Abstract

Introduction

The demographic transition is a process that involves changes from high to low fertility and mortality rates. One of the main consequences is the decrease in the young population and a steady increase in the population 65 years or older ¹1. Lee RD. Global population aging and its economic consequences. Washington DC: AEI Press; 2007.^,22. Saad PM. Demographic trends in Latin America and the Caribbean. In: Coltear D, editor. Population aging: is Latin America ready? Washington DC: World Bank Publications; 2010. p. 43-75.^,33. Turra CM, Queiroz BL. Antes de que sea demasiado tarde: transición demográfica, mano de obra disponible y problemas de la seguridad social en el Brasil. Santiago: Naciones Unidas; 2009. (Notas de Población, 86).^,44. Wong LLR, Carvalho JA. The rapid process of aging in Brazil: serious challenges for public policies. Rev Bras Estud Popul 2006; 23:5-26.. In addition to accelerated population aging, the demographic transition is accompanied by a change in mortality patterns in various stages of the epidemiological transition, leading to the increase or emergence of new diseases in the elderly ⁵5. Meslé F, Vallin J. Historical trends in mortality. In: Rogers RG, Crimmins EM, editors. International handbook of adult mortality. Paris: Springer Science; 2011. p. 9-48.^,66. Siegel JS. The demography and epidemiology of human health and aging. Dordrecht: Springer Science & Business Media; 2011.^,77. Alzheimer's Association. Alzheimer's disease facts and figures. Alzheimers Dement 2014; 10:e47-e92.^,88. Vaupel JW, Carey JR, Christensen K, Johnson TE, Yashin AI, Holm NV, et al. Biodemographic trajectories of longevity. Science 1998; 280:855-60.. One such disease that merits special attention is dementia.

Dementia is a generic term to classify a set of diseases that affect the elderly population. Dementia from Alzheimer’s disease (AD) is the most frequent ⁷7. Alzheimer's Association. Alzheimer's disease facts and figures. Alzheimers Dement 2014; 10:e47-e92.^,99. Llibre Guerra JC, Guerra Hernández MA, Perera Miniet E. Comportamiento del síndrome demencial y la enfermedad de Alzheimer. Rev Habanera Cienc Méd 2008; 7:1-14.^,1010. Sutton AL. Alzheimer disease sourcebook. 5th Ed. Detroit: Omnigraphics Inc.; 2011., accounting for 60% of all dementia cases in the world ¹¹11. Souza LC, Sarazin M, Teixeira-Júnior AL, Caramelli P, Santos AE, Dubois B. Biological markers of Alzheimer's disease. Arq Neuropsiquiatr 2014; 72:227-31.^,1212. Grinberg LT, Nitrini R, Suemoto CK, Ferretti-Rebustini REL, Leite REP, Farfel JM, et al. Prevalence of dementia subtypes in a developing country: a clinicopathological study. Clinics (São Paulo) 2013; 68:1140-5.^,1313. Kua EH, Ho E, Tan HH, Tsoi C, Thng C, Mahendran R. The natural history of dementia. Psychogeriatrics 2014; 14:196-201.. AD is currently acknowledged as a growing global public health problem ¹⁴14. Witlox J, Eurelings LSM, de Jonghe JFM, Kalisvaart KJ, Eikelenboom P, van Gool WA. Delirium in elderly patients and the risk of postdischarge mortality, institutionalization, and dementia: a meta-analysis. JAMA 2010; 304:443-51.^,1515. Ferri CP, Prince M, Brayne C, Brodaty H, Fratiglioni L, Ganguli M, et al. Global prevalence of dementia: a Delphi consensus study. Lancet 2005; 366:2112-7.^,1616. Sibener L, Zaganjor I, Snyder HM, Bain LJ, Egge R, Carrillo MC. Alzheimer's disease prevalence, costs, and prevention for military personnel and veterans. Alzheimers Dement 2014; 10(3 Suppl):S105-10., and its presence in elderly individuals greatly increases the risk of death ¹⁷17. Ganguli M, Dodge HH, Shen C, Pandav RS, DeKosky ST. Alzheimer disease and mortality: a 15-year epidemiological study. Arch Neurol 2005; 62:779-84..

