R Greville Greville demogr Epi web URL typo R
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2 R Greville Greville demogr Epi web URL typo R
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4 2% 12 30% CT (Ai) A3 *1 WHO I I II *2 *1 web *2 I ICD-10 WHO 4
5 19 National Death Index [ National Death Index 2 National Health Statistics. National Death Index. [ National Death Index National Death Index pp II 5
6 , 1998 Charnov, 1992;,
7 4.2 K K Charnov (1992) K (Hawkes et al., 1998; Alvarez, 2000) Charnov (1992) αm Charnov 7
8 (1) α (2) (3) αm (b) αb (1) 1/M = 0.4 ω 0.1 M ω (Charnov, 1992) (2) (3) 4.4 Westendorp (1998) DNA Wilmoth J Why mortality falls over time? Death human population Recognition Reaction Reduction Death 3R Wilmoth 3R-theory of mortality decline 5 8
9 1 *3 5.1 CDR Crude Death Rate ADR Age-specific Death Rate Chamberlain, 2006 Age-Specific Mortality Rate ASMR ADR DSMR 10 1 Directly Standardized Moratality Rate ADR 1000 *3 9
10 SMR ADR ADR CDR CDR ADR DSMR Standardized Mortality Ratio ISMR Indirectly standardized mortality rate CDR CDR ADR CDR SMR 1994 Smith 1992 Life expectancy Average life span ADR Health expectancy Healthy life expectancy HALE DALE PMI Health Adjusted Life Expectancy QALY Quality Adjusted Life Years) Disability Adjusted Life Expectancy DALY (Disability Adjusted Life Years) 1 1 Proportional Mortality Index Proportional Mortality Indicator 50 10
11 ICD International Statistical Classification of Diseases and Related Health Problems; 10 ICD-10 * Staetsky, 2009) Wilmoth PMR (Proportional Mortality Ratio) YLL Yeas of Life Lost Graham RiskCaT-LLE IMR Infant Mortality Rate * ICD-9 ICD-10 11
12 * NICU Toddler Mortality PIH *
13 *6 0 q x 10 *7 x x T x x l x x x + 1 [x, x+1) q x l x (1 q x /2) x x + 1 L x x x m x x d x x q x q x = m x /(1 + m x /2) * (abridged life table) Greville 5q x = 5m [ x ]] 1/5 + 5 m x [1/2 + 5/12 5m x ln( 5m x+5 ) ln( 5 m x ) 5 (Ng and Gentleman, 1995) 5 * *7 *8 x N x x x + 1 x N x + d x /2 x + 1 d x q x q x = d x N x + d x /2 = d x /N x = m x /(1 + m x /2) N x /N x + d x /2/N x 13
![/2) *8 1 1 2 3 6 1 7 5 (abridged life table) Greville 5q x = 5m [ x ]] 1/5 + 5 m x [1/2 + 5/12 5m x ln( 5m x+5 ) ln( 5 m](/docs-images/41/22686523/images/page_13.jpg "x ) 5 (Ng and Gentleman, 1995) 5 *6 http://www.mhlw.go.jp/toukei/saikin/hw/life/life08/index.")
14 ln( 5 m x+5 ) ln( 5 m x ) 5 5 m x *9 l x l x Gompertz *10 Siler R nls() optim() Siler h(t) = a 1 exp( b 1 t) + a 2 + a 3 exp(b 3 t) l x µ x = 1 dl x l x dx x µ x *9 Greville Ng and Gentleman (1995) Greville TNE (1943) Short methods of constructing abridged life tables. Rec. Am. Inst. Actuar., 32: (1963) nq(x) = nm(x) [ ] 1 n + 1 n m(x) 2 + n 12 { nm(x) ln c} c n m(x) Gompertz nm(x) = Bc x US ln c (2006) nq x = nm [ x 1 n + 1 n m x 2 + n 12 { nm x log e ( n mx+n ) n 1 } nm x Ng and Gentleman Namboodiri and Suchindran (1987) nq x = nm x (1/n) + n M x [(1/2) + (n/12)( n M x k)] k 0.09 Keyfitz Applied Mathematical Demography n µ(x + t)dt = n n m x + n3 12 n m 2 x (log n m x ) 0 Greville n 3 1 *10 Gompertz ] 14
![(1963) nq(x) = nm(x) [ ] 1 n + 1 n m(x) 2 + n 12 { nm(x) ln c} c n m(x) Gompertz nm(x) = Bc x US ln c 0.080 0.104 0.](/docs-images/41/22686523/images/page_14.jpg "09 (2006) nq x = nm [ x 1 n + 1 n m x 2 + n 12 { nm x log e ( n mx+n ) n 1 } nm x Ng and Gentleman Namboodiri and Suchindran (1987) nq x = nm x (1/n) + n M x [(1/2) + (n/12)( n M x k)] k 0.")
