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! 9: <H1 align=center><FONT color=#00006a>Computing Health Expectancies using
! 10: IMaCh</FONT></H1>
! 11: <H1 align=center><FONT color=#00006a size=5>(a Maximum Likelihood Computer
! 12: Program using Interpolation of Markov Chains)</FONT></H1>
! 13: <P align=center> </P>
! 14: <P align=center><A href="http://www.ined.fr/"><IMG border=0 height=76
! 15: src="Computing Health Expectancies using IMaCh_fichiers/logo-ined.gif"
! 16: width=151></A><IMG height=75
! 17: src="Computing Health Expectancies using IMaCh_fichiers/euroreves2.gif"
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! 19: <H3 align=center><A href="http://www.ined.fr/"><FONT
! 20: color=#00006a>INED</FONT></A><FONT color=#00006a> and </FONT><A
! 21: href="http://euroreves.ined.fr/"><FONT color=#00006a>EUROREVES</FONT></A></H3>
! 22: <P align=center><FONT color=#00006a size=4><STRONG>Version 0.97, June
! 23: 2004</STRONG></FONT></P>
! 24: <HR color=#ec5e5e SIZE=3>
! 25:
! 26: <P align=center><FONT color=#00006a><STRONG>Authors of the program:
! 27: </STRONG></FONT><A href="http://sauvy.ined.fr/brouard"><FONT
! 28: color=#00006a><STRONG>Nicolas Brouard</STRONG></FONT></A><FONT
! 29: color=#00006a><STRONG>, senior researcher at the </STRONG></FONT><A
! 30: href="http://www.ined.fr/"><FONT color=#00006a><STRONG>Institut National
! 31: d'Etudes Démographiques</STRONG></FONT></A><FONT color=#00006a><STRONG> (INED,
! 32: Paris) in the "Mortality, Health and Epidemiology" Research Unit
! 33: </STRONG></FONT></P>
! 34: <P align=center><FONT color=#00006a><STRONG>and Agnès Lièvre<BR
! 35: clear=left></STRONG></FONT></P>
! 36: <H4><FONT color=#00006a>Contribution to the mathematics: C. R. Heathcote
! 37: </FONT><FONT color=#00006a size=2>(Australian National University,
! 38: Canberra).</FONT></H4>
! 39: <H4><FONT color=#00006a>Contact: Agnès Lièvre (</FONT><A
! 40: href="mailto:lievre@ined.fr"><FONT
! 41: color=#00006a><I>lievre@ined.fr</I></FONT></A><FONT color=#00006a>) </FONT></H4>
! 42: <HR>
! 43:
! 44: <UL>
! 45: <LI><A
! 46: href="http://euroreves.ined.fr/imach/doc/imach.htm#intro">Introduction</A>
! 47: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#data">On what kind
! 48: of data can it be used?</A>
! 49: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#datafile">The data
! 50: file</A>
! 51: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#biaspar">The
! 52: parameter file</A>
! 53: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#running">Running
! 54: Imach</A>
! 55: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#output">Output files
! 56: and graphs</A>
! 57: <LI><A href="http://euroreves.ined.fr/imach/doc/imach.htm#example">Exemple</A>
! 58: </LI></UL>
! 59: <HR>
! 60:
! 61: <H2><A name=intro><FONT color=#00006a>Introduction</FONT></A></H2>
! 62: <P>This program computes <B>Healthy Life Expectancies</B> from
! 63: <B>cross-longitudinal data</B> using the methodology pioneered by Laditka and
! 64: Wolf (1). Within the family of Health Expectancies (HE), disability-free life
! 65: expectancy (DFLE) is probably the most important index to monitor. In low
! 66: mortality countries, there is a fear that when mortality declines (and therefore total life expectancy improves), the increase will not be as great, leading to an <EM>Expansion of morbidity</EM>. Most of the data collected today,
! 67: in particular by the international <A href="http://www.reves.org/">REVES</A>
! 68: network on Health Expectancy and the disability process, and most HE indices based on these data, are
! 69: <EM>cross-sectional</EM>. This means that the information collected comes from a
! 70: single cross-sectional survey: people from a variety of ages (but often old people)
! 71: are surveyed on their health status at a single date. The proportion of people
! 72: disabled at each age can then be estimated at that date. This age-specific
! 73: prevalence curve is used to distinguish, within the stationary population
! 74: (which, by definition, is the life table estimated from the vital statistics on
! 75: mortality at the same date), the disabled population from the disability-free
! 76: population. Life expectancy (LE) (or total population divided by the yearly
! 77: number of births or deaths of this stationary population) is then decomposed
! 78: into disability-free life expectancy (DFLE) and disability life
! 79: expectancy (DLE). This method of computing HE is usually called the Sullivan
! 80: method (after the author who first described it).</P>
! 81: <P>The age-specific proportions of people disabled (prevalence of disability) are
! 82: dependent upon the historical flows from entering disability and recovering in the past. The age-specific forces (or incidence rates) of entering
! 83: disability or recovering a good health, estimated over a recent period of time (as period forces of mortality), are reflecting current conditions and
! 84: therefore can be used at each age to forecast the future of this cohort <EM>if
! 85: nothing changes in the future</EM>, i.e to forecast the prevalence of disability of each cohort. Our finding (2) is that the period prevalence of disability
! 86: (computed from period incidences) is lower than the cross-sectional prevalence.
! 87: For example if a country is improving its technology of prosthesis, the
! 88: incidence of recovering the ability to walk will be higher at each (old) age,
! 89: but the prevalence of disability will only slightly reflect an improvement because
! 90: the prevalence is mostly affected by the history of the cohort and not by recent
! 91: period effects. To measure the period improvement we have to simulate the future
! 92: of a cohort of new-borns entering or leaving the disability state or
! 93: dying at each age according to the incidence rates measured today on different cohorts. The
! 94: proportion of people disabled at each age in this simulated cohort will be much
! 95: lower that the proportions observed at each age in a cross-sectional survey.