Ferri et al. ¹⁵15. Ferri CP, Prince M, Brayne C, Brodaty H, Fratiglioni L, Ganguli M, et al. Global prevalence of dementia: a Delphi consensus study. Lancet 2005; 366:2112-7. reported that in the year 2004, at least 24 million individuals had some kind of dementia around the world. In developing countries, it is suspected that at least 60% of the elderly suffer from dementia. This proportion may reach 71% by the year 2040 ¹⁸18. Wimo A, Winblad B, Aguero-Torres H, von Strauss E. The magnitude of dementia occurrence in the world. Alzheimer Dis Assoc Disord 2003; 17:63-7.^,1919. Nitrini R, Bottino CM, Albala C, Custodio Capuñay NS, Ketzoian C, Llibre Rodriguez JJ, et al. Prevalence of dementia in Latin America: a collaborative study of population-based cohorts. Int Psychogeriatr 2009; 21:622-30.^,2020. Arevalo-Rodriguez I, Smailagic N, Roqué I, Figuls M, Ciapponi A, Sanchez-Perez E, et al. Mini-Mental State Examination (MMSE) for the detection of Alzheimer's disease and other dementias in people with mild cognitive impairment (MCI). Cochrane Database Syst Rev 2015; (3):CD010783., potentially affecting 81 million individuals ¹⁵15. Ferri CP, Prince M, Brayne C, Brodaty H, Fratiglioni L, Ganguli M, et al. Global prevalence of dementia: a Delphi consensus study. Lancet 2005; 366:2112-7.. According to Wimo et al. ¹⁸18. Wimo A, Winblad B, Aguero-Torres H, von Strauss E. The magnitude of dementia occurrence in the world. Alzheimer Dis Assoc Disord 2003; 17:63-7., a significant share of individuals with dementia live in developing countries.

The interest in studying AD has grown in Latin America and the Caribbean in recent years ¹⁵15. Ferri CP, Prince M, Brayne C, Brodaty H, Fratiglioni L, Ganguli M, et al. Global prevalence of dementia: a Delphi consensus study. Lancet 2005; 366:2112-7.^,2020. Arevalo-Rodriguez I, Smailagic N, Roqué I, Figuls M, Ciapponi A, Sanchez-Perez E, et al. Mini-Mental State Examination (MMSE) for the detection of Alzheimer's disease and other dementias in people with mild cognitive impairment (MCI). Cochrane Database Syst Rev 2015; (3):CD010783.^,2121. Llibre Rodríguez J, Herrera G, Fernando R. Demencias y enfermedad de Alzheimer en América Latina y el Caribe. Rev Cuba Salud Pública 2014; 40:378-87.^,2222. Nitrini R, Caramelli P, Herrera Jr. E, Castro I, Bahia VS, Anghinah R, et al. Mortality from dementia in a community-dwelling Brazilian population. Int J Geriatr Psychiatry 2005; 20:247-53.. Nevertheless, the results of these studies vary considerably, especially regarding the AD prevalence in Latin America and the Caribbean. In some countries the prevalence estimates are lower than the ones observed in developed countries ¹⁸18. Wimo A, Winblad B, Aguero-Torres H, von Strauss E. The magnitude of dementia occurrence in the world. Alzheimer Dis Assoc Disord 2003; 17:63-7.^,2323. Kalaria RN, Maestre GE, Arizaga R, Friedland RP, Galasko D, Hall K, et al. Alzheimer's disease and vascular dementia in developing countries: prevalence, management, and risk factors. Lancet Neurol 2008; 7:812-26..

There are also difficulties in obtaining reliable estimates for the mortality rates from AD. This is due to recording as problems in vital statistics systems, leading mainly to errors in age, death records, missing information, diagnostic errors, difficulties in access to health services by the elderly population, etc. ²⁴24. James BD, Leurgans SE, Hebert LE, Scherr PA, Yaffe K, Bennett DA. Contribution of Alzheimer disease to mortality in the United States. Neurology 2014; 82:1045-50.^,2525. Lima EC, Queiroz BL. Evolution of the deaths registry system in Brazil: associations with changes in the mortality profile, under-registration of death counts, and ill-defined causes of death. Cad Saúde Pública 2014; 30:1721-30.^,2626. Steenland K, MacNeil J, Vega I, Levey A. Recent trends in Alzheimer disease mortality in the United States, 1999 to 2004. Alzheimer Dis Assoc Disord 2009; 23:165-70.. Studies on mortality from AD are thus a major challenge, since vital statistics records are the main source of information.

Our main objective is to generate adjusted estimates of mortality attributable to AD in the elderly population of the 27 Brazilian state capitals, from 2009 to 2013. Initially we provide estimates for the mortality rates from all types of dementia, based on which we obtained estimates for the specific mortality rates from AD.

Materials and methods

The study used microdata from the mortality records in Brazilian Mortality Information System (SIM; http://www.datasus.gov.br) for the 27 Brazilian state capitals, by place of residence, for the years 2009-2013. The definition of mortality from all types of dementia was based on the 10^th revision of International Classification of Diseases (ICD-10). More data can be found at https://github.com/jjsandoval/ArticuloCSP.

