Artículo de revista: Trias-Llimós, Sergi; Permanyer, Iñaki (2023) “Cause-of-death diversity from a multiple-cause perspective in the United States.” Demography, 60 (1): 73- 98 (ISSN 1533-7790) https://doi.org/10.1215/00703370-10410415 Demography (2023) 60(1):73–98 Published online: 23 January 2023 DOI 10.1215/00703370-10410415 © 2023 The Authors This is an open access arti­cle dis­trib­uted under the terms of a Creative Commons license (CC BY-NC-ND 4.0). Cause-of-Death Diversity From a Multiple-Cause Perspective in the United States Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Sergi Trias-Llimós and Iñaki Permanyer ABSTRACT Cause-of-death diver­sity cap­tures the var­i­abil­ity of deaths across causes and is an impor­tant marker of het­ero­ge­ne­ity in a pop­u­la­tion’s health. We con­trib­ute to the debate of cause-of-death diver­sity dynam­ics by fol­low­ing a novel multiple causes of death (MCOD) approach and apply­ing it to the U.S. con­text between 2003 and 2018 and across edu­ca­tion groups. Results show that cause-of-death diver­sity increased over this period, espe­cially up to 2012. These trends were mainly driven by increases in the groups aged 65 years or more. The inclu­sion of MCOD resulted in higher increases in cause-of-death diver­sity over time com­pared with merely using under­ly­ing causes of death, except for the 85 or more age group, where no dif­fer­ence was observed for males and a reverted gra­di­ent was observed for females. Results by edu­ca­tional attain­ment reveal lower diver­sity among the highest edu­cated groups and wid­en­ing dif­fer­ences across groups from around 2012 onward. The clear edu­ca­tional gra­di­ent observed at ages 30–64 dimin­ished at older ages. The observed increases in cause-of-death diver­ sity should be mon­i­tored to bet­ter under­stand mor­tal­ity dynam­ics in aging pop­ul­ a­tions. Our new MCOD diver­sity mea­sures sug­gest that tra­di­tional approaches rely­ing on sin­gle causes of death might be underestimating cause-of-death diver­sity dynam­ics, par­tic­u­larly for males. KEYWORDS Multiple causes of death • Diversity • Inequalities • Health • Multimorbidity Introduction Patterns in causes of death are known to be key indi­ca­tors of pop­u­la­tion health. Much is known about lead­ing causes of death and how they have shifted over time (e.g., from a major­ity of deaths caused by infec­tions and com­mu­ni­ca­ble dis­eases to a major­ity of deaths caused by noncommunicable dis­eases; Omran 1998). However, much less is known about the dis­per­sion of deaths across causes—cause-of-death ­diver­sity—and how it has evolved over time. Cause-of-death diver­sity refers to the extent to which some pop­u­la­tions die from more sim­i­lar or dis­sim­i­lar causes com­ pared with other pop­u­la­tions. The diver­sity in causes of death is unar­gu­ably an impor­ tant marker of pop­u­la­tion health het­ero­ge­ne­ity, with higher val­ues suggesting higher ELECTRONIC SUPPLEMENTARY MATERIAL The online ver­sion of this arti­cle (https:​­/​­/doi​­.org​­/10​­.1215​­/00703370​ ­-10410415) con­tains sup­ple­men­tary mate­rial. 74 S. Trias-Llimós and I. Permanyer disparities across causes of death, and there­fore more dif­fic­ ul­ties in diag­no­sis and treat­ment (i.e., micro-level effects) and health plan­ning (i.e., macro-level effects). The study of cause-of-death diver­sity has received very lit­tle atten­tion from aca­de­mia (Bergeron-Boucher et al. 2020) despite its impor­tant prac­ti­cal impli­ca­tions—espe­ cially in the swift aging pro­cess that is sweep­ing the world. In this arti­cle, we pro­pose a new approach to mea­sure cause-of-death diver­sity that has been adapted to the Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 specificities prevailing in low-mor­tal­ity set­tings and there­fore that is ­able to account for mul­ti­ple causes of death (MCOD). Cogent indi­ca­tors aiming to mea­sure cause-of-death diver­sity in low-mor­tal­ity set­tings should ide­ally be sen­si­tive to (1) the increas­ingly high prev­a­lence of comor- bidity and (2) the dif­fer­ences in health out­comes across pop­u­la­tion groups. On the one hand, as mor­tal­ity shifts toward older ages, the pres­ence of comorbidities becomes pro­gres­sively more prev­a­lent, thus com­pli­cat­ing the assig­na­tion of a sin­gle cause of death—which is com­monly referred to as “the under­ly­ing cause of death” (Alpérovitch et al. 2009; Tinetti et al. 2012). This is now­ad­ ays more impor­tant than ever before as mor­tal­ity has shifted toward older ages (e.g., Brown et al. 2012), and man­ag­ing comorbidities at old age has become a major chal­lenge for health care and pub­lic health man­age­ment (Barnett et al. 2012; McPhail 2016). In this con­text, some research­ers have raised con­cerns about the over­sim­pli­fic­ a­tion of under­ly­ing cause- of-death approaches given the com­plex­ity and qual­ity of cause-of-death assig­na­tion (Flagg and Anderson 2021). This sug­gests the need to go beyond the sin­gle-cause-of- death approach, for exam­ple, by explor­ing MCOD, to achieve a bet­ter under­stand­ing of cur­rent mor­tal­ity dynam­ics (Désesquelles et al. 2014). On the other hand, in a con­ text of persisting and wid­en­ing health inequalities across socio­eco­nomic groups (e.g., Chetty et al. 2016; Mackenbach et al. 2018; Montez et al. 2019; Permanyer et al. 2018; Sasson 2016), it would be desir­able if cause-of-death diver­sity mea­sures could be bro­ken down in such a way that informs the extent of diver­sity occur­ring within and between socio­eco­nomic groups. Such decom­po­si­tion could be extremely use­ful in poten­tially iden­ti­fy­ing the main locus of cause-of-death diver­sity (i.e., unveiling whether diver­sity comes from dif­fer­ences occur­ring within or between groups) and pinpointing the key driv­ers of changes over time. In this study, we exam­ine cause-of- death diver­sity in the United States by age group, sex, and edu­ca­tional attain­ment in a con­text of chang­ing mor­tal­ity dynam­ics (2003–2018) by devel­op­ing and apply­ing a new approach based on the anal­y­sis of mul­ti­ple causes of death. Focusing on the United States is par­tic­u­larly rel­e­vant given the disrupting mor­tal­ity trends expe­ri­ enced over the last decade. Background Mortality Dynamics in the United States Mortality and life expec­tancy have stag­nated in the United States over the last decade after a lon­ger period of con­sis­tent mor­tal­ity declines. These dynam­ics have posi­ tioned the coun­try in a dis­ad­van­taged mor­tal­ity sit­u­a­tion as com­pared with other low- mor­tal­ity countries (Ho and Hendi 2018; Woolf and Schoomaker 2019). Understanding mor­tal­ity pat­terns and dis­tri­bu­tion by causes of death is cru­cial to revert stag­nated Cause-of-Death Diversity From a Multiple-Cause Perspective 75 trends and, there­fore, to fur­ther con­trib­ute to life expec­tancy improve­ments. ­Several risk fac­tors and under­ly­ing causes of death, includ­ing the so-called “deaths of despair,” dia­be­tes, and obe­sity, have grown over the last decade and con­trib­ute to explaining the observed mor­tal­ity stag­na­tion trends (Barbieri 2019; Case and Deaton 2017; Janssen et al. 2020; Preston et al. 2018). For exam­ple, drug-related mor­tal­ity trends between 2010 and 2017 had a neg­a­tive impact on life expec­tancy of 0.1 and Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 0.4 years for females and males, respec­tively (Mehta et al. 2020), while obe­sity- related mor­tal­ity trends had an esti­mated neg­a­tive impact between 2000 and 2012 of 0.3 and 0.5 years for females and males, respec­tively (Vidra et al. 2019). These causes of death are par­tic­u­larly rel­e­vant among work­ing-age indi­vid­u­als, and despite their grow­ing impor­tance, these risk fac­tors are not the only driv­ers of all­-cause mor­tal­ity among such groups. Conversely, small var­ia­ ­tions in lead­ing and rel­a­tively impor­tant causes of death, for