15 5.4 frailty Kaplan-Meier R survival *11 [parish record] *
![record] *11 http://phi.med.](/docs-images/41/22686523/images/page_15.jpg "gunma-u.ac.")
16 5.5 Age-Period-Cohort APC R Epi apc.fit() apc.plot() plot.lexis() Carstensen, 2007) 6 Graunt (1662) DeMoivre (1725) l(x) x l(x) = l(0) (1 x/a) l(x) x a Graunt Gompertz-Makeham 3 Thiele 5 Siler 8 Mode-Busby Helligman and Pollard Mode-Jacobson Gage and Mode, Denny (Denny, 1997) * 12 Siler h(t) = a 1 exp( b 1 t) + a 2 + a 3 exp(b 3 t) Gage (1991) Gage 1 * a, b, c 1 l(x) = x (1 + a( + b x e 105 x 1 + c(1 e 2x ) 105 x ))3 16
17 2 3 a 1 Coale and Demeny *13 2 Brass (1968) *14 (1) (2) (3) (Gavrilov and Gavrilova, 1991 (1) s 0, s 1, s 2,..., s n,... 0, 1, 2,..., n,... λ 0 µ 0 (2) λ µ Le Bras, 1976 µ 0 (3) µ(x) = µ 0 + µλ 0 (1 exp( (λ + µ)x))/(µ + λ exp( (λ + µ)x)) λ << µ x Gompertz-Makeham frailty (Mori and Nakazawa, 2003) * [ ] 25 *14 l x l 0 (x) l x l s 2 a, b 1 2 ln( 1 l 0(x) ) = a + b l 0 (x) 2 ln( 1 l s(x) ) l s (x) 17
18 11 0.4% % S (Mori and Nakazawa, 2003) λ 0 λ 0 7 Excel R Excel R R demogr * 15 Epi * 16 *15 *
19 demogr Coale and Demeny Epi Age-Period-Cohort mortality.r(1) # mortalityj.r # rev December 2009 (C) Minato Nakazawa <minato-nakazawa@umin.net> # sample data definition and standardization # References: # # 20 2 # Mortality data of Japanese in Japan. # 2006 S60modelpopJ 60 # S60modelpopJ <- c(8180,8338,8497,8655,8814,8972,9130,9289,9400,8651,7616, 6581,5546,4511,3476,2441,1406,784)*1000 AC <- c(paste("[",0:16*5,"-",0:16*5+4,"]",sep=""),"[85-]") # same as follows: # AC <- c("[0-4]", "[5-9]", "[10-14]", "[15-19]", "[20-24]", # "[25-29]", "[30-34]", "[35-39]", "[40-44]", "[45-49]", # "[50-54]", "[55-59]", "[60-64]", "[65-69]", "[70-74]", # "[75-79]", "[80-84]", "[85-]") names(s60modelpopj) <- AC S60M <- c(6042, 1155, 1011, 3179, 3397, 3167, 4237, 7110, 10234, 15063, 24347, 30747, 30884, 38240, 55100, 65593, 59125, 48786) names(s60m) <- AC H02M <- c(4532, 844, 760, 3204, 3466, 2916, 3264, 5449, 9769, 14218, 20161, 32925, 42742, 42664, 51737, 69320, 67916, 67451) names(h02m) <- AC H07M <- c(3929, 752, 716, 2413, 3640, 3203, 3297, 4413, 8236, 15616, 21905, 30491, 47188, 59828, 60927, 68504, 77924, 87750) names(h07m) <- AC H12M <- c(2933, 438, 493, 1721, 2875, 3271, 3749, 4621, 6840, 13141, 24103, 31848, 42214, 60962, 76413, 73947, 73533, ) names(h12m) <- AC H17M <- c(2291, 409, 361, 1220, 2303, 2887, 3915, 4915, 6806, 10577, 19546, 34233, 43403, 55261, 80198, 99338, 89502, ) names(h17m) <- AC 19
![# 2006 S60modelpopJ 60 # S60modelpopJ <- c(8180,8338,8497,8655,8814,8972,9130,9289,9400,8651,7616, 6581,5546,4511,3476,2441,1406,784)*1000 AC <- c(paste("[",0:16*5,"-",0:16*5+4,"]",sep=""),"[85-]") #](/docs-images/41/22686523/images/page_19.jpg "same as follows: # AC <- c(\"[0-4]\", \"[5-9]\", \"[10-14]\", \"[15-19]\", \"[20-24]\", # \"[25-29]\", \"[30-34]\", \"[35-39]\", \"[40-44]\", \"[45-49]\", # \"[50-54]\", \"[55-59]\", \"[60-64]\", \"[65-69]\", \"[70-74]\", #")