Inclusion criteria

Deaths from dementia according to direct cause of death, 1st, 2nd, and 3rd causes that preceded death (lines A-D), and important causes of disease I and II, recorded in the vital statistics, via the search for codes G30.0-G30.9, with F00-F09 as excluded events.

Exclusion criteria

Mortality due to mental or behavioral disorders recorded as codes F1, for example, deaths caused by alcoholism, opioids, and other drugs, both avoidable and unavoidable, deaths classified as R99 (other ill-defined/unspecified causes, but recorded by physicians), and R98, deaths unattended by physicians. In addition, previous studies found few cases of age-related physical disability associated with dementia, so deaths from this cause (code R54) were excluded, totaling 3,084 cases in the study period.

Variables

For the case count, the variable I(x) was constructed, assigning 1 to death attributable to dementia and 0 otherwise. The rates’ denominator was obtained from the 2010 Brazilian Population Census, extracted from Integrate Public Use Microdata Series (IPUMS. https://international.ipums.org/international/index.shtml, accessed on 08/Sep/2015) , for the 27 state capitals. Data related to year 2010 were projected to July 1st (half of the period). For the years 2009 and 2011-2013, population projections were performed, based on information from the national census of 2000 and 2010. The count I(x) allowed obtaining the numerator for the mortality rates from dementia for each of the mortality lines in the microdata. Cases were extracted from the SIM database via an alphanumeric search using the ICD-10 codes, with the grepl function from the R software (https://www.r-project.org/).

Categories for variables sex and age coincide between the SIM and the 2010 census. For variable education however, SIM assumes categories: 0-3, 4-7, 8-11, and 12 or more years of schooling, and the census assumes different caterories. We thus performed an approximate construction using the edattaind code in IPUMS. The independent variables were: sex (1 = male, 2 = female), age (1 = 65-69, 2 = 70-74, 3 = 75-79, 4 = 80-84, and 5 = 85 years or older), education (1 = 0-3, 2 = 4-7, 3 = 8-11, and 4 = 12 or more years of schooling), and period (1 = 2009, 2 = 2010, 3 = 2011, 4 = 2012, and 5 = 2013).

The proportion of missing data was 0.5% for sex and 18.9% for years of schooling in the SIM. In the 2010 census, the proportions were 14.47% for years of schooling and one missing for sex.

For imputation of missing data, we assume “randomness” of the sample by sex and proceeded according to the tendencies shown in the mode (Bernoulli process). For education, we assume missing not at random (MNAR) and fit a Bayesian model, considering education (1 = 0, 2 = 1-3, 3 = 4-7, 4 = 8-11, and 5 = 12 or more years of schooling) as an ordinal response, dependent on age and sex. A multinomial response is assumed with parameters p _ij , i = 1, 2,…, N and j = 1,2,3,4,5, depending on: g ₁ , g ₂ , g ₃ , g ₄ , normality is assumed in g ₁ and inverse gamma distributions are assumed for the other g’s. The a priori parameters elicitation were obtained from the 2010 census, where 25% of the population 65 years or older had no formal education, 50% had from 1 to 3 years, 11% from 4 to 7, 7% from 8 to 11, and 7% more than 12 years of schooling. For further details on the parameters, see Sandoval ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016..

In addition, corrections were performed for coverage based on the estimates provided by Queiroz et al. ²⁸28. Queiroz BL, Freire FHMA, Gonzaga MR, Lima EEC. Completeness of death-count coverage and adult mortality (45q15) for Brazilian states from 1980 to 2010. Rev Bras Epidemiol 2017; 20 Suppl 1:21-33. which are calculated for the deaths in Brazilian state capitals for ages 15 to 60 years. Among the estimates presented by Queiroz et al. ²⁸28. Queiroz BL, Freire FHMA, Gonzaga MR, Lima EEC. Completeness of death-count coverage and adult mortality (45q15) for Brazilian states from 1980 to 2010. Rev Bras Epidemiol 2017; 20 Suppl 1:21-33., we considered those produced with the adjusted synthetic extinct generations method (SEG-adj) proposed by Bennett & Horiuchi ²⁹29. Bennett NG, Horiuchi S. Estimating the completeness of death registration in a closed population. Popul Index 1981; 47:207-21. and corrected by Hill et al. ³⁰30. Hill K, You D, Choi Y. Death distribution methods for estimating adult mortality: sensitivity analysis with simulated data errors. Demogr Res 2009; 21:235-54., as it they are based on more flexible assumptions. However, this method only allows initial corrections to the data, since it has limitations that will be discussed in the last section of this paper. These limitations inspired us to use Bayesian models to improve the fits of the rates, as described next.

Without correction for coverage and imputation of missing data, there were only 38,657 dementia cases (4.96% of the total) from 2009 to 2013. With correction for coverage, the total was 42,831 cases (5.5%), and with imputation of missing data ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016. total increase to 51,307 deaths (6.58%), higher than usually found in SIM sources.

