From b037a476e796e2024a6ade58c1379e647929814d Mon Sep 17 00:00:00 2001 From: "N. 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+ +

Estimation of +the force of mortality independently of the initial health status +using IMaCh

+ +

May 2004

+ +
+ + + +
+ +

Introduction

+ +

Estimating mortality from the American LSOA +surveys or from the French HID survey or from many recent +cross-longitudinal surveys in various countries is neither easy +nor accurate with classical demographical tools. Even if dates of +death are checked with data from vital statistics and are of good +quality the samples are often too small to be divided into +subgroups. Also it is mandatory to estimate the mortality of +subgroups or even of the whole sample if it suspected of biases +in comparison with national mortality estimates.Using IMaCh +(0.96d) we are able to estimate status based age specific forces +of mortality and to derive global mortality by weighting them +according to age-specific cross-sectional prevalences but here we +are interested in estimating mortality directly i.e. without +specifying any health status. This is obviously a simple problem +but which is not so easy to solve because human mortality varies +exponentially with age and age must be controlled accurately.We +adapted a special program previously used to estimate mortality +from centenarians surveys to implement a survival model which +takes into account the exact duration between the first interview +and the death if the person died before the last interview or the +exact duration between the first and the last interview if the +person is still alive.We included this program as a new feature +of the IMaCh program version 0.97.

+ +
+ +

Mathematical modelisation of the +age-specific mortality

+ +

The force of mortality is parametrized +as a Gompertz fonction mu(x)=a exp(b*x) where x is age and a and +b are the parameters. The model implemented in IMaCh is detailed +in the pdf file docmortweb.pdf

+ +
+ +

The parameter file

+ +

The parameter file should be +the same as the maximisation. The estimation of the global +mortality is obtain when mle= -3. You can also choose the waves +(firstpass and lastpass), number of observation (lastobs) and to +add weights (weights).

+ +

Example of parameter file : mortparam.imach

+ +
+ +

Output file and graph

+ +

When the run is finished, the user +should enter the caracter 'e' to get the results in a htm file. +This file contains the two parameters with confidence interval +and a graph of the age-specific mortality obtained with the +estimated parameters.

+ +

Example of output file : mortparam-mort.htm.

+ +
    +
  • Results : In this example, the two + parameters of the Gompertz fit (with confidence interval + in brackets) are
    +
    + p[1] = 0.026565 [0.022327 ; 0.030802]
    + p[2] = 0.087517 [0.075484 ; 0.099550]
    +
    + So that the Gompertz equation modelling the force of + mortality expressed in years is :
  • +
+ +
     mu(age) =0.026565*exp(0.087517*(age-71))
+
+ +
    +
  • Graph : The figure graphmort.png represents the age-specific mortality + mu(age) according to the previous equation.
  • +
+ +

+ +
+ +

 

+ + diff --git a/html/doc/mortparam-mort.htm b/html/doc/mortparam-mort.htm new file mode 100644 index 0000000..4c4ab3d --- /dev/null +++ b/html/doc/mortparam-mort.htm @@ -0,0 +1,21 @@ + +IMaCh rmortparam.txt + Imach version 0.97b, May 2004, INED-EUROREVES
$Revision$ $Date$

+Title=Mortality
Datafile=data1.txt Firstpass=2 Lastpass=4 Stepm=1 Weight=1 Model=.
+ +
+ +
Total number of observations=8000
+Youngest age at first (selected) pass 71.75, oldest age 95.08
+Interval (in months) between two waves: Min=1 Max=38 Mean=23.24
+
  • Result files

    + Force of mortality. Parameters of the Gompertz fit (with confidence interval in brackets):
    mu(age) =0.026565*exp(0.087517*(age-71)) per year

    p[1] = 0.026565 [0.022327 ; 0.030802]
    + p[2] = 0.087517 [0.075484 ; 0.099550]
    +


Local time at start Tue Jun 29 12:04:57 2004 +
Local time at end Tue Jun 29 12:05:13 2004 +
\ No newline at end of file diff --git a/html/doc/mortparam.imach b/html/doc/mortparam.imach new file mode 100644 index 0000000..69a3e1d --- /dev/null +++ b/html/doc/mortparam.imach @@ -0,0 +1,40 @@ +#Imach version 0.97, May 2004, INED-EUROREVES +title=Mortality datafile=data1.txt lastobs=8000 firstpass=2 lastpass=4 +ftol=1.000000e-009 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=-3 weight=1 +model=. +# Parameters nlstate*nlstate*ncov a12*1 + b12 * age + ... +12 0. 0. +13 0. 0. +21 0. 0. +23 0. 0. +# Scales (for hessian or gradient estimation) +12 0. 0. +13 0. 0. +21 0. 0. +23 0. 0. +# Covariance matrix +# 121 Var(a12) +# 122 Cov(b12,a12) Var(b12) +# ... +# 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) +#121 Var(a12) +#122 Cov(b12,a12) Var(b12) +#131 Cov(a13,a12) Cov(a13,b12) Var(a13) +#132 Cov(b13,a12) Cov(b13,b12) Cov(b13,a13) Var(b13) +#211 Cov(a21,a12) Cov(a21,b12) Cov(a21,a13) Cov(a21,b13) Var(a21) +#212 Cov(b21,a12) Cov(b21,b12) Cov(b21,a13) Cov(b21,b13) Cov(b21,a21) Var(b21) +#231 Cov(a23,a12) Cov(a23,b12) Cov(a23,a13) Cov(a23,b13) Cov(a23,a21) Cov(a23,b21) Var(a23) +#232 Cov(b23,a12) Cov(b23,b12) Cov(b23,a13) Cov(b23,b13) Cov(b23,a21) Cov(b23,b21) Cov(b23,a23) Var(b23) +121 0. +122 0. 0. +131 0. 0. 0. +132 0. 0. 0. 0. +211 0. 0. 0. 0. 0. +212 0. 0. 0. 0. 0. 0. +231 0. 0. 0. 0. 0. 0. 0. +232 0. 0. 0. 0. 0. 0. 0. 0. +# agemin agemax for life expectancy, bage fage (if mle==0 ie no data nor Max likelihood). +agemin=70 agemax=100 bage=70 fage=100 estepm=12 +begin-prev-date=1/1/1986 end-prev-date=1/1/2000 mov_average=0 +pop_based=1 +prevforecast=1 starting-proj-date=1/6/1988 final-proj-date=1/1/2004 mobil_average=0 -- 2.43.0