exam­ple, car­dio­vas­cu­lar causes or can­cers, also impact mor­tal­ity dynam­ics. Indeed, the observed slow­down in the decline of car­dio­vas­cu­lar mor­tal­ity over the last decade has been shown to be a key fac­tor for the observed all­-cause mor­ tal­ity stag­na­tion (Sidney et al. 2019) and is esti­mated to account for a 1.1-year decline in life expec­tancy between 2010 and 2017. In the United States, as well as in all­other low-mor­tal­ity countries, mor­tal­ity is mainly con­cen­trated at old ages. In this pop­u­la­tion aging con­text, the small mor­tal­ ity improve­ment from car­dio­vas­cu­lar causes that occurred at ages 65 and older in the United States (Sidney et al. 2019) may be wor­ri­some for the future pros­pects of mor­tal­ity decline. The higher sur­vival at older ages has con­trib­uted to increas­ing frailty and health vul­ner­a­bil­ity of indi­vid­u­als and pop­u­la­tions. As a con­se­quence, the var­i­abil­ity in age at death—or life span var­i­a­tion—among older indi­vid­ua­ ls (60+) has been increas­ing over the last decades (Engelman et al. 2010; Permanyer and Scholl 2019). This is par­tic­u­larly impor­tant in the United States and in other low-mor­tal­ity con­texts given the ele­vated num­ber of old-age deaths and the ris­ing prev­al­ence of both comorbidities (King et al. 2018) and life expec­tancy with mor- bidities (Payne 2022). These increases in health het­ero­ge­ne­ity (e.g., coex­is­tence of chronic morbidities) rep­re­sent increased com­pet­ing risks, and as the num­ber of com­pet­ing causes increases, the assig­na­tion of the under­ly­ing cause of death may become chal­leng­ing. Multiple Causes of Death Death cer­tif­i­cates allow the pos­si­bil­ity to include mul­ti­ple causes of death. The vast major­ity of stud­ies inves­ti­gat­ing cause-of-death pat­terns have relied on the so-called “under­ly­ing cause of death”—that is, “(a) the dis­ease or injury which ini­ti­ated the train of events lead­ing directly to death, or (b) the cir­cum­stances of the acci­dent or vio­lence which pro­duced the fatal injury” (World Health Organization 2016:1067). The impor­tance of list­ing all­causes in death cer­tif­i­cates, or MCOD, for bet­ter under­ stand­ing mor­tal­ity has been stressed for many decades (Janssen 1940). However, the major­ity of stud­ies on mor­tal­ity issues have neglected the non-under­ly­ing causes of death listed in the cer­tif­i­cates, poten­tially because most cause-of-death mor­tal­ity data sets include data only on the under­ly­ing cause of death (e.g., the WHO Mortality Database). This (over)sim­pli­fi­ca­tion may be par­tic­u­larly lim­it­ing when aiming to 76 S. Trias-Llimós and I. Permanyer study spe­cific causes of death, given that some broad groups of causes are more likely to be left as con­trib­u­tory causes when mul­ti­ple causes are listed, as is the case for endo­crine dis­eases (Redelings et al. 2006). The rea­sons for using these more detailed data to improve our under­stand­ing of cause-spe­cific mor­tal­ity are becom­ing increas­ingly clear in a con­text of ris­ing (multi) mor­bid­ity and shifting mor­tal­ity toward older ages. The value of MCOD is illus­trated Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 by the obser­va­tion that the num­ber of causes of death listed on death cer­tif­i­cates tends to increase with age, at least up to about age 85 (Désesquelles et al. 2016; Grundy and Stuchbury 2022), and the num­ber of dif­fer­ent causal mor­bid­ity pat­terns (multi- morbidity at death) also increases with age until about age 90 (Grippo et al. 2020). Additionally, impor­tant con­cerns have been raised regard­ing the over­sim­pli­fi­ca­tion of under­ly­ing cause-of-death approaches given the com­plex­ity of cause-of-death assig­ na­tion (Flagg and Anderson 2021; Trias-Llimós and Permanyer 2020). Concurrently, a grow­ing body of lit­er­a­ture using MCOD in mor­tal­ity stud­ies has emerged, and sev­ eral meth­od­ol­o­gies deal­ing with MCOD have been devel­oped in the last decade (e.g., Désesquelles et al. 2010, 2012; Grippo et al. 2020; Moreno-Betancur et al. 2017; Piffaretti et al. 2016). Previous Studies on Cause-of-Death Diversity The cur­rent dynam­ics of aging pop­u­la­tions, as well as the observed stag­na­tion in U.S. mor­tal­ity over recent years, demand a com­pre­hen­sive assess­ment of mor­tal­ity dynam­ics from dif­fer­ent angles. A prom­is­ing area of research explores the extent to which indi­vid­u­als die from a narrower or wider vari­ety of causes of death—that is, cause-of-death diver­sity. Such diver­sity and how it has changed over time have the poten­tial to pro­vide a new per­spec­tive that could improve the under­stand­ing of mor­tal­ity dynam­ics. While this idea was first pro­posed in the 1980s (Izsak 1986), cause-of-death diver­sity remained largely unex­plored until recently. To the best of our knowl­edge, only one pub­li­ca­tion made use of cause-of-death var­i­abil­ity indi­ ca­tors by using under­ly­ing cause-of-death mor­tal­ity data from 15 low-mor­tal­ity countries for the last cou­ple of decades (Bergeron-Boucher et al. 2020). The main find­ings of this research pointed toward an increas­ing cause-of-death diver­sity, driven par­tic­u­larly by indi­vid­u­als aged 50 or more. This seemed to be explained by the faster decline of car­dio­vas­cu­lar causes of death as com­pared with other causes (e.g., men­tal or ner­vous), which are gaining impor­tance in the cause-of- death mor­tal­ity com­po­si­tion (Bergeron-Boucher et al. 2020). Therefore, in a con­ text of grow­ing comorbidities and dif­fi­cul­ties assigning under­ly­ing causes of death, assess­ments of cause-of-death diver­sity can be greatly enhanced by incor­po­rat­ing the MCOD per­spec­tive. Growing Educational Inequalities in Mortality Socioeconomic gra­di­ents in health and mor­tal­ity exist and per­sist world­wide, and they are par­tic­u­larly strik­ing in the U.S. con­text (e.g., Brown et al. 2012; Montez et al. 2019; Sasson 2016). Inequalities in mor­tal­ity have been rap­idly ris­ing over the Cause-of-Death Diversity From a Multiple-Cause Perspective 77 last cou­ple of decades (Olshansky et al. 2012; Sasson 2016). Importantly, this can be seen in increas­ing edu­ca­tional inequalities in mor­tal­ity in two dimen­sions. On the one hand, looking at the means, we know that life expec­tancy gaps increased in favor of highly edu­cated groups. On the other hand, when looking at the dis­per­sion of ages at death (life span inequalities), we observe that low-edu­cated groups expe­ ri­ence more uncer­tainty in the tim­ing of death, with a per­sis­tent or even increas­ing Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 gap across edu­ca­tional groups over the last decades (Sasson 2016). Improving this wor­ri­some sit­u­a­tion regard­ing socio­eco­nomic inequalities in health and mor­tal­ity rep­re­sents one of the main prin­ci­ples and goals of the U.S. Department of Health and Human Services’ Healthy People 2030 (Office of Disease Prevention and Health Promotion n.d.). Education has been the most widely used indi­ca­tor in study­ing socio­eco­nomic health inequalities. Education cap­tures “the tran­si­tion from par­ents’ socio­eco­nomic posi­tion to own socio­eco­nomic posi­tion and it is also a strong deter­mi­nant of future employ­ment and income” (Galobardes et al. 2006:8). Furthermore, edu­ca­tion has been com­monly used as an impor­tant marker of indi­vid­ual life­styles, social rela­ tion­ships, and health care use (Hayward et al. 2015; Zajacova and Lawrence 2018). So far, edu­ca­tional inequalities in mor­tal­ity have been widely ana­lyzed in terms of life expec­tancy and life span var­i­a­tion, but not regard­ing cause-of-death diver­sity. A series of ques­tions regard­ing socio­eco­nomic inequalities in cause-of-death diver­sity remain unanswered and are par­tic­u­larly inter­est­ing in the U.S. con­text, which has been char­ac­ter­ized by disrupting mor­tal­ity