Nothing
R/cdmltw.R
In DDM: Death Registration Coverage Estimation
Defines functions
cdmltw
Documented in
cdmltw
#' @title Coale-Demeny model life table: West
#' @description function from now-deprecated \code{demogR} package. Originally written by Ken Wachter, modified by James Jones, and again by the current maintainer, Tim Riffe. Only minor edits to margin naming in the current version.
#' @param sex \code{"F"} or \code{"M"}
#' @return Tons of lifetable output in matrices. Age in columns, lifetable levels in rows.
#'
#' @importFrom stats approx
#' @export
cdmltw <-
function(sex="F"){
if (sex != "F" & sex !="M"){
stop("sex must be either F or M!")
}
# CD lifetables indexed by e_10 = eten
# must do a first pass of females to get eten values for both sexes
for(i in 1:2){
if(i==1){
eten <- seq(20,84, by = 2)
}else eten <- etenf
# Level 1 is ef=20, Level 25 is ef = 80
# Estimated eten values to give levels 1 to 25 (from previous runs) :
etenf <- c( 21.40560, 25.32906, 28.86371, 32.07434, 35.01080, 37.71234 )
etenf <- c( etenf, 40.21043, 42.53071, 44.69434, 46.71898, 48.61956, 50.40878 )
etenf <- c( etenf, 52.08246, 53.35279, 54.56258, 55.83396, 57.16346, 58.54585 )
etenf <- c( etenf, 59.97358, 61.43734, 62.99543, 65.49976, 68.71259, 72.92473 )
etenf <- c( etenf, 78.62524 ) # etenf values for Levels 1 to 25
eten <- etenf
# Unit vector of same length as eten
eee <- 1 + 0*eten
# ages at start of groups; later extended.
xx <- c(0, 1, seq(5,75, by=5) )
# FEMALE ax and bx are the coefficients of the simple regressions of
# the nqx's on e10
ax <- c( .53774,.39368,.10927,.08548,.10979,.1358,.15134,.17032,.18464,.1939,.20138)
ax <- c(ax,.2535,.31002,.43445,.53481,.69394,.84589)
bx <- c( -.008044,-.006162,-.001686,-.00132,-.001672,-.002051,-.002276,-.002556)
bx <- c(bx,-.002745,-.002828,-.002831,-.003487,-.004118,-.005646,-.00646,-.007713)
bx <- c(bx,-.008239)
# a1x and b1x are the coefficients of the log-regressions of the nqx's on e10.
a1x <- c( 5.8992,7.4576,6.2018,5.9627,5.9335,5.9271,5.8145,5.6578,5.3632,4.96)
a1x <- c(a1x,4.5275,4.4244,4.3131,4.3439,4.2229,4.1838,4.1294)
b1x <- c( -.05406,-.08834,-.0741,-.07181,-.06812,-.06577,-.06262,-.05875,-.05232)
b1x <- c(b1x,-.0438,-.03436,-.03004,-.02554,-.02295,-.01773,-.01376,-.00978)
#####################################################################
##### # Calculate an array of probabilities of dying nqx up to age 75
#######################################################################
# The first subscript refers to e10; the second to the age x.
nqxa <- eee %o% ax + eten %o% bx # nqx from linear model
nqxl <- (1/10000)*10^( eee %o% a1x + eten %o% b1x ) # exponential model
#
# Choose among linear, mixed, and exponential models
# on basis of crossover points and slopes.
slopechk <- ( (0*eten + 1/log(10)) %o% (bx/b1x) ) * (1/nqxl ) # Slope check
nqx <- ( nqxa + nqxl) / 2
nqx <- ifelse( nqxa <= nqxl & slopechk < 1, nqxa, nqx )
nqx <- ifelse( nqxa <= nqxl & slopechk >= 1, nqxl, nqx )
####################################################################
#### Calculate the survivorship proportions lx up to age 75
##################################################################
u <- log( 1 - nqx)
uu <- t( apply( u, c(1), cumsum ) )
km1 <- length( uu[1,]) - 1 # number of age groups minus 1
lx <- cbind( 1+0*eee, exp( uu[ , 1:km1]) )
#####################################################################
# Special extension from ages 80 to 100 (i.e. for j> 18
###############################################################
nL75 <- 5*lx[,17]*(1-nqx[,17]) + (1/2)*5*lx[,17]*nqx[,17]
leighty <- lx[,17]*(1-nqx[,17]) # Survivorship to age 80
m77 <- lx[,17]*nqx[,17]/nL75 # m77 is hazard age 77.5.
