles for the examples llustratng the other varants of the decomposton tool. The zp-fle ncludng several examples of cvs and output fles s avalable from the authors. Table 1: Example of nput specfcaton fle Q7: excel changes 2:8 nto 02: R syntax fle (.R) The R program specfes the locaton (path) and name of the nput specfcaton fle. Dfferent nput specfcaton fles can be ncluded, for example: flen <- "D:\\decomphandledng\\nput decomposton 1-DPs.csv" flen <- "D:\\decomphandledng\\nput decomposton 2-DPs.csv" flen <- "D:\\decomphandledng\\nput decomposton 3-DPs-ag.csv" flen <- "D:\\decomphandledng\\nput decomposton 4-DPs-ag.csv" flen <- "D:\\decomphandledng\\nput decomposton 6-DPs-cause.csv" Here the R program uses the last one, thus nput decomposton 6-DPs-cause.csv" and creates the output fle specfed n Q2 n each nput specfcaton fle. The double \\ and quotes are necessary. 37

38 2. Output Part I of the output serves for data nspecton and documentaton Each output fle wth the locaton (path) and name of the output fle and name of the csv fle, for example. [1] "> > > OUTPUT PART 1: DATA INSPECTION AND DOCUMENTATION < < <" [1] "d:\\decomman\\decomp-6-dp-cause.out" [1] "D:\\decomman\\nput decomposton 6-DP-cause.csv" Ths s followed by the nput fles that are used to make the lfe tables and the frst rows of these fles [1] "fles wth deaths and years-at-rsk:" [1] "d:\\decomman\\nl-dp-f-2004.csv" [1] "d:\\decomman\\it-dp-f-2004.csv" [1] "label, age, Px and Dx for populaton t:" populaton.1 age PY.at.rsk deaths 1 nlwomen [1] "label, age, Px and Dx for populaton t+n:" populaton.2 age PY.at.rsk deaths 1 twomen Ths shows whether the rght nput s specfed. Populaton s referred to as t and t+n, as n the orgnal publcaton of Nusselder and Looman (Nusselder and Looman 2004), but can refer to any populaton. We recommend the user nclude the name of the populaton n the fle wth the lfe table data, e.g. nlwomen n the fle wth the lfe table data. Next are presented the names of the nput fles wth nformaton on causes of death, and the selected causes of death. The age ntervals n the cause of death data fles determne the age ntervals n the decomposton and are the same as for the attrbutons (mrc fle). [1] "flename for cause specfc deaths for populaton t:" [1] "d:\\decomman\\nl-cod-f csv" [1] "flename for cause specfc deaths for populaton t+n:" [1] "d:\\decomman\\it-cod-f csv" [1] "selected causes for cause specfc deaths:" [1] "Heart" "stroke" "cancer" "COPD" "dabetes" "muskul" "other" Then the user choce regardng the addtonal output and starng are of the lfe table s prnted. If problems arse or results are unclear, usng 1 n Q-14 n the nput specfcaton fle gves addtonal output on the lfe table calculatons and usng 2 gves addtonal output on the Arraga analyses. Here we selected no addtonal output. [1] "no extra output" [1] "age at whch to start the lfe table:" [1] 50 38

39 It s noteworthy that n ths example age 50 s the lowest possble age as data on dsablty by cause (attrbutons) start at age 50. For partal lfe expectances also the age to stop the lfe table s gven (not ncluded here). Ths s followed by a prnt of the attrbuton table ncludng nformaton on dsablty by cause. [1] "attrbutons for populatons (t) and (t+1):" nn dsab backgrnd HEART STROKE CANCER COPD DIABETES MUSKULO OTHER nn dsab backgrnd heart stroke cancer copd dabetes muskulo other As varant 6 ncludes both causes of death and dsablty t s mportant to check that the causes are the same and n the same order. For ths reason both are lsted n the output. [1] "selected causes for dsablty attrbutons (next to background):" [1] "HEART" "STROKE" "CANCER" "COPD" "DIABETES" "MUSKULO" "OTHER" [1] "... should match wth:" [1] " causes of death:" [1] "Heart" "stroke" "cancer" "COPD" "dabetes" "muskul" "other" Part II of the output gves results of combnng nput data and descrptve calculatons. Frst the combned nformaton from the dfferent nput fles for each populaton t presented. Ths ncludes: deaths n the lfe table populaton, by cause and total lfe table parameters: ncludng: lx, Lx, Tx, dx, mx and ex proporton dsabled (p) 39

40 Next s gven the dfferences n cause-specfc dsablty prevalence between two populatons,.e., Dutch females and Italan females. In ths example Italan females have hgher dsablty due to musculoskeletal dseases at age (NL: ; IT: , dfference ). The orgnal data can be derved from the nput fle wth cause-specfc dsablty data (15.781/ = ), and s also presented n the next part wth supplementary data. The last output of part II gve the results of the calculatons of lfe expectancy, total (all varants), wth and wthout dsablty (varant 3-6) and dfferences n lfe and health expectances. Ths s the startng pont of the decomposton analyses. [1] " recaptulaton of overall lfe expectances" [1] "LE, DFLE and years wth dsablty from 50 :" wthout wth total nlwomen twomen [1] " dfference n LE:" wthout wth total