Bayesian model construction

The target response variable Y _j was the proportion of deaths attributable to all types of dementia, obtained by cross-analyzing the independent variables with the microdata base according to I(x), in a total of N = 200 subpopulations (contingency table).

Let us assume the selection of a random sample in each subpopulation defined by the covariables sex, age, year, and education, that is, j = {sex, age, year, education} y j: 1, 2,… , N. Let y _j be the observed proportion of deaths from all types of dementia in the subpopulation j among the Nj individuals exposed to the risk. The dependence between Y _j and the independent variables was modeled by the expected value of Y _j , given a random effect V _j , denoted by E(Y _j |V _j = v _j ), generalized, from Dobson & Barnett ³¹31. Dobson AJ, Barnett A. An introduction to generalized linear models. 3rd Ed. Boca Raton: Chapman & Hall/CRC; 2008. as:

We assume that where θj=expβ0+∑k=1ρβkXkj where θ _j , 0 ≤ θ _j ≤ 1, is the mortality rate for all types of dementia within the j-th subpopulation. The random effect V _j is included into the model to account for the existence of overdispersion into Y _j , assume that Vj has a gamma distribution G(r _j , r _j /μ _j ). For the parameter r _j , we consider, an inverse gamma prior distribution with fixed hyperparameters a > 0 and b > 0, which is non-informative. The rate θ _j is defined as:

Where E(Y _j ) = θ _j N _j = μ _j and N is the total number of independent subpopulations in the contingency table. One can demostrate ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016. that the unconditional marginal distribution of Y _j , in the mixed distribution of Y _j and V _j , is a negative binomial distribution.

For the Bayesian model (1), the model definition is completed by specifying the distributions of the regression parameters β _k , k = 0, 1,… , p. Such prior distributions are informative distributions which the mean and variance are specified based on information sources obtained from a meta-analysis. To complete the specification of the Bayesian model in (1), centered normal prior distributions with precision 1.0 x 10⁶ for β ₀ and for the effects of the study period. For the effects of sex, age groups, and schooling, informative prior distributions are assumed for β _k , where the mean and variance are defined from extra information obtained from a meta-analysis. In addition, for these effects, since the exploratory results of the β _k combined in the meta-analysis were unimodal and approximately symmetrical, and as recommended by Gelman et al. ³²32. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis. 2nd Ed. Milton Park: Taylor & Francis; 2004., we assumed normal prior distribution as described below.