m105 <- 0.613+ 1.75*nqx[,17]
kappa <- (1/27.5)*log( m105 / m77 ) # THIS CORRECTS COALE'S MISTAKE
m80 <- m77*exp(kappa*2.5) # Hazard at age 80
xlong <- seq(80,121, by = 0.2 ) - 80 # ages in 1/5 years -80
uu <- kappa %o% xlong
u <- (-m80/kappa) %o% ( 1 + 0*xlong)
llx <- leighty %o% ( 1 + 0*xlong)
llx <- llx * exp ( u*exp(uu) - u )
nL80 <- llx[, 1:26 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL85 <- llx[, 26:51 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL90 <- llx[, 51:76 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL95 <- llx[, 76:101 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
T100 <- as.vector( llx[, 101:201] %*% c( 1/2, rep(1,99), 1/2)*(1/5))
#################################################################
##### Compute other functions in the lifetable
#################################################################
xx <- c(0, 1, seq(5,95, by=5) ) # ages
nn <- c( diff(xx),8 ) # age group widths
lx <- cbind( lx[ , 1:17], llx[ , c(1,26,51,76)] )
qqx <- ( llx[ , c(1,26,51) ] - llx[ , c(26,51,76)] )/llx[, c(1,26,51)]
nqx <- cbind( nqx[ , 1:17], qqx, eee )
dimnames(nqx)[[1]] <- paste(seq(eten))
dimnames(nqx)[[2]] <- paste(xx)
dimnames(lx) <- dimnames(nqx)
na0 <- 0.050 + 3.00*nqx[,1]
na0 <- ifelse( nqx[,1]< 0.100, na0, 0.35 )
na1 <- 1.524 - 1.625*nqx[,1]
na1 <- ifelse( nqx[,1]< 0.100, na1, 1.361)
nax <- cbind( na0, na1, 2.25*eee)
nax <- cbind( nax, 2.6*eee %o% rep(1,13), 2.5*eee)
nax <- cbind( nax, 2.5*eee %o% rep(1,4) ) # Extend to length 21
dimnames(nax) <- dimnames(nqx)
ndx <- lx*nqx
nLx <- ( eee %o% nn )*( lx - ndx ) + nax*ndx
nLx <- cbind( nLx[ , 1:17], nL80, nL85, nL90, nL95 )
nmx <- ndx/nLx
K <- rev(seq(xx)) # Reversed indices for age groups
Tx <- t( apply( nLx[, K], c(1), cumsum) )
Tx <- ( T100 %o% rep(1,21) ) + Tx[,K]
ex <- Tx/lx
nLxf <- nLx # Save nLx for females in separate array
# TR: column labelling for easier selection afterward:
Ncol <- ncol(ex)
cols <- c(0,1,seq(5,5*(Ncol-2),by=5))
colnames(ex)<- cols # only needed for BH functions
out <- list(age=xx,width=nn,lx=lx,nqx=nqx,nax=nax,ndx=ndx,nLx=nLx,nmx=nmx,Tx=Tx,ex=ex)
##################################################################
##### Interpolate to find eten values corresponding to Levels 1,2,3...
##### This section is only used in first runs of program to determine eten
######################################################################
if(i==1){
u <- approx( ex[,1], eten, seq(20, 80, by=2.5), rule=2 )
etenf <- u$y # Estimate of eten which produce C-D LEvels
}
}
######################################################################
if(sex=="F") return(out)
else{
#
# etenm is a linear function of etenf from runs of Coale-Demeny female
# program etenm <- 2.298048 + 0.914067*etenf
etenm <- c( 21.86420, 25.45051, 28.68141, 31.61614, 34.30026, 36.76965 )
etenm <- c(etenm, 39.05308, 41.17397, 43.15167, 45.00232, 46.73959, 48.37505 )
etenm <- c(etenm, 49.90490, 51.06607, 52.17190, 53.33403, 54.54928, 55.81287 )
etenm <- c(etenm, 57.11792, 58.45590, 59.88009, 62.16922, 65.10596, 68.95614 )
etenm <- c(etenm, 74.16678 )
## eten_seq(20,86, by = 2) # Code used for first pass to find etenm values
eten <- etenm #
eee <- 1 + 0*eten # Unit vector of same length as eten
xx <- c(0, 1, seq(5,75, by=5) ) # ages at start of groups; later extended.