! 96: This new prevalence curve introduced in a life table will give a more realistic
! 97: HE level than the Sullivan method which mostly reflects the history of health
! 98: conditions in a country.</P>
! 99: <P>Therefore, the main question is how can we measure incidence rates from
! 100: cross-longitudinal surveys? This is the goal of the IMaCH program. From your
! 101: data and using IMaCH you can estimate period HE as well as the Sullivan HE. In addition the standard errors of the HE are computed.</P>
! 102: <P>A cross-longitudinal survey consists of a first survey ("cross") where
! 103: individuals of different ages are interviewed about their health status or degree
! 104: of disability. At least a second wave of interviews ("longitudinal") should
! 105: measure each individual new health status. Health expectancies are computed from
! 106: the transitions observed between waves (interviews) and are computed for each degree of
! 107: severity of disability (number of health states). The more degrees of severity considered, the more
! 108: time is necessary to reach the Maximum Likelihood of the parameters involved in
! 109: the model. Considering only two states of disability (disabled and healthy) is
! 110: generally enough but the computer program works also with more health
! 111: states.<BR><BR>The simplest model for the transition probabilities is the multinomial logistic model where
! 112: <I>pij</I> is the probability to be observed in state <I>j</I> at the second
! 113: wave conditional to be observed in state <EM>i</EM> at the first wave. Therefore
! 114: a simple model is: log<EM>(pij/pii)= aij + bij*age+ cij*sex,</EM> where
! 115: '<I>age</I>' is age and '<I>sex</I>' is a covariate. The advantage that this
! 116: computer program claims, is that if the delay between waves is not
! 117: identical for each individual, or if some individual missed an interview, the
! 118: information is not rounded or lost, but taken into account using an
! 119: interpolation or extrapolation. <I>hPijx</I> is the probability to be observed
! 120: in state <I>i</I> at age <I>x+h</I> conditional on the observed state <I>i</I>
! 121: at age <I>x</I>. The delay '<I>h</I>' can be split into an exact number
! 122: (<I>nh*stepm</I>) of unobserved intermediate states. This elementary transition
! 123: (by month or quarter, trimester, semester or year) is modeled as the above multinomial
! 124: logistic. The <I>hPx</I> matrix is simply the matrix product of <I>nh*stepm</I>
! 125: elementary matrices and the contribution of each individual to the likelihood is
! 126: simply <I>hPijx</I>. <BR></P>
! 127: <P>The program presented in this manual is a general program named
! 128: <STRONG>IMaCh</STRONG> (for <STRONG>I</STRONG>nterpolated
! 129: <STRONG>MA</STRONG>rkov <STRONG>CH</STRONG>ain), designed to analyse transitions from longitudinal surveys. The first step is the estimation of the set of the parameters of a model for the
! 130: transition probabilities between an initial state and a final state.
! 131: From there, the computer program produces indicators such as the observed and
! 132: stationary prevalence, life expectancies and their variances both numerically and graphically. Our
! 133: transition model consists of absorbing and non-absorbing states assuming the
! 134: possibility of return across the non-absorbing states. The main advantage of
! 135: this package, compared to other programs for the analysis of transition data
! 136: (for example: Proc Catmod of SAS<SUP>®</SUP>) is that the whole individual
! 137: information is used even if an interview is missing, a state or a date is
! 138: unknown or when the delay between waves is not identical for each individual.
! 139: The program is dependent upon a set of parameters inputted by the user: selection of a sub-sample,
! 140: number of absorbing and non-absorbing states, number of waves to be taken in account , a tolerance level for the
! 141: maximization function, the periodicity of the transitions (we can compute
! 142: annual, quarterly or monthly transitions), covariates in the model. IMaCh works on
! 143: Windows or on Unix platform.<BR></P>
! 144: <HR>
! 145:
! 146: <P>(1) Laditka S. B. and Wolf, D. (1998), New Methods for Analyzing
! 147: Active Life Expectancy. <I>Journal of Aging and Health</I>. Vol 10, No. 2. </P>
! 148: <P>(2) <A
! 149: href="http://taylorandfrancis.metapress.com/app/home/contribution.asp?wasp=1f99bwtvmk5yrb7hlhw3&referrer=parent&backto=issue,1,2;journal,2,5;linkingpublicationresults,1:300265,1">Lièvre
! 150: A., Brouard N. and Heathcote Ch. (2003) Estimating Health Expectancies from
! 151: Cross-longitudinal surveys. <EM>Mathematical Population Studies</EM>.- 10(4),
! 152: pp. 211-248</A>
! 153: <HR>
! 154:
! 155: <H2><A name=data><FONT color=#00006a>What kind of data is required?</FONT></A></H2>
! 156: <P>The minimum data required for a transition model is the recording of a set of
! 157: individuals interviewed at a first date and interviewed once more. From the observations of an individual, we obtain a follow-up over
! 158: time of the occurrence of a specific event. In this documentation, the event is
! 159: related to health state, but the program can be applied to many
! 160: longitudinal studies with different contexts. To build the data file
! 161: as explained
! 162: in the next section, you must have the month and year of each interview and
! 163: the corresponding health state. In order to get age, date of birth (month
! 164: and year) are required (missing values are allowed for month). Date of death
! 165: (month and year) is an important information also required if the individual is
! 166: dead. Shorter steps (i.e. a month) will more closely take into account the
! 167: survival time after the last interview.</P>
! 168: <HR>
! 169:
! 170: <H2><A name=datafile><FONT color=#00006a>The data file</FONT></A></H2>
! 171: <P>In this example, 8,000 people have been interviewed in a cross-longitudinal
! 172: survey of 4 waves (1984, 1986, 1988, 1990). Some people missed 1, 2 or 3
! 173: interviews. Health states are healthy (1) and disabled (2). The survey is not a
! 174: real one but a simulation of the American Longitudinal Survey on Aging. The
! 175: disability state is defined as dependence in at least one of four ADLs (Activities
! 176: of daily living, like bathing, eating, walking). Therefore, even if the
! 177: individuals interviewed in the sample are virtual, the information in
! 178: this sample is close to reality for the United States. Sex is not recorded
! 179: is this sample. The LSOA survey is biased in the sense that people
! 180: living in an institution were not included in the first interview in
! 181: 1984. Thus the prevalence of disability observed in 1984 is lower than
! 182: the true prevalence at old ages. However when people moved into an
! 183: institution, they were interviewed there in 1986, 1988 and 1990. Thus
! 184: the incidences of disabilities are not biased. Cross-sectional
! 185: prevalences of disability at old ages are thus artificially increasing in 1986,
! 186: 1988 and 1990 because of a greater proportion of the sample
! 187: institutionalized. Our article (Lièvre A., Brouard N. and Heathcote
! 188: Ch. (2003)) shows the opposite: the period prevalence based on the
! 189: incidences is lower at old
! 190: ages than the adjusted cross-sectional prevalence illustrating that
! 191: there has been significant progress against disability.</P>
! 192: <P>Each line of the data set (named <A
! 193: href="http://euroreves.ined.fr/imach/doc/data1.txt">data1.txt</A> in this first
! 194: example) is an individual record. Fields are separated by blanks: </P>
! 195: <UL>
! 196: <LI><B>Index number</B>: positive number (field 1)
! 197: <LI><B>First covariate</B> positive number (field 2)
! 198: <LI><B>Second covariate</B> positive number (field 3)
! 199: <LI><A name=Weight><B>Weight</B></A>: positive number (field 4) . In most
! 200: surveys individuals are weighted to account for stratification of the
! 201: sample.