20 mortality.r(2) S60F <- c(4792, 636, 638, 1033, 1272, 1558, 2496, 4017, 5650, 7644, 11504, 14828, 19961, 26490, 40891, 55657, 64448, 80930) names(s60f) <- AC H02F <- c(3451, 533, 482, 1149, 1329, 1361, 1774, 3102, 5542, 7510, 10097, 14616, 19986, 27267, 38076, 58203, 71633, ) names(h02f) <- AC H07F <- c(3111, 483, 468, 949, 1447, 1393, 1832, 2426, 4578, 8520, 11041, 14241, 21122, 29261, 41516, 56924, 79939, ) names(h07f) <- AC H12F <- c(2336, 300, 251, 676, 1160, 1546, 1847, 2425, 3639, 6595, 11740, 14144, 18466, 28096, 40115, 57053, 73527, ) names(h12f) <- AC H17F <- c(1811, 246, 229, 582, 1067, 1283, 2037, 2554, 3432, 5177, 9418, 15346, 18855, 25568, 40627, 60024, 84683, ) names(h17f) <- AC S60P <-c(7459, 8532, 10042, 8980, 8201, 7823, 9054, 10738, 9135, 8237, 7933, 7000, 5406, 4193, 3563, 2493, 1433, 785)*1000 names(s60p) <- AC H02P <- c(6493, 7467, 8527, 10007, 8800, 8071, 7788, 9004, 10658, 9018, 8088, 7725, 6745, 5104, 3818, 3018, 1833, 1122)*1000 names(h02p) <- AC H07P <- c(5995, 6541, 7478, 8558, 9895, 8788, 8126, 7822, 9006, 10618, 8922, 7953, 7475, 6396, 4695, 3289, 2301, 1580)*1000 names(h07p) <- AC H12P <- c(5904, 6022, 6547, 7488, 8421, 9790, 8777, 8115, 7800, 8916, 10442, 8734, 7736, 7106, 5901, 4151, 2615, 2233)*1000 names(h12p) <- AC H17P <- c(5578, 5928, 6015, 6568, 7351, 8280, 9755, 8736, 8081, 7726, 8796, 10255, 8545, 7433, 6637, 5263, 3412, 2927)*1000 names(h17p) <- AC ASMR ADR R 20
21 mortality.r(3) S60T <- S60M+S60F H02T <- H02M+H02F H07T <- H07M+H07F H12T <- H12M+H12F H17T <- H17M+H17F S60ASMR <- S60T/S60P; S60CDR <- sum(s60t)/sum(s60p) H02ASMR <- H02T/H02P; H02CDR <- sum(h02t)/sum(h02p) H07ASMR <- H07T/H07P; H07CDR <- sum(h07t)/sum(h07p) H12ASMR <- H12T/H12P; H12CDR <- sum(h12t)/sum(h12p) H17ASMR <- H17T/H17P; H17CDR <- sum(h17t)/sum(h17p) CDRs <- c(s60cdr, H02CDR, H07CDR, H12CDR, H17CDR) mortality.r(4) DSMR <- function(asmr) { if (length(asmr)!=18) { print("age class is inadequate."); NA } else { sum(asmr*s60modelpopj)/sum(s60modelpopj) } } DSMRs <- c(dsmr(s60asmr),dsmr(h02asmr),dsmr(h07asmr),dsmr(h12asmr),dsmr(h17asmr)) pdf mortality.r(5) pdf("mortalityj.pdf",width=8,height=8) plot(1:5,cdrs,type="l",col="black",xlab="year",axes=f,ylab="mortality", ylim=c(0,0.01)) axis(1,1:5,c("s60","h02","h07","h12","h17")) axis(2,seq(0,0.01,by=0.002)) lines(dsmrs,col="red",lty=2) legend("topright",col=c("black","red"),lty=c(1,2),legend=c("cdrs","dsmrs")) dev.off() 21
22 (mode==1) Greville (mode==2) 22