# MALE ax and bx are the coefficients of the simple regressions of the nqx's on e10.
ax <- c( 0.63726, 0.40548, 0.10393, 0.07435, 0.09880, 0.14009, 0.15785, 0.18260, 0.21175)
ax <- c( ax, 0.25049, 0.27894, 0.33729, 0.38425, 0.48968, 0.59565, 0.73085, 0.98976)
bx <- c( -0.009958, -0.006653, -0.001662, -0.001183, -0.001539, -0.002183, -0.002479)
bx <- c(bx, -0.002875, -0.003312, -0.003864, -0.004158, -0.004856, -0.005190, -0.006300)
bx <- c(bx, -0.007101, -0.007911, -0.008695 )
# MALE a1x and b1x are the coefficients of the log-regressions of the nqx's on e10.
a1x <- c( 5.8061, 7.1062, 5.4472, 5.0654, 4.8700, 5.0677, 5.2660, 5.3438, 5.2792)
a1x <- c(a1x, 5.0415, 4.6666, 4.4506, 4.2202, 4.1851, 4.1249, 4.1051, 4.1133)
b1x <- c( -0.05338, -0.08559, -0.06295, -0.05817, -0.05070, -0.05156, -0.05471)
b1x <- c(b1x, -0.05511, -0.05229, -0.04573, -0.03637, -0.02961, -0.02256 )
b1x <- c(b1x, -0.01891, -0.01491, -0.01161, -0.00895 )
#####################################################################
##### # Calculate an array of probabilities of dying nqx up to age 75
#######################################################################
# The first subscript refers to e10; the second to the age x.
nqxa <- eee %o% ax + eten %o% bx # nqx from linear model
nqxl <- (1/10000)*10^( eee %o% a1x + eten %o% b1x ) # exponential model
#
# Choose among linear, mixed, and exponential models
# on basis of crossover points and slopes.
slopechk <- ( (0*eten + 1/log(10)) %o% (bx/b1x) ) * (1/nqxl ) # Slope check
nqx <- ( nqxa + nqxl) / 2
nqx <- ifelse( nqxa <= nqxl & slopechk < 1, nqxa, nqx )
nqx <- ifelse( nqxa <= nqxl & slopechk >= 1, nqxl, nqx )
####################################################################
#### Calculate the survivorship proportions lx up to age 75
##################################################################
u <- log( 1 - nqx)
uu <- t( apply( u, c(1), cumsum ) )
km1 <- length( uu[1,]) - 1 # number of age groups minus 1
lx <- cbind( 1+0*eee, exp( uu[ , 1:km1]) )
#####################################################################
# Special extension from ages 80 to 100 (i.e. for j> 18
###############################################################
nL75 <- 5*lx[,17]*(1-nqx[,17]) + (1/2)*5*lx[,17]*nqx[,17]
leighty <- lx[,17]*(1-nqx[,17]) # Survivorship to age 80
m77 <- lx[,17]*nqx[,17]/nL75 # m77 is hazard age 77.5.