The information from a meta-analysis was obtained by a search of more than 2,000 articles in the MEDLINE and SciELO bases from 2000 to 2016. Among these, 15 studies ²¹21. Llibre Rodríguez J, Herrera G, Fernando R. Demencias y enfermedad de Alzheimer en América Latina y el Caribe. Rev Cuba Salud Pública 2014; 40:378-87.^,3333. Dong M, Peng B, Lin X, Zhao J, Zhou Y, Wang R. The prevalence of dementia in the People's Republic of China: a systematic analysis of 1980-2004 studies. Age Ageing 2007; 36:619-24.^,3434. Katz MJ, Lipton RB, Hall CB, Zimmerman ME, Sanders AE, Verghese J, et al. Age-specific and sex-specific prevalence and incidence of mild cognitive impairment, dementia, and Alzheimer dementia in blacks and whites: a report from the Einstein Aging Study. Alzheimer Dis Assoc Disord 2012; 26:335-43.^,3535. Letenneur L, Gilleron V, Commenges D, Helmer C, Orgogozo J, Dartigues J. Are sex and educational level independent predictors of dementia and Alzheimer's disease? Incidence data from the PAQUID project. J Neurol Neurosurg Psychiatry 1999; 66:177-83.^,3636. Kukull WA, Higdon R, Bowen JD, McCormick WC, Teri L, Schellenberg GD, et al. Dementia and Alzheimer disease incidence: a prospective cohort study. Arch Neurol 2002; 59:1737-46.^,3737. Edland SD, Rocca WA, Petersen RC, Cha RH, Kokmen E. Dementia and Alzheimer disease incidence rates do not vary by sex in Rochester, Minn. Arch Neurol 2002; 59:1589-93.^,3838. Chêne G, Beiser A, Au R, Preis SR, Wolf PA, Dufouil C, et al. Gender and incidence of dementia in the Framingham Heart Study from mid-adult life. Alzheimers Dement 2015; 11:310-20.^,3939. Lobo A, Lopez-Anton R, Santabárbara J, de-la-Cámara C, Ventura T, Quintanilla MA, et al. Incidence and lifetime risk of dementia and Alzheimer's disease in a Southern European population. Acta Psychiatr Scand 2011; 124:372-83.^,4040. Borenstein AR, Wu Y, Bowen JD, McCormick WC, Uomoto J, McCurry SM, et al. Incidence rates of dementia, Alzheimer disease, and vascular dementia in the Japanese American population in Seattle, WA: the Kame Project. Alzheimer Dis Assoc Disord 2014; 28:23-9.^,4141. Ancelin M-L, Ripoche E, Dupuy A-M, Barberger-Gateau P, Auriacombe S, Rouaud O, et al. Sex differences in the associations between lipid levels and incident dementia. J Alzheimers Dis 2013; 34:519-28.^,4242. Herrera E, Caramelli P, Silveira ASB, Nitrini R. Epidemiologic survey of dementia in a community-dwelling Brazilian population. Alzheimer Dis Assoc Disord 2002; 16:103-8.^,4343. Nitrini R, Caramelli P, Herrera Jr. E, Bahia VS, Caixeta LF, Radanovic M, et al. Incidence of dementia in a community-dwelling Brazilian population. Alzheimer Dis Assoc Disord 2004; 18:241-6.^,4444. Tom SE, Hubbard RA, Crane PK, Haneuse SJ, Bowen J, McCormick WC, et al. Characterization of dementia and Alzheimer's disease in an older population: updated incidence and life expectancy with and without dementia. Am J Public Health 2015; 105:408-13.^,4545. Villarejo A, Bermejo-Pareja F, Trincado R, Olazarán J, Benito-León J, Rodríguez C, et al. Memory impairment in a simple recall task increases mortality at 10 years in non-demented elderly. Int J Geriatr Psychiatry 2011; 26:182-7.^,4646. Brookmeyer R, Evans DA, Hebert L, Langa KM, Heeringa SG, Plassman BL, et al. National estimates of the prevalence of Alzheimer's disease in the United States. Alzheimers Dement 2011; 7:61-73. satisfied the criteria for the meta-analysis. The selected articles were original studies that included information on the risk factors associated with dementia. Selection was based on the diagnostic criteria for “dementia”, “dementia not otherwise specified”, “education” and “dementia”, “sex and dementia”, “dementia and age”, “prevalence”, “risk factors”, and “epidemiology”, excluding studies that used any other term that did not allow comparison with the others.

Informative hyperparameters were obtained from prior available information about risk factors for dementia. In particular, estimates of the odds ratios (OR) by education and relative risks (RR) by sex and age groups were used for this purpose.

For the effect of sex, a normal prior distribution with a mean of -0.01 and standard deviation (SD) of 0.114 is assumed; for the effects of age groups, normal distributions were obtained with means and SDs given, respectively, by: 0.833 and 0.141 (group 70-74 years), 1.56 and 0.141 (group 75-79), 2.21 and 0.138 (group 80-84), and 2.59 and 0.289 (group 85 years or older); for the effect of schooling, normal prior distributions were considered with means and SDs, given, respectively by: 1.09 and 0.253 (group with no schooling), 0.95 and 0.253 (1-3 years), 0.84 and 0.084 (4-7 years), and 0.37 and 0.084 (8-11 years of schooling) ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016..

Model (1) is known as a Bayesian log-linear regression model ⁴⁷47. Paulino CDM, Turkman MAA, Murteira B. Estatística bayesiana. Lisboa: Fundação Calouste Gulbenkian; 2003.. Processing and analysis of the information required MCMC simulation methods and was performed, using the R and JAGS software (http://mcmc-jags.sourceforge.net/). The following results were based on estimates of θ _j , specific mortality rates (SMR), using 95% highest posterior density (HPD) credible intervals (CI) and the a posteriori median in all types of dementia. According to the estimates previously obtained by meta-analysis, the proportion of AD was 72% (95%CI: 58.9; 84.7) of all dementias ²⁷.

Results

Table 1 shows the estimated specific mortality rates. Mortality for men was 10% higher than in women, but without statistical significance. For all dementias, there was an increase of 9.5% in the mortality rate 70-74-year group, if compared to the 65-69-year group. This contribution increases considerably with age, such that in the group 85 or older, it is 84% higher than in the youngest group. For education, the contribution was 6% in the group with 0-3 years of schooling if compared to such group with 12 years or more. For AD, the contribution was only 4.4%, however it was twice higher on average, than in the other schooling groups.

For identification of trends by age and schooling, a graphic for the logarithm of AD-specific mortality rates for men and women is presented (Figure 1). Figure 1a shows the highest SMRs in the groups with the lowest education level (less than 7 years) in all the age groups. From 4 to 11 years of education, the SMR logarithm was similarly stable. However, the trends in the SMR across all the age groups decay similarly, from the lowest level (0-3 years) to the highest level of formal education (12 years or more).