23 lifetable.r(1) # lifetable.r # rev December 2009 (C) Minato Nakazawa <minato-nakazawa@umin.net> # function definition to make a life table. # included data is lifetable <- function(mx,class=5,mode=1) { nc <- length(mx) if (length(mx)!=nc) exit qx <- numeric(nc) if (mode==1) { qx <- mx/(1+mx/2) } else { for (i in 1:(nc-1)) { qx[i] <- mx[i] / (1/class+mx[i]*(1/2+class/12*(mx[i]-(log(mx[i+1])-log(mx[i]))/class))) / class } qx[nc] <- mx[nc] / (1/class+mx[nc]*(1/2+class/12*mx[nc])) / class } dx <- numeric(nc) lx <- numeric(nc) Lx <- numeric(nc) lx[1] < for (i in 1:(nc-1)) { dx[i] <- lx[i]*qx[i]*class lx[i+1] <- lx[i]-dx[i] Lx[i] <- (lx[i]+lx[i+1])/2*class } Tx <- cumsum(lx[nc:1])[nc:1] ex <- Tx/lx data.frame(mx,qx,lx,lx,tx,ex) } 23
24 lifetable.r(2) qxjmh20 <- c( , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ) names(qxjmh20) <- c(sprintf("%d",0:104),"105-") qxjfh20 <- c( , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ) names(qxjfh20) <- c(sprintf("%d",0:104),"105-") 20 q x q x 24
25 lifetable.r(3) clifetable <- function(qx) { nc <- length(qx) lx <- numeric(nc) dx <- numeric(nc) Lx <- numeric(nc) lx[1] < for (i in 1:(nc-1)) { dx[i] <- lx[i]*qx[i] lx[i+1] <- lx[i]-dx[i] Lx[i] <- (lx[i]+lx[i+1])/2 } Tx <- cumsum(lx[nc:1])[nc:1] ex <- Tx/lx data.frame(qx,lx,dx,lx,tx,ex) } <nminato@med.gunma-u.ac.jp> clifetable(qxjmh20) 60 Greville lifetable.r(4) lifetable(s60asmr,class=5,mode=2) 25
26 mx qx lx Lx Tx ex [0-4] [5-9] [10-14] [15-19] [20-24] [25-29] [30-34] [35-39] [40-44] [45-49] [50-54] [55-59] [60-64] [65-69] [70-74] [75-79] [80-84] [85-] R optim() Siler Gompertz-Makeham q(x) optim() Denny l(x) R 26
27 lifetable.r(5) # H20 Siler Gompertz-Makeham Denny clx <- function(qx) { nc <- length(qx); lx <- numeric(nc); dx <- numeric(nc) lx[1] <- 1 for (i in 1:(nc-1)) { dx[i] <- lx[i]*qx[i]; lx[i+1] <- lx[i]-dx[i] } lx[nc] <- 0 lx } Siler <- function(a1,b1,a2,a3,b3,t) { rval <- a1*exp(-b1*t)+a2+a3*exp(b3*t); ifelse(rval<0,0,rval) } fsilerm <- function(x) { sum((siler(x[1],x[2],x[3],x[4],x[5],ages[1:105])-qxjmh20[1:105])^2) } (rs <- optim(rep(0,5),fsilerm)) GompertzMakeham <- function(a,b,c,t) { rval <- A + B*C^t; ifelse(rval<0,0,rval) } fgompertzmakehamm <- function(x) { sum((gompertzmakeham(x[1],x[2],x[3],ages[1:105])-qxjmh20[1:105])^2) } (rg <- optim(rep(0.1,3),fgompertzmakehamm)) Denny <- function(a,b,c,t) { 1/(1+a*(t/(105-t))^3)+b*sqrt(exp(t/(105-t))-1)+c*(1-exp(-2*t)) } fdennym <- function(x) { sum((denny(x[1],x[2],x[3],ages[1:105])-clx(qxjmh20[1:105]))^2) } (rd <- optim(rep(0,3),fdennym)) layout(t(1:2)) plot(ages,qxjmh20, main="models fitted for Japanese males\n qx in 2008",ylab="qx") lines(ages,siler(rs$par[1],rs$par[2],rs$par[3],rs$par[4],rs$par[5],ages), col="blue",lty=1,lwd=2) lines(ages,gompertzmakeham(rg$par[1],rg$par[2],rg$par[3],ages), col="red",lty=2,lwd=2) legend("topleft",lty=1:2,lwd=2,col=c("blue","red"), legend=c("siler","gompertz-makeham")) plot(ages,clx(qxjmh20), main="models fitted for Japanese males\n qx or converted lx in 2008",ylab="lx") lines(ages,clx(siler(rs$par[1],rs$par[2],rs$par[3],rs$par[4],rs$par[5],ages)), col="blue",lty=1,lwd=2) lines(ages,clx(gompertzmakeham(rg$par[1],rg$par[2],rg$par[3],ages)), col="red",lty=2,lwd=2) lines(ages,denny(rd$par[1],rd$par[2],rd$par[3],ages),col="black",lty=3,lwd=2) legend("bottomleft",lty=1:3,lwd=2,col=c("blue","red","black"), legend=c("siler","gompertz-makeham","denny")) 27