m105 <- 0.613+ 1.75*nqx[,17]
kappa <- (1/27.5)*log( m105 / m77 ) # THIS CORRECTS COALE'S MISTAKE
m80 <- m77*exp(kappa*2.5) # Hazard at age 80
xlong <- seq(80,121, by = 0.2 ) - 80 # ages in 1/5 years -80
uu <- kappa %o% xlong
u <- (-m80/kappa) %o% ( 1 + 0*xlong)
llx <- leighty %o% ( 1 + 0*xlong)
llx <- llx * exp ( u*exp(uu) - u )
nL80 <- llx[, 1:26 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL85 <- llx[, 26:51 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL90 <- llx[, 51:76 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL95 <- llx[, 76:101 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
T100 <- as.vector( llx[, 101:201] %*% c( 1/2, rep(1,99), 1/2)*(1/5))
#################################################################
##### Compute other functions in the lifetable
#################################################################
xx <- c(0, 1, seq(5,95, by=5) ) # ages
nn <- c( diff(xx),8 ) # age group widths
lx <- cbind( lx[ , 1:17], llx[ , c(1,26,51,76)] )
qqx <- ( llx[ , c(1,26,51) ] - llx[ , c(26,51,76)] )/llx[, c(1,26,51)]
nqx <- cbind( nqx[ , 1:17], qqx, eee )
dimnames(nqx)[[1]] <- paste(seq(eten))
dimnames(nqx)[[2]] <- paste(xx)
dimnames(lx) <- dimnames(nqx)
na0 <- 0.050 + 3.00*nqx[,1]
na0 <- ifelse( nqx[,1]< 0.100, na0, 0.35 )
na1 <- 1.524 - 1.625*nqx[,1]
na1 <- ifelse( nqx[,1]< 0.100, na1, 1.361)
nax <- cbind( na0, na1, 2.25*eee)
nax <- cbind( nax, 2.6*eee %o% rep(1,13), 2.5*eee)
nax <- cbind( nax, 2.5*eee %o% rep(1,4) ) # Extend to length 21
dimnames(nax) <- dimnames(nqx)
ndx <- lx*nqx
nLx <- ( eee %o% nn )*( lx - ndx ) + nax*ndx
nLx <- cbind( nLx[ , 1:17], nL80, nL85, nL90, nL95 )
nmx <- ndx/nLx
K <- rev(seq(xx)) # Reversed indices for age groups
Tx <- t( apply( nLx[, K], c(1), cumsum) )
Tx <- ( T100 %o% rep(1,21) ) + Tx[,K]
ex <- Tx/lx
nLxm <- nLx # Save nLx for males in separate array
# TR: column labelling for easier selection afterward:
Ncol <- ncol(ex)
cols <- c(0,1,seq(5,5*(Ncol-2),by=5))
colnames(ex)<- cols # only needed for BH functions
out <- list(age=xx,width=nn,lx=lx,nqx=nqx,nax=nax,ndx=ndx,nLx=nLx,nmx=nmx,Tx=Tx,ex=ex)
return(out)
}
}
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Defines functions cdmltw
Documented in cdmltw
#' @title Coale-Demeny model life table: West
#' @description function from now-deprecated \code{demogR} package. Originally written by Ken Wachter, modified by James Jones, and again by the current maintainer, Tim Riffe. Only minor edits to margin naming in the current version.
#' @param sex \code{"F"} or \code{"M"}
#' @return Tons of lifetable output in matrices. Age in columns, lifetable levels in rows.
#'
#' @importFrom stats approx
#' @export
cdmltw <-
function(sex="F"){
if (sex != "F" & sex !="M"){
stop("sex must be either F or M!")
}
# CD lifetables indexed by e_10 = eten
# must do a first pass of females to get eten values for both sexes
for(i in 1:2){
if(i==1){
eten <- seq(20,84, by = 2)
}else eten <- etenf
# Level 1 is ef=20, Level 25 is ef = 80
# Estimated eten values to give levels 1 to 25 (from previous runs) :
etenf <- c( 21.40560, 25.32906, 28.86371, 32.07434, 35.01080, 37.71234 )
etenf <- c( etenf, 40.21043, 42.53071, 44.69434, 46.71898, 48.61956, 50.40878 )
etenf <- c( etenf, 52.08246, 53.35279, 54.56258, 55.83396, 57.16346, 58.54585 )
etenf <- c( etenf, 59.97358, 61.43734, 62.99543, 65.49976, 68.71259, 72.92473 )
etenf <- c( etenf, 78.62524 ) # etenf values for Levels 1 to 25
eten <- etenf
# Unit vector of same length as eten
eee <- 1 + 0*eten
# ages at start of groups; later extended.
xx <- c(0, 1, seq(5,75, by=5) )
# FEMALE ax and bx are the coefficients of the simple regressions of
# the nqx's on e10
ax <- c( .53774,.39368,.10927,.08548,.10979,.1358,.15134,.17032,.18464,.1939,.20138)
ax <- c(ax,.2535,.31002,.43445,.53481,.69394,.84589)
bx <- c( -.008044,-.006162,-.001686,-.00132,-.001672,-.002051,-.002276,-.002556)
bx <- c(bx,-.002745,-.002828,-.002831,-.003487,-.004118,-.005646,-.00646,-.007713)
bx <- c(bx,-.008239)