Figure 1b shows a high increase in the rates as the ages increase for in all the schooling levels. The specific mortality rates are also statistically higher in individuals with less formal education (0-3 years) than in the other groups, according to the HPD CIs. Two major groups were clearly distinguished: the group with 0-3 years of schooling and the joint group, whitall indivuduals with higher education (Figure 1b).

Table 2 again features for the differences in SMR by age groups at each level of education. For example, the 65-69-year age group, the SMR from AD is 24.05 (95%CI: 20.06; 28.67) for every 100,000 women with 3 years or less of formal education. For individuals with 4-7 years of education, the Alzheimer SMR was 15.88 (95%CI: 12.89; 19.37). The SMR showed a slight increase for 8-11 years of education (18.82; 95%CI: 15.59; 22.32), but it is not significantly different from the previous level, and decreased until reaching 13.42 (95%CI: 11.2; 15.62) in the group with 12 years or more of schooling. There were no differences in the HPD CI for the mortality rates of of education groups. The opposite is observed for the group with 0-3 years of education (Figure 1b).

Analogous results were obtained with population 85 years or older, except for those indiviuals with 12 years or more of schooling, showing some statistical differences at some levels of education.

Tables 3 and 4 show the regional results. The sex-adjusted estimates for SMR were not statistically significant, as already observed in the overall results. The medians were similar and the confidence intervals overlapped. For the North of Brazil, we analyzed the cities of Porto Velho (Rondônia State), Manaus (Amazonas State), and Rio Branco (Acre State). Results for the city of Porto Velho should be highlight as because it had the lowest estimates in the region from 2009 and 2013, ranging from 5.5 to 9.9 deaths per 100,000 inhabitants (Table 3). The 95%CI indicated high posterior variability and no significant differences between the SMR in the 65-69 age group, when comparing the three cities. Posterior distributions of SMR in women with 85 years or older in Porto Velho, displayed wide dispersion with a median of 94.7 (95%CI: 26.5; 203.1) for 2009 and 169.2 (95%CI: 64.3; 344.4) for 2013 in Porto Velho. For the city of Río Branco, the rates were nearly double of those obteined for the other two cities, and there were no statistical differences when comparing the respective age groups.

In the Northeast, we selected the cities of Salvador (Bahia State), Recife (Pernambuco State), São Luís (Maranhão State), and Natal (Rio Grande do Norte State). There was an increase in the SMR if compared to the SMR cities in the North of Brazil. The estimates SMR were very close to those obtained for the city of Río Branco, for example. Importantly, the HPD intervals showed less variation in this region, indicating greater precision in the SMR estimates if compared to the ones obtained for state capitals in the North. However, there were no statistically significant differences by age or years of schooling.

In the Central region, we selected the cities of Cuiabá (Mato Grosso State), Goiânia (Goiás State), and Campo Grande (Mato Grosso do Sul State). The SMR estimates in the region reduced to approximately half of those in the North. However, there were no statistically significant differences at 95%. It is noteworthy that the city of Brasília also displayed similar rates to the posterior median for cities in the Central region.

The Southeast and South regions of Brazil presented the best vital statistics. The Southeast also showed highest SMR in individuals 85 or older, among all the populations analyzed. The posterior variations of the HPD CI, by year and all the cities, were also much smaller than that obtained in the other regions.

Discussion

In this study, we provide adjusted mortality estimates from Alzheimer’s disease in Brazil, for the years 2009 to 2013, by combining the rigorous search for cases attributable to dementia with indirect estimation methods. We hope our results are useful for the public health sector and can also call attention to the importance of examining data errors in the vital statistics of developing countries, such as recommended by Luy ⁴⁸48. Luy M. A classification of the nature of mortality data underlying the estimates for the 2004 and 2006 United Nations' World Population Prospects. Comparative Population Studies 2011; 35:315-35.. However, there are significant limitations to our study.

First, our work is limited to mortality data for the state capitals in Brazil. Therefore, it is not representative of the whole country. We restrict the analysis to state capitals hoping to reduce the loss of information due to the underreporting of deaths, that usually are more prevalent in the less developed areas. However, we had to use correction factors for the under-registration of deaths that are specific for the entire state populations, all causes of death, ages 15 to 60, provided by Queiroz et al. ²⁸28. Queiroz BL, Freire FHMA, Gonzaga MR, Lima EEC. Completeness of death-count coverage and adult mortality (45q15) for Brazilian states from 1980 to 2010. Rev Bras Epidemiol 2017; 20 Suppl 1:21-33.. So, we had to assume that the same factors apply for capitals, AD, and ages over 60. This assumption may be too strong. For example, in the less developed states, we may be overestimating the level of under-registration of deaths, since data quality should be higher in their capital cities. Also, we know little about the variation of under-registration of deaths by age, and nothing guarantees that correction factors of reported deaths at adult ages apply to older ages. Nevertheless, given our ignorance about the actual size of the underreporting of deaths from dementia ⁴⁹49. Ganguli M, Du Y, Rodriguez EG, Mulsant BH, McMichael KA, Vander Bilt J. Discrepancies in information provided to primary care physicians by patients with and without dementia: the Steel Valley Seniors Survey. Am J Geriatr Psychiatry 2006; 14:446-55., we hope that a correction factor of 10% (on average), such as the one we used, provides at least some correction for the potential under-registration of deaths for AD. Also, correction factors at the state level allow us, at the minimum, to incorporate regional variations in data quality.