dynam­ics over the last decade. For exam­ ple, are less advan­taged edu­ca­tional groups dying from more dis­sim­i­lar sets of causes of death or from more sim­il­ ar sets of causes of death com­pared with the most advan­ taged edu­ca­tional groups? Data and Methods Data We use indi­vid­ual-level mul­ti­ple causes of death mor­tal­ity data for the period 2003– 2018 from the Centers for Disease Control and Prevention cov­er­ing the entire U.S. pop­ul­a­tion (Centers for Disease Control and Prevention 2021). We restrict our data to adult deaths at age 30 or more and assume that edu­ca­tion is com­pleted by age 30. Cause-of-death mor­tal­ity data are clas­si­fied into 13 groups, fol­low­ing the stan­dards of the International Classification of Diseases revi­sion 10 (ICD-10) main (groups of) chap­ters. We select the more com­monly used chap­ters as under­ly­ing causes of death: Infectious (ICD-10 codes: A00–B99), Neoplasms (C00–D48), Metabolic (E00–E88), Mental (F01–F99), Nervous (G00–G98), Cardiovascular (I00–I99), Respiratory (J00– J98), Digestive (K00–K92), Musculoskeletal (M00–M99), Genitourinary (N00–N98), and Ill-defined (R00–R99); we group all­ External causes within one cat­e­gory (S00– Y89), and we group the remaining chap­ters under the label of Other Causes (blood (D50–D89), eye and ear (H00–H93), skin (L00–L98), preg­nancy (O00–O99), peri­ na­tal (P00–P96), and con­gen­i­tal (Q00–Q99)). This implies that, for exam­ple, a death ­cer­tif­i­cate with sev­eral causes belong­ing to the same group (e.g., ische­mic heart dis­eases and hyper­ten­sive dis­eases) is assumed to have only one cause of death (a car­dio­vas­cu­lar 78 S. Trias-Llimós and I. Permanyer Females Males 1.00 .75 Death Distribution Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 .50 .25 .00 2005 2010 2015 2005 2010 2015 Year Years: 0–11 12 13+ Missing Fig. 1 Death distribution by sex, year, and highest educational level (years of education) at ages 30 and over in the United States, 2003–2018 cause, in this exam­ple). These 13 groups of causes are labeled as Ci , and the set of all­ pos­si­ble causes of death con­sid­ered in this study is denoted as C = {C1 , . . . , C13}­. As for the non-underlying causes of death, we use in all analyses the record axis codes var­ i­ables in the orig­i­nal data (i.e., those codes that have been com­pletely data-processed and that reflect “cleaned” data). Mortality in the United States in the period 2003–2018 reached an abso­lute fig­ ure of nearly 41 mil­lion deaths, representing more than one mil­lion deaths per sex and year. Educational attain­ment was used as a proxy of socio­eco­nomic sta­ tus. Education was cat­e­go­rized according to either the 1989 or the 2003 revi­sion depending on the year and state. The 1989 revi­sion clas­si­fied edu­ca­tion according to the com­pleted num­ber of years of school­ing, whereas the 2003 revi­sion clas­si­ fied edu­ca­tion according to the highest level of edu­ca­tion com­pleted (e.g., bach­e­ lor’s degree) (Rostron et al. 2010). We har­mo­nized edu­ca­tion into three categories according to com­pleted years of edu­ca­tion: 0–11 years (low edu­ca­tion), 12 years (high), and 13+ years (at least some col­lege). The edu­ca­tional dis­tri­bu­tion of deaths in the pooled data was the fol­low­ing: 23.9% of deaths with low edu­ca­tion, 41.5% with high edu­ca­tion, 31.1% with at least some col­lege, and 3.5% were miss­ing infor­ma­tion. This last group was excluded from the ana­ly­ses. Figure 1 depicts the com­po­si­tion of deaths by edu­ca­tional attain­ment over time. This com­po­si­tion has been chang­ing over time, as reflected in the increas­ing share of deaths with higher edu­ca­tional lev­els. All ana­ly­ses are performed sep­a­rately by sex and time period for the adult pop­u­ la­tion (aged 30 or more), as well as for the age-spe­cific sub­sam­ples of 30–64, 65–84, and 85+. Specific ana­ly­ses by edu­ca­tional attain­ment and strat­i­fy­ing by the var­i­ables men­tioned are also presented. All ana­ly­ses were conducted using R ver­sion 4.0.5 in RStudio 1.3.959. Cause-of-Death Diversity From a Multiple-Cause Perspective 79 Methods In the MCOD set­ting, we use the nota­tion (v;i) to for­mally indi­cate that a given death has been attrib­uted to an under­ly­ing cause and poten­tially other causes, where v = (v1 ,…,v13 ) ∈{0,1}13 \ 0 is a 13-dimen­sional vec­tor of zeros and ones (with a “1” in posi­tion j to indi­cate that cause-of-death j has con­trib­uted to that spe­cific death, and “0” Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 for the oppo­site), and i ∈{1,…,13} indi­cates which of the 13 ele­ments of C (causes of death) is the under­ly­ing cause of death.1 To illus­trate: the vec­tor (a;2) = ((1,1,1,0,…,0);2) will be used for those death cer­tif­i­cates indi­cat­ing that C2 is the under­ly­ing cause of death and C1 and C3 are con­trib­ut­ing causes of death. The generic ele­ments (v;i) will be referred to as “sets of causes of death.” We restricted our sam­ple to the 500 most prev­al­ent sets of causes of death in 2018, which turn out to rep­re­sent 95% of the total deaths across the ana­lyzed period (rang­ing between 95.5% in 2003 and 93.9 in 2018). Our approach to mea­sur­ing cause-of-death diver­sity in an MCOD set­ting requires mak­ing assess­ments of the extent of sim­i­lar­ity or dis­sim­i­lar­ity among any two sets of causes of death (e.g., (a;i) vs. (b;k); see below). To make this com­par­i­son, one must first decide the degree to which under­ly­ing causes of death are more impor­tant or rel­e­ vant than the other causes listed in the death cer­tif­i­cate. Since this is a highly con­text- spe­cific issue that is likely to vary con­sid­er­ably across indi­vid­ual deaths, we make some sim­pli­fy­ing assump­tions. First, we assign a weight W > 0 to the under­ly­ing cause of death and another weight ω ≥ 0 to all­the remaining causes of death listed in the death cer­tif­i­cate, with the restric­tion that W ≥ ω. Second, we fur­ther assume that in a hypo­ thet­i­cal death cer­tif­i­cate list­ing all­13 causes of death as con­trib­ut­ing causes, the sum of the cor­re­spond­ing “impor­tance weights” must equal 1 (a stan­dard nor­mal­i­za­tion pro­ce­ dure). Since there is only one under­ly­ing cause of death and poten­tially 12 con­trib­u­tory causes in our approach, the fol­low­ing restric­tion must hold: W + 12ω = 1. Thus, fix­ing W , one must have that 1− W ω= . 12 Imposing these mild restric­tions, we con­clude that the val­ues of W are allowed to move between 1/13 and 1. While the choice of W is arbi­trary, the mean­ing of its extreme val­ ues is clear. If we choose W = 1, then ω = 0 and we are in the stan­dard sin­gle-cause-of- death set­ting where the causes in the death cer­tif­i­cate other than the under­ly­ing cause of death are ignored. At the other extreme, when W = 1/ 13, then ω = 1/ 13, so we are in a set­ting where the under­ly­ing cause of death is only as impor­tant as, and not more impor­ tant than, the other causes included in the death cer­tif­i­cate. For all­ other inter­me­di­ate val­ues of W , the under­ly­ing cause of death is more impor­tant than the other causes of death included in the list in vary­ing degrees. In the empir­i­cal sec­tion of the arti­cle, we 1 Observe that at least one of the vi included in v must be a 1 (i.e., there must be at least one cause of death). 80 S. Trias-Llimós and I. Permanyer pres­ent all­our find­ings for dif­fer­ent val­ues of W (1/13, 0.2, 0.5, and 1), and we pres­ent the results for the inter­me­di­ate value of W = 0.5 in the results by edu­ca­tional attain­ ment, leav­ing the results derived from using other W val­ues in the robust­ness checks shown in the online sup­ple­men­tary mate­ri­als. Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Measuring Cause-of-Death Diversity in an MCOD Setting The approach we fol­low to mea­sure cause-of-death diver­sity is sim­ple: take two death cer­tif­i­cates at ran­dom and mea­sure how sim­i­lar or dis­sim­i­lar the cor­re­spond­ ing sets of causes of death are. In this way, we obtain an esti­mate of the extent of (dis)sim­i­lar­ity among deaths occur­ring in the pop­u­la­tion. The suggested approach has two steps. First, we mea­sure the extent of (dis)sim­i­lar­ity between any two sets of causes of death (i.e., dis­tances). Second, we aver­age such mea­sures across all­pos­si­ble pairs. Step 1: Define Distances Given any two sets of causes of death ( a;i ) = (( a ,…,a ) ;i ) and (b; j ) = (( b ,…,b ); j ) , we define the dis­tance between them as 1 13 1 13 (( ) ( )) 13 d a;i , b; j = ∑ wi,k ak − w j,k bk , k =1 (1) (1) where wi,k (respec­tively, w j,k ) equals W when­ever i = k (respec­tively, j = k) and equals ω oth­er­wise. This dis­tance func­tion com­pares the sim­i­lar­ity between the two causes- of-death vec­tors. The func­tion is sen­si­tive to the degree of over­lap between the vec­ tors a and b (i.e., it increases when the dif­fer­ent causes of death in the two vec­tors do not coin­cide) and to the cor­re­spond­ing under­ly­ing causes of death ( i, j). Implicitly, it assumes that the dis­tance between any two sin­gle under­ly­ing, but dif­fer­ent, causes of death is the same (see Example 2 below). We illus­trate how this mea­sure behaves in exam­ples pro­vided in Box 1. Step 2: Average Across Pairs After defin­ing how to mea­sure the extent of (dis)sim­i­lar­ity between any two sets of causes of death, we then aver­age the results across all­pos­si­ble pairs. Following this approach, we obtain the fol­low­ing mea­sure of MCOD diver­sity: D = ∑ (a;i ) ∈ Ω (b; j ) ∈ Ω ( ) ∑ p(*a,i) p(*b, j ) d ( a;i ) , ( b; j ) , ( 2) (2) where Ω = ({0,1}13 \ 0) ×{1,…,13} is the set of all­pos­si­ble sets of causes of death, and p(*a,i) is the life table–adjusted share of death cer­tif­i­cates hav­ing (a;i) as the cor­re­spond­ ing set of causes of death. The use of life table–adjusted shares of death cer­tif­i­cates facil­i­tates an accu­rate com­par­i­son of our cause-of-death diver­sity across edu­ca­tional groups and over time. This adjust­ment was done by mul­ti­ply­ing the share of deaths by Cause-of-Death Diversity From a Multiple-Cause Perspective 81 Box 1 Basic examples to represent the estimation of distances between sets of causes of death Example 1 Let ( ; 1) = (1,1,0, ... , 0); 1 represent a death certificate indicating the presence of two causes of death (Infectious ( ) and Neoplasms ( )), with the first one being the underlying Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 cause of death. Likewise, ( ; 2) = (1,1,0, ... , 0); 2 indicates the presence of the same two causes, but with the second one being the underlying cause of death; and let ( ; 3) = ((0,0,1,1,0, ... , 0); 3) represent a death certificate indicating the presence of Metabolic ( ) and Mental ( ) as causes of death, with the former being the underlying cause. The degree of (dis)similarity among these sets of causes of death according to the abovementioned distance function can be calculated as follows: ( ; 1), ( ; 2) = | · 1 − ω · 1| + |ω · 1 − · 1| = 2( − ω) ( ; 1), ( ; 3) = | · 1 − ω · 0| + |ω · 1 − ω · 0| + |ω · 0 − · 1| + |ω · 0 − ω · 1| = 2( + ω) ( ; 2), ( ; 3) = |ω · 1 − ω · 0| + | · 1 − ω · 0| + |ω · 0 − · 1| + |ω · 0 − ω · 1| = 2( + ω). Thus, for all admissible values of ≥ ω > 0, the distance between ( ; 1) and ( ; 2) is smaller than the distance between ( ; 1) and ( ; 3). This coheres with the fact that ( ; 1) and ( ; 2) share the same set of causes of death, while ( ; 1) and ( ; 3) do not have in common any cause. Example 2 How does the distance function behave when comparing death certificates indicating the presence of a different single cause of death? In that case, it is easy to show that the distance function equals | · 1 − ω · 0| + |ω · 0 − · 1| = 2 . Comparing this distance with respect to the distances obtained in the previous example, we have that 2( − ω) < 2 < 2( + ω). Again, this coheres with the intuition that (i) ( ; 1) and ( ; 2) should be closer between them than the single-cause-of death profiles ((1,0, ... , 0);1) and ((0,1,0, ... , 0); 2) because the former share the same sets of causes of death; and (ii) ( ; 1) and ( ; 3) should be further away between them than is the case for the single-cause-of death profiles ((1,0, ... , 0); 1)and ((0,0,1,0, ... , 0); 3), because the former profiles have less in common than the latter. 82 S. Trias-Llimós and I. Permanyer the cor­re­spond­ing d x pro­por­tion from life tables. This pro­ce­dure is equiv­a­lent to using mul­ti­ple-dec­re­ment life table data. To be a­ ble to com­pute life tables, pop­u­la­tion data from the Human Mortality Database and the edu­ca­tion dis­tri­bu­tion of the pop­u­la­tion from the Current Population Survey were used (see online appen­dix A for fur­ther details). The cause-of-death diver­sity indi­ca­tor D can be interpreted as the mean dis­tance between sets of causes of death, or in other words, as the expected dis­tance between two Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 ran­domly cho­sen deaths. In a hypo­thet­i­cal soci­ety where every­one died from the exact same set of causes (the low­est level of diver­sity), the dis­tance func­tion would always be 0, so D would also be equal to 0. At the other extreme, when indi­vid­u­als tend to die from a more var­ie­gated set of causes, the dis­tance func­tion tends to increase, and so does the cor­re­spond­ing diver­sity indi­ca­tor D.2 To com­pare our results across dif­fer­ent W val­ues and over time, we nor­mal­ized the results using 2003 as the base­line (D2003 = 1) for any given W. The diver­sity indi­ca­tor D belongs to a widely used class of social indi­ca­tors designed to mea­sure “diver­sity” in dif­fer­ent forms. For instance, very sim­i­lar indi­ces have been used to assess cul­tural, eth­nic, or reli­gious diver­sity in var­i­ous set­tings (Bossert et al. 2011). In all­ cases, the indi­ces are defined as the mean level of dis­sim­i­lar­ity that exists among the ele­ments being com­pared. Indeed, the well-known Gini coef­fic­ ient for income inequal­ity has a very sim­il­ar func­tional form and can be interpreted exactly in this way: it is the mean income dif­fer­ence between all­pairs of indi­vid­u­als. If the suggested MCOD diver­sity indi­ca­tor is applied to a dis­tri­bu­tion of “sin­gle causes of death” (i.e., assum­ing the only infor­ma­tion we take into con­sid­er­ation is the under­ly­ing cause of death, so W = 1), we end up with a (mul­ti­ple of a) well-known mea­sure of diver­sity: the index of frac­tion­al­iza­tion (hence­forth denoted as F). Under the afore­men­tioned assump­tions, D can be writ­ten as 13 ⎛ 13 ⎞ D = 2 ∑ ∑ pi* p*j = 2 ⎜ 1− ∑ pi*2 ⎟ = 2F, (3) i =1 j ≠ i ⎝ i =1 ⎠ where pi* is the adjusted share of deaths attrib­ut­­able to cause Ci (the der­i­va­tion of this for­mula is shown in the online appen­dix B). The frac­tion­al­iza­tion index applied in a “sin­gle causes of death” set­ting sim­ply can be under­stood as the prob­a­bil­ity that two ran­domly cho­sen deaths are attrib­ut­­able to dif­fer­ent causes. Thus, the MCOD diver­ sity indi­ca­tor pro­posed in this study can be seen as a gen­er­al­iza­tion of the F index to a broader and richer set­ting. Decomposing Cause-of-Death Diversity by Educational Groups Another attrac­tive char­ac­ter­is­tic of our diver­sity index D is that it admits decom­po­ si­tions that are easy to inter­pret. Assume the pop­ul­a­tion under study is partitioned across G groups. In the appen­dix we show that D can be decomposed into within- and between-group com­po­nents, as 2 Our diver­sity indi­ca­tor D is max­i­mized when­ever all­deaths are evenly dis­trib­uted across the dif­fer­ent “sin­gle-cause-of-death pro­files” (i.e., those sets of causes of death where there is only one under­ly­ing cause of death). When this hap­pens, the max­i­mum of D equals 2W (k − 1) / k , where k is the num­ber of causes of