# a1x and b1x are the coefficients of the log-regressions of the nqx's on e10.
a1x <- c( 5.8992,7.4576,6.2018,5.9627,5.9335,5.9271,5.8145,5.6578,5.3632,4.96)
a1x <- c(a1x,4.5275,4.4244,4.3131,4.3439,4.2229,4.1838,4.1294)
b1x <- c( -.05406,-.08834,-.0741,-.07181,-.06812,-.06577,-.06262,-.05875,-.05232)
b1x <- c(b1x,-.0438,-.03436,-.03004,-.02554,-.02295,-.01773,-.01376,-.00978)
#####################################################################
##### # Calculate an array of probabilities of dying nqx up to age 75
#######################################################################
# The first subscript refers to e10; the second to the age x.
nqxa <- eee %o% ax + eten %o% bx # nqx from linear model
nqxl <- (1/10000)*10^( eee %o% a1x + eten %o% b1x ) # exponential model
#
# Choose among linear, mixed, and exponential models
# on basis of crossover points and slopes.
slopechk <- ( (0*eten + 1/log(10)) %o% (bx/b1x) ) * (1/nqxl ) # Slope check
nqx <- ( nqxa + nqxl) / 2
nqx <- ifelse( nqxa <= nqxl & slopechk < 1, nqxa, nqx )
nqx <- ifelse( nqxa <= nqxl & slopechk >= 1, nqxl, nqx )
####################################################################
#### Calculate the survivorship proportions lx up to age 75
##################################################################
u <- log( 1 - nqx)
uu <- t( apply( u, c(1), cumsum ) )
km1 <- length( uu[1,]) - 1 # number of age groups minus 1
lx <- cbind( 1+0*eee, exp( uu[ , 1:km1]) )
#####################################################################
# Special extension from ages 80 to 100 (i.e. for j> 18
###############################################################
nL75 <- 5*lx[,17]*(1-nqx[,17]) + (1/2)*5*lx[,17]*nqx[,17]
leighty <- lx[,17]*(1-nqx[,17]) # Survivorship to age 80
m77 <- lx[,17]*nqx[,17]/nL75 # m77 is hazard age 77.5.
m105 <- 0.613+ 1.75*nqx[,17]
kappa <- (1/27.5)*log( m105 / m77 ) # THIS CORRECTS COALE'S MISTAKE
m80 <- m77*exp(kappa*2.5) # Hazard at age 80
xlong <- seq(80,121, by = 0.2 ) - 80 # ages in 1/5 years -80
uu <- kappa %o% xlong
u <- (-m80/kappa) %o% ( 1 + 0*xlong)
llx <- leighty %o% ( 1 + 0*xlong)
llx <- llx * exp ( u*exp(uu) - u )
nL80 <- llx[, 1:26 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL85 <- llx[, 26:51 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL90 <- llx[, 51:76 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL95 <- llx[, 76:101 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
T100 <- as.vector( llx[, 101:201] %*% c( 1/2, rep(1,99), 1/2)*(1/5))
#################################################################
##### Compute other functions in the lifetable
#################################################################
xx <- c(0, 1, seq(5,95, by=5) ) # ages
nn <- c( diff(xx),8 ) # age group widths
lx <- cbind( lx[ , 1:17], llx[ , c(1,26,51,76)] )
qqx <- ( llx[ , c(1,26,51) ] - llx[ , c(26,51,76)] )/llx[, c(1,26,51)]
nqx <- cbind( nqx[ , 1:17], qqx, eee )
dimnames(nqx)[[1]] <- paste(seq(eten))
dimnames(nqx)[[2]] <- paste(xx)
dimnames(lx) <- dimnames(nqx)
na0 <- 0.050 + 3.00*nqx[,1]
na0 <- ifelse( nqx[,1]< 0.100, na0, 0.35 )
na1 <- 1.524 - 1.625*nqx[,1]
na1 <- ifelse( nqx[,1]< 0.100, na1, 1.361)
nax <- cbind( na0, na1, 2.25*eee)
nax <- cbind( nax, 2.6*eee %o% rep(1,13), 2.5*eee)
nax <- cbind( nax, 2.5*eee %o% rep(1,4) ) # Extend to length 21
dimnames(nax) <- dimnames(nqx)
ndx <- lx*nqx
nLx <- ( eee %o% nn )*( lx - ndx ) + nax*ndx
nLx <- cbind( nLx[ , 1:17], nL80, nL85, nL90, nL95 )
nmx <- ndx/nLx
K <- rev(seq(xx)) # Reversed indices for age groups
Tx <- t( apply( nLx[, K], c(1), cumsum) )
Tx <- ( T100 %o% rep(1,21) ) + Tx[,K]
ex <- Tx/lx
nLxf <- nLx # Save nLx for females in separate array
# TR: column labelling for easier selection afterward:
Ncol <- ncol(ex)
cols <- c(0,1,seq(5,5*(Ncol-2),by=5))
colnames(ex)<- cols # only needed for BH functions
out <- list(age=xx,width=nn,lx=lx,nqx=nqx,nax=nax,ndx=ndx,nLx=nLx,nmx=nmx,Tx=Tx,ex=ex)