! 202: <LI><B>Date of birth</B>: coded as mm/yyyy. Missing dates are coded as 99/9999
! 203: (field 5)
! 204: <LI><B>Date of death</B>: coded as mm/yyyy. Missing dates are coded as 99/9999
! 205: (field 6)
! 206: <LI><B>Date of first interview</B>: coded as mm/yyyy. Missing dates are coded
! 207: as 99/9999 (field 7)
! 208: <LI><B>Status at first interview</B>: positive number. Missing values ar coded
! 209: -1. (field 8)
! 210: <LI><B>Date of second interview</B>: coded as mm/yyyy. Missing dates are coded
! 211: as 99/9999 (field 9)
! 212: <LI><STRONG>Status at second interview</STRONG> positive number. Missing
! 213: values ar coded -1. (field 10)
! 214: <LI><B>Date of third interview</B>: coded as mm/yyyy. Missing dates are coded
! 215: as 99/9999 (field 11)
! 216: <LI><STRONG>Status at third interview</STRONG> positive number. Missing values
! 217: ar coded -1. (field 12)
! 218: <LI><B>Date of fourth interview</B>: coded as mm/yyyy. Missing dates are coded
! 219: as 99/9999 (field 13)
! 220: <LI><STRONG>Status at fourth interview</STRONG> positive number. Missing
! 221: values are coded -1. (field 14)
! 222: <LI>etc </LI></UL>
! 223: <P> </P>
! 224: <P>If you do not wish to include information on weights or
! 225: covariates, you must fill the column with a number (e.g. 1) since all
! 226: fields must be present.</P>
! 227: <HR>
! 228:
! 229: <H2><FONT color=#00006a>Your first example parameter file</FONT><A
! 230: href="http://euroreves.ined.fr/imach"></A><A name=uio></A></H2>
! 231: <H2><A name=biaspar></A>#Imach version 0.97b, June 2004, INED-EUROREVES </H2>
! 232: <P>This first line was a comment. Comments line start with a '#'.</P>
! 233: <H4><FONT color=#ff0000>First uncommented line</FONT></H4><PRE>title=1st_example datafile=data1.txt lastobs=8600 firstpass=1 lastpass=4</PRE>
! 234: <UL>
! 235: <LI><B>title=</B> 1st_example is title of the run.
! 236: <LI><B>datafile=</B> data1.txt is the name of the data set. Our example is a
! 237: six years follow-up survey. It consists of a baseline followed by 3
! 238: reinterviews.
! 239: <LI><B>lastobs=</B> 8600 the program is able to run on a subsample where the
! 240: last observation number is lastobs. It can be set a bigger number than the
! 241: real number of observations (e.g. 100000). In this example, maximisation will
! 242: be done on the first 8600 records.
! 243: <LI><B>firstpass=1</B> , <B>lastpass=4 </B>If there are more than two interviews
! 244: in the survey, the program can be run on selected transitions periods.
! 245: firstpass=1 means the first interview included in the calculation is the
! 246: baseline survey. lastpass=4 means that the last interview to be
! 247: included will be by the 4th. </LI></UL>
! 248: <P> </P>
! 249: <H4><A name=biaspar-2><FONT color=#ff0000>Second uncommented
! 250: line</FONT></A></H4><PRE>ftol=1.e-08 stepm=1 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</PRE>
! 251: <UL>
! 252: <LI><B>ftol=1e-8</B> Convergence tolerance on the function value in the
! 253: maximisation of the likelihood. Choosing a correct value for ftol is
! 254: difficult. 1e-8 is the correct value for a 32 bit computer.
! 255: <LI><B>stepm=1</B> The time unit in months for interpolation. Examples:
! 256: <UL>
! 257: <LI>If stepm=1, the unit is a month
! 258: <LI>If stepm=4, the unit is a trimester
! 259: <LI>If stepm=12, the unit is a year
! 260: <LI>If stepm=24, the unit is two years
! 261: <LI>... </LI></UL>
! 262: <LI><B>ncovcol=2</B> Number of covariate columns included in the datafile
! 263: before the column for the date of birth. You can include covariates
! 264: that will not be used in the model as this number is not the number of covariates that will
! 265: be specified by the model. The 'model' syntax describes the covariates to be
! 266: taken into account during the run.
! 267: <LI><B>nlstate=2</B> Number of non-absorbing (alive) states. Here we have two
! 268: alive states: disability-free is coded 1 and disability is coded 2.
! 269: <LI><B>ndeath=1</B> Number of absorbing states. The absorbing state death is
! 270: coded 3.
! 271: <LI><B>maxwav=4</B> Number of waves in the datafile.
! 272: <LI><A name=mle><B>mle</B></A><B>=1</B> Option for the Maximisation Likelihood
! 273: Estimation.
! 274: <UL>
! 275: <LI>If mle=1 the program does the maximisation and the calculation of health
! 276: expectancies
! 277: <LI>If mle=0 the program only does the calculation of the health
! 278: expectancies and other indices and graphs but without the maximization.
! 279: There are also other possible values:
! 280: <UL>
! 281: <LI>If mle=-1 you get a template for the number of parameters
! 282: and the size of the variance-covariance matrix. This is useful if the model is
! 283: complex with many covariates.
! 284: <LI>If mle=-3 IMaCh computes the mortality but without any health status
! 285: (May 2004)
! 286: <LI>If mle=2 IMach likelihood corresponds to a linear interpolation
! 287: <LI>If mle=3 IMach likelihood corresponds to an exponential
! 288: inter-extrapolation
! 289: <LI>If mle=4 IMach likelihood corresponds to no inter-extrapolation, thus biasing the results.
! 290: <LI>If mle=5 IMach likelihood corresponds to no inter-extrapolation, and
! 291: before the correction of the Jackson's bug (avoid this). </LI></UL></LI></UL>
! 292: <LI><B>weight=0</B> Provides the possibility of adding weights.
! 293: <UL>
! 294: <LI>If weight=0 no weights are included
! 295: <LI>If weight=1 the maximisation integrates the weights which are in field
! 296: <A href="http://euroreves.ined.fr/imach/doc/imach.htm#Weight">4</A>
! 297: </LI></UL></LI></UL>
! 298: <H4><FONT color=#ff0000>Covariates</FONT></H4>
! 299: <P>Intercept and age are automatically included in the model. Additional
! 300: covariates can be included with the command: </P><PRE>model=<EM>list of covariates</EM></PRE>
! 301: <UL>
! 302: <LI>if<STRONG> model=. </STRONG>then no covariates are included
! 303: <LI>if <STRONG>model=V1</STRONG> the model includes the first covariate (field
! 304: 2)
! 305: <LI>if <STRONG>model=V2 </STRONG>the model includes the second covariate
! 306: (field 3)
! 307: <LI>if <STRONG>model=V1+V2 </STRONG>the model includes the first and the
! 308: second covariate (fields 2 and 3)
! 309: <LI>if <STRONG>model=V1*V2 </STRONG>the model includes the product of the
! 310: first and the second covariate (fields 2 and 3)
! 311: <LI>if <STRONG>model=V1+V1*age</STRONG> the model includes the product
! 312: covariate*age </LI></UL>
! 313: <P>In this example, we have two covariates in the data file (fields 2 and 3).