death. In our set­ting (where k = 13), this max­i­mum is approx­i­ma­tely equal to 1.85⋅W . Cause-of-Death Diversity From a Multiple-Cause Perspective 83 G G −1 G D = ∑ pg2 Dg + ∑ ∑ 2 pg ph Dgh, g =1 !" # # $ ! g = 1 h = g+1 ###"### $ (4) Within-component Between-component where pg is the pop­u­la­tion share of group g, Dg is the diver­sity index applied within Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 group g, and Dgh is the diver­sity between groups g and h—that is, the expected dis­ tance between a ran­domly cho­sen indi­vid­ual from group g and a ran­domly cho­sen indi­vid­ual from group h. The der­i­va­tion of this for­mula is shown in the online appen­ dix C. This decom­po­si­tion will be applied to assess the extent to which the observed changes in cause-of-death diver­sity between 2003 and 2018 are attrib­ut­­able to the con­tri­bu­tion of between edu­ca­tional groups cause-of-death diver­sity and within edu­ ca­tional groups cause-of-death diver­sity. The Role of the Changing Composition of the Population As shown in Figure 1, the edu­ca­tion com­po­si­tion of the deaths dis­tri­bu­tion has been shifting over time for the period we ana­lyzed. We per­form a sen­si­tiv­ity anal­y­sis aiming to assess the extent to which the observed changes in cause-of-death diver­sity between 2003 and 2018 are due to: (1) changes in the com­po­si­tion of the pop­u­la­tion by edu­ca­ tional level and (2) changes in the diver­sity between and within edu­ca­tional groups. Our cause-of-death diver­sity indi­ca­tor can be writ­ten in time t as Dt = f pt ,Dt ; ( ) that is, D is a func­tion of the vec­tor of pop­ul­a­tion shares (i.e., the dif­fer­ent pg ) and the vec­tor containing the within-group (Dg ) and between-group (Dgh) diver­sity lev­els, all­ mea­sured in year t (see Eq. (4)). The diver­sity changes over time can be decomposed as ( ) ( ) ΔD = D2 − D1 = f p2 , D2 − f p1 , D1 = Δ p + Δ D , (5) (5) where Δ p can be interpreted as the con­tri­bu­tion of com­po­si­tional changes to changes in diver­sity, while Δ D mea­sures the con­tri­bu­tion of the within- and between-group diver­sity changes to changes in over­all diver­sity. Following Kitagawa’s decom­po­si­ tion (Kitagawa 1964; Shkolnikov et al. 2012), ( ( ) ( )) ( ( ⎡ f p2 ,D 2 − f p1 ,D 2 + f p2 ,D1 − f p1 ,D1 ⎤ Δp = ⎣ ) ⎦, ( )) ⎡⎣6 ⎤⎦ (6) 2 ( ( ) ( )) ( ( ⎡ f p2 ,D 2 − f p2 ,D1 + f p1 ,D 2 − f p1 ,D1 ⎤ ΔD = ⎣ ) ⎦. ( )) ⎡⎣7 ⎤⎦ (7) 2 Results Number of Causes Listed in Death Certificates Figure 2 depicts the mean num­ber of dif­fer­ent causes listed in the death cer­tif­i­cates by age group and sex. For males, the num­ber of listed causes increased from 1.99 in 2003 84 S. Trias-Llimós and I. Permanyer Females All 2.02 2.19 85+ 2.03 2.11 65–84 2.06 2.27 30–64 1.89 2.20 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Males All 1.99 2.23 85+ 2.09 2.21 65–84 2.06 2.32 30–64 1.81 2.11 2005 2010 2015 Year Mean number of groups of causes: 1.9 2.0 2.1 2.2 2.3 Fig. 2 Mean number of groups of causes listed in death certificates by age and sex in the United States, 2003–2018 to 2.23 in 2018, while for females the cor­re­spond­ing num­bers were 2.02 and 2.19. These increases were observed across all­age groups, but they tended to be larger for the work­ing-age group and at com­ pa­ ra­ ble lev­ els across edu­ ca­tional groups (online Figure S2). Shares (Sets of Causes of Death) In 2018, the most prev­a­lent groups of causes of death were car­dio­vas­cu­lar, respi­ra­tory, neo­plasms, men­tal, met­a­bolic, and ill-defined (Figure 3). For exam­ple, for males, more than 180,000 deaths—12.6% of the total num­ber deaths—had only car­dio­vas­cu­lar cause/s listed in their death cer­tif­i­cates. The first com­bi­na­tion of two or more major causes of death was that of met­a­bolic and car­dio­vas­cu­lar causes, which summed to around 55,000 deaths (3.8%). The hor­i­zon­tal lines on the lower left side of the Figure 3 plots show the total num­ber of cases for each indi­vid­ual cause. For exam­ple, about 800,000 males died with a car­dio­vas­cu­lar cause listed in the death cer­tif­i­cate (54.7%). For females, car­ dio­vas­cu­lar causes were also pres­ent in around 760,000 death cer­tif­i­cates (54.9%), and they were also the first group of causes with more than 180,000 deaths (13.2%). Among females, the first com­bi­na­tion of mul­ti­ple major causes of death was that of respi­ra­tory and car­dio­vas­cu­lar causes, which summed to more than 45,000 deaths (3.3%). Cause-of-Death Diversity Cause-of-death diver­sity trends are presented in Figure 4. The dif­fer­ent val­ues of W rep­ re­sent the impor­tance of the under­ly­ing ver­sus other causes of death listed in the death cer­tif­i­cate. When W equals 1, we are in the under­ly­ing cause of death set­ting. When W Cause-of-Death Diversity From a Multiple-Cause Perspective Fig. 3 Combinations of causes of death (selection of 30 major combinations of causes, vertical bars) and number of deaths with each single cause listed in the death certificate (horizontal bars) at ages 30 and over, United States, 2018 85 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 S. Trias-Llimós and I. Permanyer Fig. 3 (continued) 86 Cause-of-Death Diversity From a Multiple-Cause Perspective 87 Females Males 1.08 Normalized Diversity W Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 1/13 1.05 0.2 0.5 1 1.02 2003 2006 2009 2012 2015 2018 2003 2006 2009 2012 2015 2018 Year Fig. 4 Trends in normalized (D2003 = 1) cause-of-death diversity according to the importance of the under- lying versus other causes of death (W), United States, 2003–2018. When W = 1, we are in a single/underly- ing cause-of-death setting where the causes in the death certificate other than the underlying cause of death are ignored. At the other extreme, when W = 1/13, we are in a setting where the underlying cause of death is only equally important and not more important than the other causes included in the death certificate. For all other intermediate values of W, the underlying cause of death is more important than the other causes of death included in the list in varying degrees. equals 1/13, we are in an MCOD set­ting in which each group of cause listed in the death cer­tif­i­cate has the same impor­tance, irrespective of its posi­tion. For W val­ues rang­ing between 1/13 and 1, the under­ly­ing cause is assumed to be more impor­tant than the other causes included in the death cer­tif­i­cate. For any given W, we observe increases in cause-of-death diver­sity trends. These increases are more pro­nounced in the first half of the ana­lyzed period (2003–2010) and are more remark­able as W declines (e.g., with grow­ing impor­tance of MCOD). In the sec­ond half of the period (2010–2018), increases in cause-of-death diver­sity slowed down, par­tic­u­larly for females, and in the sce­nario when uniquely under­ly­ing causes of death are con­sid­ered (W   = 1) for males. Trends in cause-of-death diver­sity have increased across all­age groups (Figure 5). These increases were rather con­stant over the time span for ages 30–84, whereas for the older age group they stag­nated from around 2012 onward. Furthermore, increases in cause-of-death diver­sity were found to have clear age-spe­cific pat­terns regard­ing the rel­a­tive impor­tance of the under­ly­ing cause of death ver­sus the other causes listed in the death cer­tif­i­cate. That is, at work­ing ages (30–64), cause-of-death diver­sity over the period 2003–2018 increased by 11% and 14% for males and females, respec­ tively, when all­causes in the death cer­tif­i­cate were accounted to be equally impor­tant (W   = 1/13), whereas diver­sity was much smaller in a con­text of under­ly­ing causes of death (W   = 1): 2% for males and 6% for females. At ages 65–84, dif­fer­ences in the cause-of-death diver­sity increased as W val­ues decreased. Specifically, increases ranged between 6–7% (W   = 1) and 11–12% (W   = 1/13) for both males and females. Finally, at