##################################################################
##### Interpolate to find eten values corresponding to Levels 1,2,3...
##### This section is only used in first runs of program to determine eten
######################################################################
if(i==1){
u <- approx( ex[,1], eten, seq(20, 80, by=2.5), rule=2 )
etenf <- u$y # Estimate of eten which produce C-D LEvels
}
}
######################################################################
if(sex=="F") return(out)
else{
#
# etenm is a linear function of etenf from runs of Coale-Demeny female
# program etenm <- 2.298048 + 0.914067*etenf
etenm <- c( 21.86420, 25.45051, 28.68141, 31.61614, 34.30026, 36.76965 )
etenm <- c(etenm, 39.05308, 41.17397, 43.15167, 45.00232, 46.73959, 48.37505 )
etenm <- c(etenm, 49.90490, 51.06607, 52.17190, 53.33403, 54.54928, 55.81287 )
etenm <- c(etenm, 57.11792, 58.45590, 59.88009, 62.16922, 65.10596, 68.95614 )
etenm <- c(etenm, 74.16678 )
## eten_seq(20,86, by = 2) # Code used for first pass to find etenm values
eten <- etenm #
eee <- 1 + 0*eten # Unit vector of same length as eten
xx <- c(0, 1, seq(5,75, by=5) ) # ages at start of groups; later extended.
# MALE ax and bx are the coefficients of the simple regressions of the nqx's on e10.
ax <- c( 0.63726, 0.40548, 0.10393, 0.07435, 0.09880, 0.14009, 0.15785, 0.18260, 0.21175)
ax <- c( ax, 0.25049, 0.27894, 0.33729, 0.38425, 0.48968, 0.59565, 0.73085, 0.98976)
bx <- c( -0.009958, -0.006653, -0.001662, -0.001183, -0.001539, -0.002183, -0.002479)
bx <- c(bx, -0.002875, -0.003312, -0.003864, -0.004158, -0.004856, -0.005190, -0.006300)
bx <- c(bx, -0.007101, -0.007911, -0.008695 )
# MALE a1x and b1x are the coefficients of the log-regressions of the nqx's on e10.
a1x <- c( 5.8061, 7.1062, 5.4472, 5.0654, 4.8700, 5.0677, 5.2660, 5.3438, 5.2792)
a1x <- c(a1x, 5.0415, 4.6666, 4.4506, 4.2202, 4.1851, 4.1249, 4.1051, 4.1133)
b1x <- c( -0.05338, -0.08559, -0.06295, -0.05817, -0.05070, -0.05156, -0.05471)
b1x <- c(b1x, -0.05511, -0.05229, -0.04573, -0.03637, -0.02961, -0.02256 )
b1x <- c(b1x, -0.01891, -0.01491, -0.01161, -0.00895 )