! 314: The number of covariates included in the data file between the id and the date
! 315: of birth is ncovcol=2 (it was named ncov in version prior to 0.8). If you have 3
! 316: covariates in the datafile (fields 2, 3 and 4), you will set ncovcol=3. Then you
! 317: can run the programme with a new parametrisation taking into account the third
! 318: covariate. For example, <STRONG>model=V1+V3 </STRONG>estimates a model with the
! 319: first and third covariates. More complicated models can be used, but this will
! 320: take more time to converge. With a simple model (no covariates), the programme
! 321: estimates 8 parameters. Adding covariates increases the number of parameters :
! 322: 12 for <STRONG>model=V1, </STRONG>16 for <STRONG>model=V1+V1*age </STRONG>and 20
! 323: for <STRONG>model=V1+V2+V3.</STRONG></P>
! 324: <H4><FONT color=#ff0000>Guess values for optimization</FONT><FONT color=#00006a>
! 325: </FONT></H4>
! 326: <P>You must write the initial guess values of the parameters for optimization.
! 327: The number of parameters, <EM>N</EM> depends on the number of absorbing states
! 328: and non-absorbing states and on the number of covariates in the model (ncovmodel). <BR><EM>N</EM> is
! 329: given by the formula <EM>N</EM>=(<EM>nlstate</EM> +
! 330: <EM>ndeath</EM>-1)*<EM>nlstate</EM>*<EM>ncovmodel</EM> . <BR><BR>Thus in
! 331: the simple case with 2 covariates in the model(the model is log (pij/pii) = aij + bij * age
! 332: where intercept and age are the two covariates), and 2 health states (1 for
! 333: disability-free and 2 for disability) and 1 absorbing state (3), you must enter
! 334: 8 initials values, a12, b12, a13, b13, a21, b21, a23, b23. You can start with
! 335: zeros as in this example, but if you have a more precise set (for example from
! 336: an earlier run) you can enter it and it will speed up the convergence<BR>Each of the four
! 337: lines starts with indices "ij": <B>ij aij bij</B> </P>
! 338: <BLOCKQUOTE><PRE># Guess values of aij and bij in log (pij/pii) = aij + bij * age
1.1 brouard 339: 12 -14.155633 0.110794
340: 13 -7.925360 0.032091
341: 21 -1.890135 -0.029473
1.5 ! lievre 342: 23 -6.234642 0.022315 </PRE></BLOCKQUOTE>
! 343: <P>or, to simplify (in most of cases it converges but there is no warranty!):
! 344: </P>
! 345: <BLOCKQUOTE><PRE>12 0.0 0.0
1.1 brouard 346: 13 0.0 0.0
347: 21 0.0 0.0
1.5 ! lievre 348: 23 0.0 0.0</PRE></BLOCKQUOTE>
! 349: <P>In order to speed up the convergence you can make a first run with a large
! 350: stepm i.e stepm=12 or 24 and then decrease the stepm until stepm=1 month. If
! 351: newstepm is the new shorter stepm and stepm can be expressed as a multiple of
! 352: newstepm, like newstepm=n stepm, then the following approximation holds: </P><PRE>aij(stepm) = aij(n . stepm) - ln(n)
! 353: </PRE>
! 354: <P>and </P><PRE>bij(stepm) = bij(n . stepm) .</PRE>
! 355: <P>For example if you already ran with stepm=6 (a 6 months interval) and got:<BR></P><PRE># Parameters
1.1 brouard 356: 12 -13.390179 0.126133
357: 13 -7.493460 0.048069
358: 21 0.575975 -0.041322
359: 23 -4.748678 0.030626
1.5 ! lievre 360: </PRE>
! 361: <P>Then you now want to get the monthly estimates, you can guess the aij by
! 362: subtracting ln(6)= 1.7917<BR>and running using<BR></P><PRE>12 -15.18193847 0.126133
1.1 brouard 363: 13 -9.285219469 0.048069
364: 21 -1.215784469 -0.041322
365: 23 -6.540437469 0.030626
1.5 ! lievre 366: </PRE>
! 367: <P>and get<BR></P><PRE>12 -15.029768 0.124347
1.1 brouard 368: 13 -8.472981 0.036599
369: 21 -1.472527 -0.038394
370: 23 -6.553602 0.029856
371:
1.5 ! lievre 372: <P>which is closer to the results. The approximation is probably useful
1.1 brouard 373: only for very small intervals and we don't have enough experience to
1.5 ! lievre 374: know if you will speed up the convergence or not.<BR></P>
! 375: </PRE><PRE> -ln(12)= -2.484
1.1 brouard 376: -ln(6/1)=-ln(6)= -1.791
377: -ln(3/1)=-ln(3)= -1.0986
378: -ln(12/6)=-ln(2)= -0.693
1.5 ! lievre 379: </PRE>In version 0.9 and higher you can still have valuable results even if your
! 380: stepm parameter is bigger than a month. The idea is to run with bigger stepm in
! 381: order to have a quicker convergence at the price of a small bias. Once you know
! 382: which model you want to fit, you can put stepm=1 and wait hours or days to get
! 383: the convergence! To get unbiased results even with large stepm we introduce the
! 384: idea of pseudo likelihood by interpolating two exact likelihoods. In
! 385: more detail:
! 386: <P>If the interval of <EM>d</EM> months between two waves is not a multiple of
! 387: 'stepm', but is between <EM>(n-1) stepm</EM> and <EM>n stepm</EM> then
! 388: both exact likelihoods are computed (the contribution to the likelihood at <EM>n
! 389: stepm</EM> requires one matrix product more) (let us remember that we are
! 390: modelling the probability to be observed in a particular state after <EM>d</EM>
! 391: months being observed at a particular state at 0). The distance, (<EM>bh</EM> in
! 392: the program), from the month of interview to the rounded date of <EM>n
! 393: stepm</EM> is computed. It can be negative (interview occurs before <EM>n
! 394: stepm</EM>) or positive if the interview occurs after <EM>n stepm</EM> (and
! 395: before <EM>(n+1)stepm</EM>). <BR>Then the final contribution to the total
! 396: likelihood is a weighted average of these two exact likelihoods at <EM>n
! 397: stepm</EM> (out) and at <EM>(n-1)stepm</EM>(savm). We did not want to compute
! 398: the third likelihood at <EM>(n+1)stepm</EM> because it is too costly in time, so
! 399: we used an extrapolation if <EM>bh</EM> is positive. <BR>The formula
! 400: for the inter/extrapolation may vary according to the value of parameter mle: <PRE>mle=1 lli= log((1.+bbh)*out[s1][s2]- bbh*savm[s1][s2]); /* linear interpolation */
! 401:
! 402: mle=2 lli= (savm[s1][s2]>(double)1.e-8 ? \
1.2 brouard 403: log((1.+bbh)*out[s1][s2]- bbh*(savm[s1][s2])): \
404: log((1.+bbh)*out[s1][s2])); /* linear interpolation */
1.5 ! lievre 405: mle=3 lli= (savm[s1][s2]>1.e-8 ? \
1.2 brouard 406: (1.+bbh)*log(out[s1][s2])- bbh*log(savm[s1][s2]): \
407: log((1.+bbh)*out[s1][s2])); /* exponential inter-extrapolation */
408:
409: mle=4 lli=log(out[s[mw[mi][i]][i]][s[mw[mi+1][i]][i]]); /* No interpolation */
410: no need to save previous likelihood into memory.