Knowing about the limitations of traditional methods for correcting for underreporting of deaths, we also perform additional adjustments to the observed rates. We used a negative binomial Bayesian regression model, based on the hypothesis that there is a much higher percentage of underreporting of mortality from dementia than other causes; a common phenomenon in many countries ¹⁸18. Wimo A, Winblad B, Aguero-Torres H, von Strauss E. The magnitude of dementia occurrence in the world. Alzheimer Dis Assoc Disord 2003; 17:63-7.^,4242. Herrera E, Caramelli P, Silveira ASB, Nitrini R. Epidemiologic survey of dementia in a community-dwelling Brazilian population. Alzheimer Dis Assoc Disord 2002; 16:103-8. Despite the evolution in medical technologies and health systems ⁵⁰50. Uauy R, Monteiro CA. The challenge of improving food and nutrition in Latin America. Food Nutr Bull 2004; 25:175-82., this percentage may remain around 50%. In the specific case of Brazil, Nitrini et al. ²²22. Nitrini R, Caramelli P, Herrera Jr. E, Castro I, Bahia VS, Anghinah R, et al. Mortality from dementia in a community-dwelling Brazilian population. Int J Geriatr Psychiatry 2005; 20:247-53. found that only 12.5% of the death certificates in the mortality database (SIM) mentioned AD or dementia among individuals with dementia. This figure gives an idea of how low the coverage can get. Therefore, we believe that the corrections we made to the original data sources, based on a priori information from a meta-analysis, were necessary so that the estimates become consistent with the probable mortality levels from this cause of death.

Except for significant interactions between age and sex, which indicated a higher risk of death among men in the younger age groups ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016., we found no significant overall sex differences for mortality from dementia. Without the proposed adjustments, the differences by sex would exist and would go in the opposite direction compared to reported AD incidence rates by sex. Teixeira et al. ⁵¹51. Teixeira JB, Souza Junior PRB, Higa J, Theme Filha MM. Mortality from Alzheimer's disease in Brazil, 2000-2009. Cad Saúde Pública 2015; 31:850-60. found Alzheimer-specific mortality rates of 88.5 per 100,000 among men and 112 per 100,000 among women in 2009. These estimates were similar to our crude rates, calculated before the proposed adjustments. There is an extensive discussion in Mazure & Swendsen ⁵²52. Mazure CM, Swendsen J. Sex differences in Alzheimer's disease and other dementias. Lancet Neurol 2016; 15:451-2. about this subject, but it is important to note that other studies ³⁴34. Katz MJ, Lipton RB, Hall CB, Zimmerman ME, Sanders AE, Verghese J, et al. Age-specific and sex-specific prevalence and incidence of mild cognitive impairment, dementia, and Alzheimer dementia in blacks and whites: a report from the Einstein Aging Study. Alzheimer Dis Assoc Disord 2012; 26:335-43.^,3737. Edland SD, Rocca WA, Petersen RC, Cha RH, Kokmen E. Dementia and Alzheimer disease incidence rates do not vary by sex in Rochester, Minn. Arch Neurol 2002; 59:1589-93.^,3838. Chêne G, Beiser A, Au R, Preis SR, Wolf PA, Dufouil C, et al. Gender and incidence of dementia in the Framingham Heart Study from mid-adult life. Alzheimers Dement 2015; 11:310-20. found no statistically significant differences in AD incidence by sex, which is consistent with our results ⁵³53. Colimon K-M. Fundamentos de epidemiología. Madrid: Ediciones Díaz de Santos; 1990..

The regional differences in SMR are another critical result. Curiously, mortality from AD is higher in the Southeast and South regions of Brazil. One explanation is that the reporting of AD cases may be of higher quality in the more developed regions. Although we adjusted for the underreporting of deaths by state, mortality levels (including overall mortality) may still be underestimated at the higher ages, particularly in the less developed regions, for other reasons like age misreporting in the death records. On the other hand, the fact that the less developed regions are at a less advanced stage in the epidemiological transition may imply in a higher incidence of other causes of mortality, thereby reducing the relative importance of dementia than in the more developed regions (Southeast and South).