#####################################################################
##### # Calculate an array of probabilities of dying nqx up to age 75
#######################################################################
# The first subscript refers to e10; the second to the age x.
nqxa <- eee %o% ax + eten %o% bx # nqx from linear model
nqxl <- (1/10000)*10^( eee %o% a1x + eten %o% b1x ) # exponential model
#
# Choose among linear, mixed, and exponential models
# on basis of crossover points and slopes.
slopechk <- ( (0*eten + 1/log(10)) %o% (bx/b1x) ) * (1/nqxl ) # Slope check
nqx <- ( nqxa + nqxl) / 2
nqx <- ifelse( nqxa <= nqxl & slopechk < 1, nqxa, nqx )
nqx <- ifelse( nqxa <= nqxl & slopechk >= 1, nqxl, nqx )
####################################################################
#### Calculate the survivorship proportions lx up to age 75
##################################################################
u <- log( 1 - nqx)
uu <- t( apply( u, c(1), cumsum ) )
km1 <- length( uu[1,]) - 1 # number of age groups minus 1
lx <- cbind( 1+0*eee, exp( uu[ , 1:km1]) )
#####################################################################
# Special extension from ages 80 to 100 (i.e. for j> 18
###############################################################
nL75 <- 5*lx[,17]*(1-nqx[,17]) + (1/2)*5*lx[,17]*nqx[,17]
leighty <- lx[,17]*(1-nqx[,17]) # Survivorship to age 80
m77 <- lx[,17]*nqx[,17]/nL75 # m77 is hazard age 77.5.
m105 <- 0.613+ 1.75*nqx[,17]
kappa <- (1/27.5)*log( m105 / m77 ) # THIS CORRECTS COALE'S MISTAKE
m80 <- m77*exp(kappa*2.5) # Hazard at age 80
xlong <- seq(80,121, by = 0.2 ) - 80 # ages in 1/5 years -80
uu <- kappa %o% xlong
u <- (-m80/kappa) %o% ( 1 + 0*xlong)
llx <- leighty %o% ( 1 + 0*xlong)
llx <- llx * exp ( u*exp(uu) - u )
nL80 <- llx[, 1:26 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL85 <- llx[, 26:51 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL90 <- llx[, 51:76 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
nL95 <- llx[, 76:101 ] %*% c( 1/2, rep(1,24), 1/2)*(1/5)
T100 <- as.vector( llx[, 101:201] %*% c( 1/2, rep(1,99), 1/2)*(1/5))
#################################################################
##### Compute other functions in the lifetable
#################################################################
xx <- c(0, 1, seq(5,95, by=5) ) # ages
nn <- c( diff(xx),8 ) # age group widths
lx <- cbind( lx[ , 1:17], llx[ , c(1,26,51,76)] )
qqx <- ( llx[ , c(1,26,51) ] - llx[ , c(26,51,76)] )/llx[, c(1,26,51)]
nqx <- cbind( nqx[ , 1:17], qqx, eee )
dimnames(nqx)[[1]] <- paste(seq(eten))
dimnames(nqx)[[2]] <- paste(xx)
dimnames(lx) <- dimnames(nqx)
na0 <- 0.050 + 3.00*nqx[,1]
na0 <- ifelse( nqx[,1]< 0.100, na0, 0.35 )
na1 <- 1.524 - 1.625*nqx[,1]
na1 <- ifelse( nqx[,1]< 0.100, na1, 1.361)
nax <- cbind( na0, na1, 2.25*eee)
nax <- cbind( nax, 2.6*eee %o% rep(1,13), 2.5*eee)
nax <- cbind( nax, 2.5*eee %o% rep(1,4) ) # Extend to length 21
dimnames(nax) <- dimnames(nqx)
ndx <- lx*nqx
nLx <- ( eee %o% nn )*( lx - ndx ) + nax*ndx
nLx <- cbind( nLx[ , 1:17], nL80, nL85, nL90, nL95 )
nmx <- ndx/nLx
K <- rev(seq(xx)) # Reversed indices for age groups
Tx <- t( apply( nLx[, K], c(1), cumsum) )
Tx <- ( T100 %o% rep(1,21) ) + Tx[,K]
ex <- Tx/lx
nLxm <- nLx # Save nLx for males in separate array
# TR: column labelling for easier selection afterward:
Ncol <- ncol(ex)
cols <- c(0,1,seq(5,5*(Ncol-2),by=5))
colnames(ex)<- cols # only needed for BH functions
out <- list(age=xx,width=nn,lx=lx,nqx=nqx,nax=nax,ndx=ndx,nLx=nLx,nmx=nmx,Tx=Tx,ex=ex)
return(out)
}
}
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