1.5 ! lievre 411: </PRE>
! 412: <P>If the death occurs between the first and second pass, and for example more
! 413: precisely between <EM>n stepm</EM> and <EM>(n+1)stepm</EM> the contribution of
! 414: these people to the likelihood is simply the difference between the probability
! 415: of dying before <EM>n stepm</EM> and the probability of dying before
! 416: <EM>(n+1)stepm</EM>. There was a bug in version 0.8 and death was treated as any
! 417: other state, i.e. as if it was an observed death at second pass. This was not
! 418: precise but correct, although when information on the precise month of
! 419: death came (death occuring prior to second pass) we did not change the
! 420: likelihood accordingly. We thank Chris Jackson for correcting it. In earlier
1.2 brouard 421: versions (fortunately before first publication) the total mortality
1.5 ! lievre 422: was thus overestimated (people were dying too early) by about 10%. Version
! 423: 0.95 and higher are correct.
1.1 brouard 424:
1.5 ! lievre 425: <P>Our suggested choice is mle=1 . If stepm=1 there is no difference between
! 426: various mle options (methods of interpolation). If stepm is big, like 12 or 24
! 427: or 48 and mle=4 (no interpolation) the bias may be very important if the mean
! 428: duration between two waves is not a multiple of stepm. See the appendix in our
! 429: main publication concerning the sine curve of biases.
! 430: <H4><FONT color=#ff0000>Guess values for computing variances</FONT></H4>
! 431: <P>These values are output by the maximisation of the likelihood <A
! 432: href="http://euroreves.ined.fr/imach/doc/imach.htm#mle">mle</A>=1 and
! 433: can be used as an input for a second run in order to get the various output data
! 434: files (Health expectancies, period prevalence etc.) and figures without
! 435: rerunning the long maximisation phase (mle=0). </P>
! 436: <P>The 'scales' are small values needed for the computing of numerical
! 437: derivatives. These derivatives are used to compute the hessian matrix of the
! 438: parameters, that is the inverse of the covariance matrix. They are often used
! 439: for estimating variances and confidence intervals. Each line consists of indices
! 440: "ij" followed by the initial scales (zero to simplify) associated with aij and
! 441: bij. </P>
! 442: <UL>
! 443: <LI>If mle=1 you can enter zeros:
! 444: <LI>
! 445: <BLOCKQUOTE><PRE># Scales (for hessian or gradient estimation)
1.1 brouard 446: 12 0. 0.
447: 13 0. 0.
448: 21 0. 0.
1.5 ! lievre 449: 23 0. 0. </PRE></BLOCKQUOTE>
! 450: <LI>If mle=0 (no maximisation of Likelihood) you must enter a covariance
! 451: matrix (usually obtained from an earlier run). </LI></UL>
! 452: <H4><FONT color=#ff0000>Covariance matrix of parameters</FONT></H4>
! 453: <P>The covariance matrix is output if <A
! 454: href="http://euroreves.ined.fr/imach/doc/imach.htm#mle">mle</A>=1. But it can be
! 455: also be used as an input to get the various output data files (Health
! 456: expectancies, period prevalence etc.) and figures without rerunning
! 457: the maximisation phase (mle=0). <BR>Each line starts with indices
! 458: "ijk" followed by the covariances between aij and bij:<BR>
! 459: </P><PRE> 121 Var(a12)
1.1 brouard 460: 122 Cov(b12,a12) Var(b12)
461: ...
1.5 ! lievre 462: 232 Cov(b23,a12) Cov(b23,b12) ... Var (b23) </PRE>
! 463: <UL>
! 464: <LI>If mle=1 you can enter zeros.
! 465: <LI><PRE># Covariance matrix
1.1 brouard 466: 121 0.
467: 122 0. 0.
468: 131 0. 0. 0.
469: 132 0. 0. 0. 0.
470: 211 0. 0. 0. 0. 0.
471: 212 0. 0. 0. 0. 0. 0.
472: 231 0. 0. 0. 0. 0. 0. 0.
1.5 ! lievre 473: 232 0. 0. 0. 0. 0. 0. 0. 0.</PRE>
! 474: <LI>If mle=0 you must enter a covariance matrix (usually obtained from an
! 475: earlier run). </LI></UL>
! 476: <H4><FONT color=#ff0000>Age range for calculation of stationary prevalences and
! 477: health expectancies</FONT></H4><PRE>agemin=70 agemax=100 bage=50 fage=100</PRE>
! 478: <P>Once we obtained the estimated parameters, the program is able to calculate
! 479: period prevalence, transitions probabilities and life expectancies at any age.
! 480: Choice of the age range is useful for extrapolation. In this example,
! 481: the age of people interviewed varies from 69 to 102 and the model is
! 482: estimated using their exact ages. But if you are interested in the
! 483: age-specific period prevalence you can start the simulation at an
! 484: exact age like 70 and stop at 100. Then the program will draw at
! 485: least two curves describing the forecasted prevalences of two cohorts,
! 486: one for healthy people at age 70 and the second for disabled people at
! 487: the same initial age. And according to the mixing property
! 488: (ergodicity) and because of recovery, both prevalences will tend to be
! 489: identical at later ages. Thus if you want to compute the prevalence at
! 490: age 70, you should enter a lower agemin value.
! 491: <P>Setting bage=50 (begin age) and fage=100 (final age), let the program compute
! 492: life expectancy from age 'bage' to age 'fage'. As we use a model, we can
! 493: interessingly compute life expectancy on a wider age range than the age range
! 494: from the data. But the model can be rather wrong on much larger intervals.
! 495: Program is limited to around 120 for upper age! <PRE></PRE>
! 496: <UL>
! 497: <LI><B>agemin=</B> Minimum age for calculation of the period prevalence
! 498: <LI><B>agemax=</B> Maximum age for calculation of the period prevalence
! 499: <LI><B>bage=</B> Minimum age for calculation of the health expectancies
! 500: <LI><B>fage=</B> Maximum age for calculation of the health expectancies
! 501: </LI></UL>
! 502: <H4><A name=Computing><FONT color=#ff0000>Computing</FONT></A><FONT
! 503: color=#ff0000> the cross-sectional prevalence</FONT></H4><PRE>begin-prev-date=1/1/1984 end-prev-date=1/6/1988 estepm=1</PRE>
! 504: <P>Statements 'begin-prev-date' and 'end-prev-date' allow the user to
! 505: select the period in which the observed prevalences in each state. In
! 506: this example, the prevalences are calculated on data survey collected
! 507: between 1 January 1984 and 1 June 1988. </P>
! 508: <UL>
! 509: <LI><STRONG>begin-prev-date= </STRONG>Starting date (day/month/year)
! 510: <LI><STRONG>end-prev-date= </STRONG>Final date (day/month/year)
! 511: <LI><STRONG>estepm= </STRONG>Unit (in months).We compute the life expectancy
! 512: from trapezoids spaced every estepm months. This is mainly to measure the
! 513: difference between two models: for example if stepm=24 months pijx are given
! 514: only every 2 years and by summing them we are calculating an estimate of the
! 515: Life Expectancy assuming a linear progression inbetween and thus
! 516: overestimating or underestimating according to the curvature of the survival
! 517: function. If, for the same date, we estimate the model with stepm=1 month, we
! 518: can keep estepm to 24 months to compare the new estimate of Life expectancy
! 519: with the same linear hypothesis. A more precise result, taking into account a
! 520: more precise curvature will be obtained if estepm is as small as stepm.