The risk of dying from dementia and AD increases with age ²⁴24. James BD, Leurgans SE, Hebert LE, Scherr PA, Yaffe K, Bennett DA. Contribution of Alzheimer disease to mortality in the United States. Neurology 2014; 82:1045-50.^,4646. Brookmeyer R, Evans DA, Hebert L, Langa KM, Heeringa SG, Plassman BL, et al. National estimates of the prevalence of Alzheimer's disease in the United States. Alzheimers Dement 2011; 7:61-73.. At older ages, the highest mortality rates from Alzheimer’s disease were among adults with less schooling (0-3 years). In this case, the rates were around 1,710.5 deaths per 100,000 inhabitants, almost twice as large as among adults in the highest education group. Education works as a possible protective factor against all types of dementia. “Cognitive reserve” is relevant since we found that individuals with all types of dementia in lowest educational level (0-3 years) contributed with 6% of overall adult mortality, and 4.4% in the case of AD. The estimates by education were a significant challenge in our study. Missing data by educational level could have impacted the final results, which justified the data imputation. Nevertheless, the imputation was also not trivial, given the volume of missing data and the uncertainty about the actual distribution of cases by educational level. Also, it was challenging to measure the impact of the inconsistency in the information reported by education in the mortality and population records, since these two data sources were collected separately ⁵⁴54. Martins-Ribeiro M. Mortalidade adulta por níveis de escolaridade no estado e município de São Paulo: uma proposta de estimação a partir do Censo Demográfico de 2010 [Tesis de Doctorado]. Belo Horizonte: Universidade Federal de Minas Gerais; 2016.. Even so, there was evidence of greater consistency in the model with the addition of imputed data ²⁷27. Sandoval JJ. Mortalidad adulta atribuible a la demencia debido a la enfermedad de Alzheimer, Brasil 2009-2013: una perspectiva bayesiana [Tesis de Doctorado]. Belo Horizonte: Faculdade de Ciências Econômicas, Universidade Federal de Minas Gerais; 2016..

In relation to the risk of dying from dementia or AD, our results indicated a clear qualitative difference between 3 years of schooling or less and 4 years or more, which has also been observed in other contexts ²²22. Nitrini R, Caramelli P, Herrera Jr. E, Castro I, Bahia VS, Anghinah R, et al. Mortality from dementia in a community-dwelling Brazilian population. Int J Geriatr Psychiatry 2005; 20:247-53.^,4444. Tom SE, Hubbard RA, Crane PK, Haneuse SJ, Bowen J, McCormick WC, et al. Characterization of dementia and Alzheimer's disease in an older population: updated incidence and life expectancy with and without dementia. Am J Public Health 2015; 105:408-13.^,4545. Villarejo A, Bermejo-Pareja F, Trincado R, Olazarán J, Benito-León J, Rodríguez C, et al. Memory impairment in a simple recall task increases mortality at 10 years in non-demented elderly. Int J Geriatr Psychiatry 2011; 26:182-7.^,5555. Lopes MA, Bottino CMC. Prevalence of dementia in several regions of the world: analysis of epidemiologic studies from 1994 to 2000. Arq Neuropsiquiatr 2002; 60:61-9. in Brazil. Highly educated individuals tend to have better opportunities and probably more comfortable retirement ⁵⁶56. Leandro-França C, Giardini Murta S. Prevention and promotion of mental health in aging: concepts and interventions. Psicol Ciênc Prof 2014; 34:318-29.. We thus believe that education appears as a proxy variable explaining socioeconomic inequalities, more than the relationship of education and mortality from AD at older ages per se.

The increase in life expectancy, new technologies, and better diagnostics can lead to the impression that AD is increasing. In fact, the higher incidence may be due to our better capacity for diagnosis as the elderly population grows. Therefore, cases not previously detected and that were classified as other types of diseases may now be identified more accurately. In addition, environmental factors can now be included in the analysis ⁵⁷57. Hall KS, Gao S, Baiyewu O, Lane KA, Gureje O, Shen J, et al. Prevalence rates for dementia and Alzheimer's disease in African Americans: 1992 versus 2001. Alzheimers Dement 2009; 5:227-33..

Acknowledgments

The present work was carried out with financial support from the Graduate Studies Coordinating Board (Capes, Code 001), which funds the Demography Program of the Federal University of Minas Gerais. C. M. Turra and R. H. Loschi, thank the support received by the Brazilian National Research Council (CNPq). The authors also thank Professors Laura Wong, Bernardo Queiroz, Deise Afonso, Renato Veras and Paulo Caramelli for their reading and suggestions offered for the improvement of this research.

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