older ages, dif­fer­ences in the trends by W were non­ex­is­tent for males and were found to be in the oppo­site direc­tion for females—with greater increases within 88 S. Trias-Llimós and I. Permanyer Females Males 1.10 30–64 1.05 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 1.00 Normalized Diversity W 1.10 1/13 65–84 0.2 1.05 0.5 1 1.00 1.10 85+ 1.05 1.00 2003 2006 2009 2012 2015 2018 2003 2006 2009 2012 2015 2018 Year Fig. 5 Trends in normalized (D2003 = 1) cause-of-death diversity according to the importance of the under- lying versus other causes of death (W) by age groups, United States, 2003–2018. When W = 1, we are in a single/underlying cause-of-death setting where the causes in the death certificate other than the underlying cause of death are ignored. At the other extreme, when W = 1/13, we are in a setting where the underlying cause of death is only equally important and not more important than the other causes included in the death certificate. For all other intermediate values of W, the underlying cause of death is more important than the other causes of death included in the list in varying degrees. the under­ly­ing cause of death approach. That is, the use of under­ly­ing causes of death results in a 12% increase in cause-of-death diver­sity between 2003 and 2018 for females and an 8% increase for males, whereas con­sid­er­ing all­causes listed in the death cer­tif­i­cate to be equally impor­tant results in reduced increases of around 8% for both females and males (W   = 1/13). These results were robust when cer­tif­i­cates with miss­ing edu­ca­tion were included in the ana­ly­ses (see online Figures S3 and S4). Diversity by Educational Groups Cause-of-death diver­sity trends by edu­ca­tional group are presented for a sce­nario con­ sid­er­ing mul­ti­ple causes of death that gives a high impor­tance to the under­ly­ing cause (W = 0.5) (Figure 6). In gen­eral, diver­sity is slightly higher for females than for males. For both sexes and edu­ca­tional groups, cause-of-death diver­sity increased over the ana­ lyzed period, and lev­els were lower among higher edu­cated groups and higher among the low­est edu­cated groups. A visual inspec­tion of trends over time sug­gests that cause- of-death diver­sity increases slow down after 2012 for the highest edu­cated group as com­pared with the period 2003–2012. From 2012 onward, higher edu­cated groups pre- sented over­all smaller increases over time as com­pared with lower edu­cated groups. Cause-of-Death Diversity From a Multiple-Cause Perspective 89 Females Males .88 .86 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Education Diversity 0–11 .84 12 13+ .82 .80 2003 2006 2009 2012 2015 2018 2003 2006 2009 2012 2015 2018 Year Fig. 6 Trends in cause-of-death diversity by sex and educational level at ages 30 and over, W = 0.5, United States, 2003–2018 Results for other lev­els of W are gen­er­ally in line with those presented, but for lower val­ues of W, a clearer edu­ca­tional gra­di­ent (lower cause-of-death diver­sity among higher edu­cated groups) for females was clearly observed (see online Figure S5). When bro­ken down by age groups, the results sug­gest a clear edu­ca­tional gra­di­ent at work­ing ages, par­tic­u­larly for females (Figure 7). This gra­di­ent dimin­ished at ages 65 and over. For females, the edu­ca­tional gra­di­ents were min­i­mal at ages 85 and over, except for the lat­est years. For males aged 65–84, a visual inspec­tion of trends sug­gests edu­ca­tional dif­fer­ences when com­par­ing the low-edu­cated group with the mid­dle- and high-edu­cated group, but not when com­par­ing the last two. Furthermore, time trends do not sug­gest impor­tant dif­fer­ences in cause-of-death diver­sity across edu­ca­tional groups, that is, increases were com­pa­ra­ble across all­age groups. Estimates for other lev­els of W are in line with these results and can be found in online Figure S6. Contribution of Between Versus Within Educational Groups to Cause-of-Death Diversity The observed changes in cause-of-death diver­sity between 2003 and 2018 by age group, sex, and W are attrib­ut­­able to dif­fer­ent extents of (1) changes between edu­ca­ tional groups and (2) changes in the con­tri­bu­tion of cause-of-death diver­sity within edu­ca­tional groups, as presented in Figure 8. In all­sub­pop­u­la­tions, and for the dif­fer­ ent val­ues of W, the increases in diver­sity were mostly driven by increases in diver­ sity within edu­ca­tional groups, which accounted for at least 75% of the total increases in diver­sity—except for females aged 85+. The dynam­ics of diver­si­ties between edu­ ca­tional groups played a smaller and almost resid­ual role. Finally, we have quan­ti­fied the extent to which changes in the edu­ca­tional com­ po­si­tion of deaths could explain the observed cause-of-death diver­sity dynam­ics between 2003 and 2018 (online Figure S7). For all­age groups, sex, and W val­ues, the 90 S. Trias-Llimós and I. Permanyer Females Males .90 30–64 .85 .80 Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Education .85 Diversity 0–11 65–84 12 13+ .80 .85 .80 85+ .75 2003 2006 2009 2012 2015 2018 2003 2006 2009 2012 2015 2018 Year Fig. 7 Trends in cause-of-death diversity by sex, age group, and educational level at ages 30 and over, W = 0.5, United States, 2003–2018 Females Males .02 1/13 .00 .05 .02 0.2 .00 Contribution of Value between .10 within .05 0.5 .02 .00 .15 .10 .05 1 .02 .00 30–64 65–84 85+ All 30–64 65–84 85+ All Age Group Fig. 8 Decomposition of cause-of-death diversity increases between 2003 and 2018 between dynamics of between and within educational group contributions at ages 30 and over, United States Cause-of-Death Diversity From a Multiple-Cause Perspective 91 observed changes in cause-of-death diver­sity are almost entirely explained (at least 99%) by changes in the dynam­ics between and within edu­ca­tional group cause-of- death diver­sity, and not by changes in the com­po­si­tion of deaths by edu­ca­tion. Discussion Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 Using detailed mul­ti­ple causes of death, we have shown that cause-of-death diver­sity has been increas­ing in the United States from 2003 onward, when ana­lyz­ing deaths from both the “under­ly­ing cause” and an MCOD per­spec­tive. The lat­ter suggested faster increases in cause-of-death diver­sity com­pared with merely con­sid­er­ing under­ ly­ing causes of death, espe­cially for males. These trends were par­tic­u­larly pro­nounced until around 2012, and decel­er­ated there­af­ter owing to the stag­na­tion observed in the age group of 85 and over. Our results by edu­ca­tional attain­ment show an impor­tant and wid­en­ing edu­ca­tional gra­di­ent as lower edu­cated groups presented higher cause-of- death diver­sity, mainly at work­ing ages, but with nota­ble dif­fer­ences across age groups. Evaluation of Data and Methods We relied on the use of mul­ti­ple causes of death rather than merely focus­ing on under­ ly­ing causes of death, as typ­i­cally done in most mor­tal­ity stud­ies that use cause-of- death data. In our view, this is par­tic­u­larly rel­e­vant in aging soci­e­ties because of the shift in mor­tal­ity toward older ages and the increase in comorbidities (King et al. 2018). Given the rec­og­nized chal­lenges in deter­min­ing the under­ly­ing cause of death at old ages (Alpérovitch et al. 2009; Flagg and Anderson 2021), the use of MCOD may lessen cod­ing issues and improve our under­stand­ing of mor­tal­ity dynam­ics. Of course, this does not imply that MCOD are per­fectly recorded, and it is pos­si­ble that social, bio­med­i­cal, and cod­ing fac­tors may bias both under­ly­ing cause and MCOD assign­ment. These fac­tors may change over time, and there­fore when looking at time trends we can­not rule out the pos­si­bil­ity that cod­ing prac­tices may influ­ence cause- of-death diver­sity dynam­ics. Coming up with a rea­son­able approach to con­trol for the