! 521: </LI></UL>
! 522: <H4><FONT color=#ff0000>Population- or status-based health
! 523: expectancies</FONT></H4><PRE>pop_based=0</PRE>
! 524: <P>The program computes status-based health expectancies, i.e health
! 525: expectancies which depend on the initial health state. If you are healthy, your
! 526: healthy life expectancy (e11) is higher than if you were disabled (e21, with e11
! 527: > e21).<BR>To compute a healthy life expectancy 'independent' of the initial
! 528: status we have to weight e11 and e21 according to the probability of
! 529: being in each state at initial age which correspond to the proportions
! 530: of people in each health state (cross-sectional prevalences).
! 531: <P>We could also compute e12 and e12 and get e.2 by weighting them according to
! 532: the observed cross-sectional prevalences at initial age.
! 533: <P>In a similar way we could compute the total life expectancy by summing e.1
! 534: and e.2 . <BR>The main difference between 'population based' and 'implied' or
! 535: 'period' is in the weights used. 'Usually', cross-sectional prevalences of
! 536: disability are higher than period prevalences particularly at old ages. This is
! 537: true if the country is improving its health system by teaching people how to
! 538: prevent disability by promoting better screening, for example of people
! 539: needing cataract surgery. Then the proportion of disabled people at
! 540: age 90 will be lower than the current observed proportion.
! 541: <P>Thus a better Health Expectancy and even a better Life Expectancy value is
! 542: given by forecasting not only the current lower mortality at all ages but also a
! 543: lower incidence of disability and higher recovery. <BR>Using the period
! 544: prevalences as weight instead of the cross-sectional prevalences we are
! 545: computing indices which are more specific to the current situations and
! 546: therefore more useful to predict improvements or regressions in the future as to
! 547: compare different policies in various countries.
! 548: <UL>
! 549: <LI><STRONG>popbased= 0 </STRONG>Health expectancies are computed at each age
! 550: from period prevalences 'expected' at this initial age.
! 551: <LI><STRONG>popbased= 1 </STRONG>Health expectancies are computed at each age
! 552: from cross-sectional 'observed' prevalence at the initial age. As all the
! 553: population is not observed at the same exact date we define a short period
! 554: where the observed prevalence can be computed as follows:<BR>we simply sum all people
! 555: surveyed within these two exact dates who belong to a particular age group
! 556: (single year) at the date of interview and are in a particular health state.
! 557: Then it is easy to get the proportion of people in a particular
! 558: health state as a percentage of all people of the same age group.<BR>If both dates are spaced and are
! 559: covering two waves or more, people being interviewed twice or more are counted
! 560: twice or more. The program takes into account the selection of individuals
! 561: interviewed between firstpass and lastpass too (we don't know if
! 562: this is useful). </LI></UL>
! 563: <H4><FONT color=#ff0000>Prevalence forecasting (Experimental)</FONT></H4><PRE>starting-proj-date=1/1/1989 final-proj-date=1/1/1992 mov_average=0 </PRE>
! 564: <P>Prevalence and population projections are only available if the interpolation
! 565: unit is a month, i.e. stepm=1 and if there are no covariate. The programme
! 566: estimates the prevalence in each state at a precise date expressed in
! 567: day/month/year. The programme computes one forecasted prevalence a year from a
! 568: starting date (1 January 1989 in this example) to a final date (1 January
! 569: 1992). The statement mov_average allows computation of smoothed forecasted
! 570: prevalences with a five-age moving average centered at the mid-age of the
! 571: fiveyear-age period. <BR></P>
! 572: <H4><FONT color=#ff0000>Population forecasting (Experimental)</FONT></H4>
! 573: <UL>
! 574: <LI><STRONG>starting-proj-date</STRONG>= starting date (day/month/year) of
! 575: forecasting
! 576: <LI><STRONG>final-proj-date= </STRONG>final date (day/month/year) of
! 577: forecasting
! 578: <LI><STRONG>mov_average</STRONG>= smoothing with a five-age moving average
! 579: centered at the mid-age of the fiveyear-age period. The command<STRONG>
! 580: mov_average</STRONG> takes value 1 if the prevalences are smoothed and 0
! 581: otherwise. </LI></UL>
! 582: <UL type=disc>
! 583: <LI><B>popforecast= 0 </B>Option for population forecasting. If popforecast=1,
! 584: the programme does the forecasting<B>.</B>
! 585: <LI><B>popfile= </B>name of the population file
! 586: <LI><B>popfiledate=</B> date of the population population
! 587: <LI><B>last-popfiledate</B>= date of the last population projection
! 588: </LI></UL>
! 589: <HR>
! 590:
! 591: <H2><A name=running></A><FONT color=#00006a>Running Imach with this
! 592: example</FONT></H2>
! 593: <P>We assume that you have already typed your <A
! 594: href="http://euroreves.ined.fr/imach/doc/biaspar.imach">1st_example parameter
! 595: file</A> as explained <A
! 596: href="http://euroreves.ined.fr/imach/doc/imach.htm#biaspar">above</A>. To run
! 597: the program under Windows you should either: </P>
! 598: <UL>
! 599: <LI>click on the imach.exe icon and either:
! 600: <UL>
! 601: <LI>enter the name of the parameter file which is for example
! 602: <TT>C:\home\myname\lsoa\biaspar.imach</TT>
! 603: <LI>or locate the biaspar.imach icon in your folder such as
! 604: <TT>C:\home\myname\lsoa</TT> and drag it, with your mouse, on the already
! 605: open imach window. </LI></UL>
! 606: <LI>With version (0.97b) if you ran setup at installation, Windows is supposed
! 607: to understand the ".imach" extension and you can right click the biaspar.imach
! 608: icon and either edit with wordpad (better than notepad) the parameter file or
! 609: execute it with IMaCh. </LI></UL>
! 610: <P>The time to converge depends on the step unit used (1 month is more
! 611: precise but more cpu time consuming), on the number of cases, and on the number of
! 612: variables (covariates).
! 613: <P>The program outputs many files. Most of them are files which will be plotted
! 614: for better understanding. </P>To run under Linux is mostly the same.
! 615: <P>It is no more difficult to run IMaCh on a MacIntosh.
! 616: <HR>
! 617:
! 618: <H2><A name=output><FONT color=#00006a>Output of the program and graphs</FONT>
! 619: </A></H2>
! 620: <P>Once the optimization is finished (once the convergence is reached), many
! 621: tables and graphics are produced.
! 622: <P>The IMaCh program will create a subdirectory with the same name as your
! 623: parameter file (here mypar) where all the tables and figures will be
! 624: stored.<BR>Important files like the log file and the output parameter file
! 625: (the latter contains the maximum likelihood estimates) are stored at
! 626: the main level not in this subdirectory. Files with extension .log and
! 627: .txt can be edited with a standard editor like wordpad or notepad or
! 628: even can be viewed with a browser like Internet Explorer or Mozilla.
