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6: <title>Computing global mortality using IMaCh</title>
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12:
13: <p align="center"><font color="#004080" size="5">Estimation of
14: the force of mortality independently of the initial health status
15: using IMaCh</font></p>
16:
17: <p align="center"><font color="#004080" size="5">May 2004</font></p>
18:
19: <hr size="3" color="#EC5E5E">
20:
21: <ul>
22: <li><a href="#intro"><font color="#004080">Introduction</font></a></li>
23: <li><a href="#math"><font color="#004080">Mathematical
24: modelisation of the age-specific mortality</font></a></li>
25: <li><a href="#param"><font color="#004080">The parameter file</font></a></li>
26: <li><a href="#graph"><font color="#004080">Output file and
27: graph</font></a></li>
28: </ul>
29:
30: <hr>
31:
32: <p><font color="#004080" size="4">Introduction</font><a
33: name="intro"></a></p>
34:
35: <p><font
36: color="#000000">Estimating mortality from the American LSOA
37: surveys or from the French HID survey or from many recent
38: cross-longitudinal surveys in various countries is neither easy
39: nor accurate with classical demographical tools. Even if dates of
40: death are checked with data from vital statistics and are of good
41: quality the samples are often too small to be divided into
42: subgroups. Also it is mandatory to estimate the mortality of
43: subgroups or even of the whole sample if it suspected of biases
44: in comparison with national mortality estimates.Using IMaCh
45: (0.96d) we are able to estimate status based age specific forces
46: of mortality and to derive global mortality by weighting them
47: according to age-specific cross-sectional prevalences but here we
48: are interested in estimating mortality directly i.e. without
49: specifying any health status. This is obviously a simple problem
50: but which is not so easy to solve because human mortality varies
51: exponentially with age and age must be controlled accurately.We
52: adapted a special program previously used to estimate mortality
53: from centenarians surveys to implement a survival model which
54: takes into account the exact duration between the first interview
55: and the death if the person died before the last interview or the
56: exact duration between the first and the last interview if the
57: person is still alive.We included this program as a new feature
58: of the IMaCh program version 0.97. </font></p>
59:
60: <hr>
61:
62: <p><font color="#004080" size="4">Mathematical modelisation of the
63: age-specific mortality</font><a name="math"></a></p>
64:
65: <p><font color="#000000" size="3">The force of mortality is parametrized
66: as a Gompertz fonction mu(x)=a exp(b*x) where x is age and a and
67: b are the parameters. The model implemented in IMaCh is detailed
68: in the pdf file </font><a href="docmortweb.pdf"><font
69: color="#000000" size="3">docmortweb.pdf</font></a></p>
70:
71: <hr>
72:
73: <p><font color="#004080" size="4">The parameter file</font><a
74: name="param"></a></p>
75:
76: <p><font color="#000000" size="3">The parameter file should be
77: the same as the maximisation. The estimation of the global
78: mortality is obtain when mle= -3. You can also choose the waves
79: (firstpass and lastpass), number of observation (lastobs) and to
80: add weights (weights).</font></p>
81:
82: <p><font color="#FF0000" size="3">Example of parameter file : </font><a
83: href="mortparam.imach"><font color="#FF0000" size="3">mortparam.imach</font></a></p>
84:
85: <hr>
86:
87: <p><font color="#004080" size="4">Output file and graph</font><a
88: name="graph"></a></p>
89:
90: <p><font color="#000000">When the run is finished, the user
91: should enter the caracter 'e' to get the results in a htm file.
92: This file contains the two parameters with confidence interval
93: and a graph of the age-specific mortality obtained with the
94: estimated parameters.</font></p>
95:
96: <p><font color="#FF0000" size="3">Example of output file :</font><font
97: color="#FF0000"> </font><a href="mortparam-mort.htm"><font
98: color="#FF0000">mortparam-mort.htm.</font></a></p>
99:
100: <ul>
101: <li><font color="#000000">Results : In this example, the two
102: parameters of the Gompertz fit (with confidence interval
103: in brackets) are<br>
104: <br>
105: p[1] = 0.026565 [0.022327 ; 0.030802]<br>
106: p[2] = 0.087517 [0.075484 ; 0.099550]<br>
107: <br>
108: So that the Gompertz equation modelling the force of
109: mortality expressed in years is :</font></li>
110: </ul>
111:
112: <pre><font color="#000000"> </font><font color="#000000"
113: size="4">mu(age) =0.026565*exp(0.087517*(age-71))</font><font
114: color="#000000">
115: </font></pre>
116:
117: <ul>
118: <li><font color="#000000">Graph : The figure </font><a
119: href="graphmort.png"><font color="#000000">graphmort.png</font></a><font
120: color="#000000"> represents the age-specific mortality
121: mu(age) according to the previous equation.</font></li>
122: </ul>
123:
124: <p><font color="#004080"><img src="graphmort.gif" width="415"
125: height="311"></font></p>
126:
127: <hr>
128:
129: <p> </p>
130: </body>
131: </html>
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