effect of such fac­tors would at least require hav­ing data to reli­ably mea­sure those con­cepts—an inter­est­ing line of research that is well beyond the scope of this study. Yet, MCOD data are still highly rel­e­vant for complementing under­ly­ing cause-of- death ana­ly­ses. To make good use of the data, we used a broad and well-defined cause-of-death group­ing (e.g., car­dio­vas­cu­lar, respi­ra­tory), which was con­ve­nient because no changes in the International Classification of Diseases have occurred over the ana­ lyzed period, and there­fore poten­tial minor changes in cod­ing prac­tices are unlikely to have played a major role in our esti­mated results. This group­ing was also con­ve­nient in terms of keep­ing the ana­lyt­i­cal strat­egy rel­a­tively man­age­able in com­pu­ta­tional terms. The down­side of using such a broad clas­si­fi­ca­tion is that it becomes more dif­ fi­cult to assess the role of spe­cific causes of death on cause-of-death diver­sity. Finally, we acknowl­edge that diver­sity is depen­dent on the num­ber of causes of death used, and there­fore study­ing the effect that more gran­u­lar clas­si­fi­ca­tions can have on cause- of-death diver­sity mea­sures would be of great added value in future research. 92 S. Trias-Llimós and I. Permanyer Our esti­ma­tes were based on dif­fer­ent assump­tions regard­ing the rel­a­tive impor­tance of the under­ly­ing cause of death. At one extreme, we con­sid­ered sce­ nar­ios where only the under­ly­ing cause of death was rel­e­vant (W = 1), and at the other extreme, we con­sid­ered sce­nar­ios where all­causes listed in the death cer­ tif­i­cate were equally impor­tant (W = 1/13 in this study). The lat­ter can be seen as a strong assump­tion, but it is suf­fi­ciently infor­ma­tive to be included. However, Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 a plau­si­ble good s­ olu­tion may lie with val­ues within this range. To facil­i­tate the read­ing of the results by edu­ca­tion, we presented the results for a mid­dle sce­ nario (W = 0.5), and we placed the results for other W val­ues in the sup­ple­men­tary mate­rial. Our meth­od­o­log­i­cal approach on the esti­ma­tion of cause-of-death diver­sity is an adap­ta­tion of pop­u­lar approaches com­monly applied to assess het­ero­ge­ne­ity in human soci­e­ties or ani­mal eco­sys­tems (Alesina et al. 2003; Bossert et al. 2011; Mouchet et al. 2010). While the num­ber of indi­ces mea­sur­ing the con­cept of “diver­sity” is very large, they tend to be highly cor­re­lated (Davydov and Weber 2016). The choice of one mea­sure or another is often guided by the prop­er­ties it satisfies. The advan­tage of our pro­posed diver­sity mea­sure is that it can be bro­ken down into clearly inter­ pret­able within-group and between-group com­po­nents when the pop­u­la­tion under study is partitioned across socially rel­e­vant groups. However, our meth­od­ol­ogy is sub­ject to cer­tain assump­tions that deserve some dis­cus­sion. First, a crit­i­cal part of our approach is the mea­sure­ment of dis­tances between groups of causes of death. For the sake of par­si­mony, we assumed that all­dif­fer­ent causes are equally dis­tant from one another. However, we allowed the under­ly­ing cause of death to play a more prominent role than the other causes listed in the death cer­tif­i­cate, as detailed in the Methods sec­tion and in Box 1. We acknowl­edge that the assump­tion of equal dis­tance between causes may be argu­­able. For exam­ple, car­dio­vas­cu­lar causes may be eti­o­log­ i­cally closer when com­pared to respi­ra­tory causes than, for exam­ple, exter­nal causes of death. However, the objec­tive of this study was to esti­mate diver­sity across a broad group of causes of death and not across eti­o­log­i­cal fac­tors. Therefore, an objec­tive and eti­o­log­i­cal mea­sure­ment of cause-of-death dis­tances needs to be addressed by future stud­ies on this topic. Second, one might argue that our find­ings could be affected by the mean num­ber of causes listed in the death cer­tif­i­cates, which tends to grad­u­ally increase over time (see Figure 2 and online Figure S2). Yet, the fact that those mean val­ues are higher does not imply that cause-of-death diver­sity must be nec­es­sar­ily higher (an increas­ ing num­ber of causes repeat­ing across most indi­vid­u­als would decrease diver­sity). Our approach is not based merely on counting the num­ber of causes listed in death cer­tif­i­cates, but rather on com­par­ing the sim­il­ar­it­ies or dissimilarities that might exist among them, while account­ing for the poten­tially dif­fer­ent role of the under­ly­ing cause of death. Third, a chal­lenge to be addressed in all­ edu­ca­tion-spe­cific time trends pop­ u­la­tion health stud­ies relates to changes in the pop­u­la­tion com­po­si­tion by edu­ ca­tional attain­ment, which is pos­tu­lated to partly account for life expec­tancy dynam­ics (e.g., Hendi, 2015, 2017; Montez and Zajacova 2014). The results of our sen­si­tiv­ity anal­y­sis sug­gest that the chang­ing edu­ca­tion com­po­si­tion in the United States has played a neg­li­gi­ble role on cause-of-death diver­sity trends (see online Figure S7). Cause-of-Death Diversity From a Multiple-Cause Perspective 93 Comparison and Explanation of Results Our all­-age and age-spe­cific results when con­sid­er­ing “under­ly­ing causes of death” only (W = 1) are in line with those from a recent study using under­ly­ing cause of death data and the Shannon index of entropy as a mea­sure of diver­sity (Bergeron- Boucher et al. 2020). Our results for MCOD suggested faster increases in cause-of- Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 death diver­sity over time as com­pared with merely using under­ly­ing causes of death, espe­cially for males. This implies that the pre­vi­ously esti­mated cause-of-death diver­ sity increases may be con­ser­va­tive (Bergeron-Boucher et al. 2020). A nota­ble excep­ tion is that for the oldest age group, dif­fer­ences in the time trends for dif­fer­ent given impor­tance of MCOD were not found in males and were found to be in the oppo­site direc­tion for females. This result seems to be supported by the grow­ing comorbidity prev­a­lence among older women (King et al. 2018), given that older indi­vid­u­als with comorbidities may tend to die from more sim­i­lar causes of death when MCOD are taken into the anal­y­sis than when using under­ly­ing causes of death. Consider the fol­low­ing hypo­thet­i­cal exam­ple: the cause-of-death diver­sity D among three women dying from three dif­fer­ent under­ly­ing causes of death (e.g., car­dio­vas­cu­lar, respi­ra­ tory, and men­tal), but from over­all iden­ti­cal mul­ti­ple causes of death (e.g., car­dio­ vas­cu­lar, respi­ra­tory, and men­tal), would be larger when only the under­ly­ing cause is con­sid­ered (W = 1) than when MCOD were taken into con­sid­er­ation. According to Bergeron-Boucher et al. (2020), the main driver of the recent increases in cause-of-death diver­sity over time in low-mor­tal­ity countries was the decline of the most prev­a­lent cause of death: car­dio­vas­cu­lar deaths. Our find­ings on the decel­er­a­tion of cause-of-death diver­sity increases around the early 2010s coin­cide with the stag­na­tion of car­dio­vas­cu­lar mor­tal­ity (Glynn et al. 2019; Mehta et al. 2020; Sidney et al. 2019), so car­dio­vas­cu­lar causes may be an impor­tant deter­mi­nant of our results. However, in an MCOD frame­work, car­dio­vas­cu­lar causes of death may be less impor­tant, given that the decel­er­a­tion of diver­sity increases is not evi­dent among males. Nonetheless, explaining the role of spe­cific causes of death given their posi­ tions in death cer­tif­i­cates to the observed cause-of-death diver­sity trends was beyond the scope of this study. A bet­ter under­stand­ing of the mech­a­nism behind the observed increases in cause-of-death diver­sity remains to be elu­ci­dated. Educational Gradients Our results by