! 629: <P>The main html file is also named with the same name <A
! 630: href="http://euroreves.ined.fr/imach/doc/biaspar.htm">biaspar.htm</A>. You can
! 631: click on it by holding your shift key in order to open it in another window
! 632: (Windows).
! 633: <P>Our grapher is Gnuplot, an interactive plotting program (GPL) which can
! 634: also work in batch mode. A gnuplot reference manual is available <A
! 635: href="http://www.gnuplot.info/">here</A>. <BR>When the run is finished, and in
! 636: order that the window doesn't disappear, the user should enter a character like
! 637: <TT>q</TT> for quitting. <BR>These characters are:<BR></P>
! 638: <UL>
! 639: <LI>'e' for opening the main result html file <A
! 640: href="http://euroreves.ined.fr/imach/doc/biaspar.htm"><STRONG>biaspar.htm</STRONG></A>
! 641: file to edit the output files and graphs.
! 642: <LI>'g' to graph again
! 643: <LI>'c' to start again the program from the beginning.
! 644: <LI>'q' for exiting. </LI></UL>The main gnuplot file is named
! 645: <TT>biaspar.gp</TT> and can be edited (right click) and run again.
! 646: <P>Gnuplot is easy and you can use it to make more complex graphs. Just click on
! 647: gnuplot and type plot sin(x) to see how easy it is.
! 648: <H5><FONT size=4><STRONG>Results files </STRONG></FONT><BR><BR><FONT
! 649: color=#ec5e5e size=3><STRONG>- </STRONG></FONT><A
! 650: name="cross-sectional prevalence in each state"><FONT color=#ec5e5e
! 651: size=3><STRONG>cross-sectional prevalence in each state</STRONG></FONT></A><FONT
! 652: color=#ec5e5e size=3><STRONG> (and at first pass)</STRONG></FONT><B>: </B><A
! 653: href="http://euroreves.ined.fr/imach/doc/biaspar/prbiaspar.txt"><B>biaspar/prbiaspar.txt</B></A><BR></H5>
! 654: <P>The first line is the title and displays each field of the file. First column
! 655: corresponds to age. Fields 2 and 6 are the proportion of individuals in states 1
! 656: and 2 respectively as observed at first exam. Others fields are the numbers of
! 657: people in states 1, 2 or more. The number of columns increases if the number of
! 658: states is higher than 2.<BR>The header of the file is </P><PRE># Age Prev(1) N(1) N Age Prev(2) N(2) N
1.1 brouard 659: 70 1.00000 631 631 70 0.00000 0 631
660: 71 0.99681 625 627 71 0.00319 2 627
1.5 ! lievre 661: 72 0.97125 1115 1148 72 0.02875 33 1148 </PRE>
! 662: <P>It means that at age 70 (between 70 and 71), the prevalence in state 1 is
! 663: 1.000 and in state 2 is 0.00 . At age 71 the number of individuals in state 1 is
! 664: 625 and in state 2 is 2, hence the total number of people aged 71 is 625+2=627.
! 665: <BR></P>
! 666: <H5><FONT color=#ec5e5e size=3><B>- Estimated parameters and covariance
! 667: matrix</B></FONT><B>: </B><A
! 668: href="http://euroreves.ined.fr/imach/doc/rbiaspar.txt"><B>rbiaspar.imach</B></A></H5>
! 669: <P>This file contains all the maximisation results: </P><PRE> -2 log likelihood= 21660.918613445392
1.1 brouard 670: Estimated parameters: a12 = -12.290174 b12 = 0.092161
671: a13 = -9.155590 b13 = 0.046627
672: a21 = -2.629849 b21 = -0.022030
673: a23 = -7.958519 b23 = 0.042614
674: Covariance matrix: Var(a12) = 1.47453e-001
675: Var(b12) = 2.18676e-005
676: Var(a13) = 2.09715e-001
677: Var(b13) = 3.28937e-005
678: Var(a21) = 9.19832e-001
679: Var(b21) = 1.29229e-004
680: Var(a23) = 4.48405e-001
681: Var(b23) = 5.85631e-005
1.5 ! lievre 682: </PRE>
! 683: <P>By substitution of these parameters in the regression model, we obtain the
! 684: elementary transition probabilities:</P>
! 685: <P><IMG height=300
! 686: src="Computing Health Expectancies using IMaCh_fichiers/pebiaspar11.png"
! 687: width=400></P>
! 688: <H5><FONT color=#ec5e5e size=3><B>- Transition probabilities</B></FONT><B>:
! 689: </B><A
! 690: href="http://euroreves.ined.fr/imach/doc/biaspar/pijrbiaspar.txt"><B>biaspar/pijrbiaspar.txt</B></A></H5>
! 691: <P>Here are the transitions probabilities Pij(x, x+nh). The second column is the
! 692: starting age x (from age 95 to 65), the third is age (x+nh) and the others are
! 693: the transition probabilities p11, p12, p13, p21, p22, p23. The first column
! 694: indicates the value of the covariate (without any other variable than age it is
! 695: equal to 1) For example, line 5 of the file is: </P><PRE>1 100 106 0.02655 0.17622 0.79722 0.01809 0.13678 0.84513 </PRE>
! 696: <P>and this means: </P><PRE>p11(100,106)=0.02655
1.1 brouard 697: p12(100,106)=0.17622
698: p13(100,106)=0.79722
699: p21(100,106)=0.01809
700: p22(100,106)=0.13678
1.5 ! lievre 701: p22(100,106)=0.84513 </PRE>
! 702: <H5><FONT color=#ec5e5e size=3><B>- </B></FONT><A
! 703: name="Period prevalence in each state"><FONT color=#ec5e5e size=3><B>Period
! 704: prevalence in each state</B></FONT></A><B>: </B><A
! 705: href="http://euroreves.ined.fr/imach/doc/biaspar/plrbiaspar.txt"><B>biaspar/plrbiaspar.txt</B></A></H5><PRE>#Prevalence
1.1 brouard 706: #Age 1-1 2-2
707:
708: #************
709: 70 0.90134 0.09866
710: 71 0.89177 0.10823
711: 72 0.88139 0.11861
1.5 ! lievre 712: 73 0.87015 0.12985 </PRE>
! 713: <P>At age 70 the period prevalence is 0.90134 in state 1 and 0.09866 in state 2.
! 714: This period prevalence differs from the cross-sectional prevalence and
! 715: we explaining. The cross-sectional prevalence at age 70 results from
! 716: the incidence of disability, incidence of recovery and mortality which
! 717: occurred in the past for the cohort. Period prevalence results from a
! 718: simulation with current incidences of disability, recovery and
! 719: mortality estimated from this cross-longitudinal survey. It is a good
! 720: prediction of the prevalence in the future if "nothing changes in the
! 721: future". This is exactly what demographers do with a period life
! 722: table. Life expectancy is the expected mean survival time if current
! 723: mortality rates (age-specific incidences of mortality) "remain
! 724: constant" in the future.