28 8 Alvarez HP (2000) Grandmother hypothesis and primate life histories. American Journal of Physical Anthropology, 113: Carstensen B (2007) Age-period-cohort models for the Lexis diagram. Statistics in Medicine, 26(15): CDC: Deaths and Mortality. [ Chamberlain AT (2006) Demography in Archaeology. Cambridge University Press. Charnov EL (1992) Life History Invariants. Oxford University Press. Denny C (1997) A model of the probability of survival from birth. Mathematical and Computer Modelling, 26: Gage TB (1991) Causes of death and the components of mortality: Testing the biological interpretations of a competing hazards model. American Journal of Human Biology, 3(3): Gage TB, Mode CJ (1993) Some laws of mortality: How well do they fit? Human Biology, 65: Gavrilov LA, Gavrilova NS (1991) The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York. Hawkes KJF, O Connell NG, Blurton-Jones HA, Charnov EL (1998) Grandmothering, menopause, and the evolution of human life histories. Proceedings of National Academy of Sciences, USA, 95:
29 (1992). [ ] (2006). Keyfitz N, Caswell H (2005) Applied Mathematical Demography. Science+Business Media, Inc., New York. 3rd Ed., Springer (1994). (1980) 1966., 20: Mori Y, Nakazawa M (2003) A new simple etiological model of human death. Journal of Population Studies (Jinko-Gaku-Kenkyu), 33: Ng E, Gentleman JF (1995) The impact of estimation method and population adjustment on Canadian life table estimates. Health Reports, 7(3): Smith DP (1992) Formal Demography. Plenum Press. Staetsky L (2009) Diverging trends in female old-age mortality: A reappraisal. Demographic Research, 21: 30. [ (1998). (1968). (2006) Excel. Westendorp RGJ, Kirkwood TBL (1998) Human longevity at the cost of reproductive success. Nature, 396: The 29
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IMES DISCUSSION PAPER SERIES Discussion Paper No. 99-J-17 INSTITUTE FOR MONETARY AND ECONOMIC STUDIES BANK OF JAPAN 100-8630 203 IMES Discussion Paper Series 99-J-17 1999 6 * JEL classification E52 E58
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Kobe University Repository : Kernel タイトル Title 著者 Author(s) 掲載誌 巻号 ページ Citation 刊行日 Issue date 資源タイプ Resource Type 版区分 Resource Version 権利 Rights DOI
Kobe University Repository : Kernel タイトル Title 著者 Author(s) 掲載誌 巻号 ページ Citation 刊行日 Issue date 資源タイプ Resource Type 版区分 Resource Version 権利 Rights DOI 成人寿命の増加と国民貯蓄率に関する実証研究 (An Empirical Analysis on Increase
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