edu­ca­tional groups high­light impor­tant age-spe­cific pat­terns that raise new ques­tions in pop­u­la­tion health inequal­ity stud­ies in the United States. Our find­ ings pointed toward a clear edu­ca­tional gra­di­ent in cause-of-death diver­sity, with the low­est edu­cated groups presenting the highest cause-of-death diver­sity (i.e., more het­ero­ge­ne­ity in their cause of death pat­terns), and vice versa. These results could be related to the dis­ad­van­tages of low socio­eco­nomic class in terms of low-paid and more phys­i­cally demand­ing occu­pa­tions, worse liv­ing con­di­tions, lim­ited access to health ser­vices or net­works, or unhealthier life­styles (e.g., Case and Deaton 2021; Davey Smith et al. 1998; Hayward et al. 2015). That is, our results are gen­er­ally in line with pre­vi­ous results on edu­ca­tion-spe­cific life expec­tancy and life span var­i­a­ tion esti­ma­tes, as the low­est edu­cated groups also showed lower life expec­tancy and 94 S. Trias-Llimós and I. Permanyer higher life span var­i­a­tion com­pared with their more edu­cated coun­ter­parts (Case and Deaton 2021; Sasson 2016). It seems, there­fore, that the higher the life span var­i­a­ tion, the higher the cause-of-death diver­sity, which coheres with the fact that deaths at more dis­sim­i­lar ages are likely to be caused by a more var­ie­gated set of fac­tors than deaths occur­ring at more sim­i­lar ages.3 Additionally, impor­tant and chang­ing com­po­nents of the mor­tal­ity com­po­si­tion in the United States are the grow­ing role Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 of obe­sity, alco­hol, drug-related mor­tal­ity, and over­all deaths of despair (Case and ­Deaton 2017; Janssen et al. 2020; Sasson and Hayward 2019; White et al. 2020), which tend to have a larger impact on low-socio­eco­nomic groups (Richardson et al. 2015; Siddiqi et al. 2015). Nonetheless, cause-of-death diver­sity has increased across all­edu­ca­tional groups, but these dif­fer­en­tials seem to have wid­ened since the 2010s. These find­ings are not sur­pris­ing given the well-documented increases in socio­eco­nomic inequalities in mor­tal­ity in the United States over recent years (Leive and Ruhm 2022; Sasson and ­Hayward 2019). Clear edu­ca­tional gra­di­ents were observed across the ana­lyzed period for work­ing-age pop­u­la­tions, but time trends at higher age groups showed lower dif­ fer­ences across edu­ca­tional groups. For exam­ple, at ages 65 and over the edu­ca­tional gra­di­ents seemed smaller, which is in line with well-documented declines in mor­tal­ ity inequalities across edu­ca­tional groups at older ages (Elo and Preston 1996). This com­mon pat­tern of declin­ing inequalities with age could be partly explained by selec­ tion. That is, those from low-edu­ca­tional groups that reach old age are more selected com­pared with those from high-edu­ca­tional groups. In addi­tion, we should con­sider that edu­ca­tion is a strong socio­eco­nomic proxy at work­ing ages and for recent gen­ er­a­tions, but that for older groups and birth cohorts, other socio­eco­nomic indi­ca­tors (e.g., house­hold income) might more accu­rately reflect indi­vid­u­als’ socio­eco­nomic posi­tion (Galobardes et al. 2006). Unfortunately, other socio­eco­nomic var­i­ables that would bet­ter reflect wealth were not avail­­able in the data. Final Reflections Assessing cause-of-death diver­sity trends from an MCOD per­spec­tive yields valu­able infor­ma­tion on the var­i­abil­ity of groups of causes to be tack­led in order to con­trib­ute to all­-cause mor­tal­ity reduc­tion. Because indi­vid­u­als tend to die from increas­ingly het­ero­ge­neous sets of causes, the effort toward reduc­ing mor­tal­ity should be divided within a larger group of causes. This implies that mor­tal­ity improve­ments may have a higher cost as mor­tal­ity from more causes of death would need to be addressed to fur­ ther con­trib­ute to reduc­ing all­-cause mor­tal­ity. In other words, a higher ­diver­si­fi­ca­tion 3 A pos­it­ive rela­tion­ship between the lev­els of life span var­i­a­tion and cause-of-death diver­sity can also be iden­ti­fied in the find­ings reported in Bergeron-Boucher et al. (2020). While in that paper one can see that, when life span var­ia­ ­tion decreases in a given coun­try, the cor­re­spond­ing level of cause-of-death diver­sity tends to increase, when one com­pares these two var­i­ables across countries for a fixed moment in time, the rela­tion­ship is seem­ingly pos­i­tive (see panel B in their Figures 4 and E1). That is, at a fixed moment in time, in those countries where life span var­i­a­tion is larger, cause of death var­i­a­tion tends to be larger as well. This is pre­cisely the pat­tern we observe in the United States when com­par­ing edu­ca­tional groups rather than countries. Cause-of-Death Diversity From a Multiple-Cause Perspective 95 of causes of death might require a wider vari­ety of spe­cific treat­ments, there­fore poten­tially reduc­ing the effec­tive­ness of health pol­i­cies. The cur­rent COVID-19 pan­demic rep­re­sents an addi­tional chal­lenge for health sys­ tems and may drive impor­tant changes in the dis­tri­bu­tion of deaths across causes that may be reflected in cause-of-death diver­sity increases. This is espe­cially ­impor­tant in the United States, which has been lag­ging behind other low-mor­tal­ity countries Downloaded from http://read.dukeupress.edu/demography/article-pdf/60/1/73/1803507/73triasllimos.pdf by UAB/SALA DE REVISTES user on 09 March 2023 over the last decade. In addi­tion, the rise of socio­eco­nomic inequalities in health and mor­tal­ity over recent decades calls for increased invest­ment in pub­lic health for the lower socio­eco­nomic clas­ses as well as for over­all pop­u­la­tion health. Given the well- known mor­tal­ity dif­fer­ences across U.S. states (Montez et al. 2019), fur­ther stud­ies on the topic should exam­ine the role of geog­ra­phy in improv­ing our under­stand­ing of the most recent mor­tal­ity dynam­ics. In con­clu­sion, cause-of-death diver­sity has increased in the United States, these increases were higher for males when mul­ti­ple causes of death were accounted for, and the socio­eco­nomic gap increased over the last decade. Given the large and increas­ing prev­a­lence of comorbidity in low-mor­tal­ity pop­u­la­tions, cause-of-death stud­ies based on sin­gle causes of death alone might be miss­ing the mark. Monitoring cause-of-death diver­sity can be seen as a com­ple­ment to cur­rently existing approaches that mea­sure het­ero­ge­ne­ity in pop­u­la­tion health. Future cause-of-death diver­sity stud­ies should fur­ther dis­en­tan­gle the role of dif­fer­ ent sets of causes of death in cause-of-death diver­sity and assess dif­fer­ences across socio­eco­nomic groups to best guide equi­ta­ble pub­lic health inter­ven­tions. ■ Acknowledgments This study was supported with funding pro­vided by the Euro­pean Research Council (ERC-2019-COG agree­ment 864616, HEALIN) and by the Span­ish Ministry of Science and Innovation (pro­ jects PID2020-113934RB-I00 and PID2021-128892OB-I00). S.T.L. acknowl­edges research funding from the Juan de la Cierva-Formación and from the Ramón y Cajal pro­grams of the Span­ish Ministry of Science and Innovation (FJC-2019-039314-I and RYC2021-033123-I, respec­tively). References Alesina, A., Devleeschauwer, A., Easterly, W., Kurlat, S., & Wacziarg, R. (2003). 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Sergi Trias-Llimós (cor­re­spond­ing author) strias@ced.uab.cat Trias-Llimós • Centre d’Estudis Demogràfics, Centres de Recerca de Catalunya (CERCA), Universitat Autònoma de Barcelona, Bellaterra, Spain; https:​­/​­/orcid​­.org​­/0000​­-0002​­-8052​­-6736 Permanyer • Centre d’Estudis Demogràfics, Centres de Recerca de Catalunya (CERCA), Universitat Autònoma de Barcelona, Bellaterra, Spain; Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain; https:​­/​­/orcid​­.org​­/0000​­-0002​­-7051​­-5144