! 725: </P>
! 726: <H5><FONT color=#ec5e5e size=3><B>- Standard deviation of period
! 727: prevalence</B></FONT><B>: </B><A
! 728: href="http://euroreves.ined.fr/imach/doc/biaspar/vplrbiaspar.txt"><B>biaspar/vplrbiaspar.txt</B></A></H5>
! 729: <P>The period prevalence has to be compared with the cross-sectional prevalence.
! 730: But both are statistical estimates and therefore have confidence intervals.
! 731: <BR>For the cross-sectional prevalence we generally need information on the
! 732: design of the surveys. It is usually not enough to consider the number of people
! 733: surveyed at a particular age and to estimate a Bernouilli confidence interval
! 734: based on the prevalence at that age. But you can do it to have an idea of the
! 735: randomness. At least you can get a visual appreciation of the randomness by
! 736: looking at the fluctuation over ages.
! 737: <P>For the period prevalence it is possible to estimate the confidence interval
! 738: from the Hessian matrix (see the publication for details). We are supposing that
! 739: the design of the survey will only alter the weight of each individual. IMaCh
! 740: scales the weights of individuals-waves contributing to the likelihood by
! 741: making the sum of the weights equal to the sum of individuals-waves
! 742: contributing: a weighted survey doesn't increase or decrease the size of the
! 743: survey, it only give more weight to some individuals and thus less to the
! 744: others.
! 745: <H5><FONT color=#ec5e5e size=3>-cross-sectional and period prevalence in state
! 746: (2=disable) with confidence interval</FONT>:<B> </B><A
! 747: href="http://euroreves.ined.fr/imach/doc/biaspar/vbiaspar21.htm"><B>biaspar/vbiaspar21.png</B></A></H5>
! 748: <P>This graph exhibits the period prevalence in state (2) with the confidence
! 749: interval in red. The green curve is the observed prevalence (or proportion of
! 750: individuals in state (2)). Without discussing the results (it is not the purpose
! 751: here), we observe that the green curve is somewhat below the period
! 752: prevalence. If the data were not biased by the non inclusion of people
! 753: living in institutions we would have concluded that the prevalence of
! 754: disability will increase in the future (see the main publication if
! 755: you are interested in real data and results which are opposite).</P>
! 756: <P><IMG height=300
! 757: src="Computing Health Expectancies using IMaCh_fichiers/vbiaspar21.png"
! 758: width=400></P>
! 759: <H5><FONT color=#ec5e5e size=3><B>-Convergence to the period prevalence of
! 760: disability</B></FONT><B>: </B><A
! 761: href="Computing Health Expectancies using IMaCh_fichiers/pbiaspar11.png"><B>biaspar/pbiaspar11.png</B></A><BR><IMG
! 762: height=300
! 763: src="Computing Health Expectancies using IMaCh_fichiers/pbiaspar11.png"
! 764: width=400> </H5>
! 765: <P>This graph plots the conditional transition probabilities from an initial
! 766: state (1=healthy in red at the bottom, or 2=disabled in green on the top) at age
! 767: <EM>x </EM>to the final state 2=disabled<EM> </EM>at age <EM>x+h
! 768: </EM> where conditional means conditional on being alive at age <EM>x+h </EM>which is
! 769: <I>hP12x</I> + <EM>hP22x</EM>. The curves <I>hP12x/(hP12x</I> + <EM>hP22x)
! 770: </EM>and <I>hP22x/(hP12x</I> + <EM>hP22x) </EM>converge with <EM>h, </EM>to the
! 771: <EM>period prevalence of disability</EM>. In order to get the period prevalence
! 772: at age 70 we should start the process at an earlier age, i.e.50. If the
! 773: disability state is defined by severe disability criteria with only a
! 774: small chance of recovering, then the incidence of recovery is low and the time to convergence is
! 775: probably longer. But we don't have experience of this yet.</P>
! 776: <H5><FONT color=#ec5e5e size=3><B>- Life expectancies by age and initial health
! 777: status with standard deviation</B></FONT><B>: </B><A
! 778: href="http://euroreves.ined.fr/imach/doc/biaspar/erbiaspar.txt"><B>biaspar/erbiaspar.txt</B></A></H5><PRE># Health expectancies
1.1 brouard 779: # Age 1-1 (SE) 1-2 (SE) 2-1 (SE) 2-2 (SE)
1.2 brouard 780: 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
781: 71 10.4786 (0.1184) 3.2093 (0.3212) 4.3384 (0.0875) 4.4820 (0.2076)
782: 72 9.9551 (0.1103) 3.2236 (0.2827) 4.0426 (0.0885) 4.4827 (0.1966)
783: 73 9.4476 (0.1035) 3.2379 (0.2478) 3.7621 (0.0899) 4.4825 (0.1858)
784: 74 8.9564 (0.0980) 3.2522 (0.2165) 3.4966 (0.0920) 4.4815 (0.1754)
785: 75 8.4815 (0.0937) 3.2665 (0.1887) 3.2457 (0.0946) 4.4798 (0.1656)
786: 76 8.0230 (0.0905) 3.2806 (0.1645) 3.0090 (0.0979) 4.4772 (0.1565)
787: 77 7.5810 (0.0884) 3.2946 (0.1438) 2.7860 (0.1017) 4.4738 (0.1484)
788: 78 7.1554 (0.0871) 3.3084 (0.1264) 2.5763 (0.1062) 4.4696 (0.1416)
789: 79 6.7464 (0.0867) 3.3220 (0.1124) 2.3794 (0.1112) 4.4646 (0.1364)
790: 80 6.3538 (0.0868) 3.3354 (0.1014) 2.1949 (0.1168) 4.4587 (0.1331)
791: 81 5.9775 (0.0873) 3.3484 (0.0933) 2.0222 (0.1230) 4.4520 (0.1320)
1.5 ! lievre 792: </PRE><PRE>For example 70 11.0180 (0.1277) 3.1950 (0.3635) 4.6500 (0.0871) 4.4807 (0.2187)
1.2 brouard 793: means
1.5 ! lievre 794: e11=11.0180 e12=3.1950 e21=4.6500 e22=4.4807 </PRE><PRE><IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/expbiaspar21.png" width=400><IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/expbiaspar11.png" width=400></PRE>
! 795: <P>For example, life expectancy of a healthy individual at age 70 is 11.0 in the
! 796: healthy state and 3.2 in the disability state (total of 14.2 years). If he was
! 797: disabled at age 70, his life expectancy will be shorter, 4.65 years in the
! 798: healthy state and 4.5 in the disability state (=9.15 years). The total life
! 799: expectancy is a weighted mean of both, 14.2 and 9.15. The weight is the
! 800: proportion of people disabled at age 70. In order to get a period index (i.e.
! 801: based only on incidences) we use the <A
! 802: href="http://euroreves.ined.fr/imach/doc/imach.htm#Period prevalence in each state">stable
! 803: or period prevalence</A> at age 70 (i.e. computed from incidences at earlier
! 804: ages) instead of the <A
! 805: href="http://euroreves.ined.fr/imach/doc/imach.htm#cross-sectional prevalence in each state">cross-sectional
! 806: prevalence</A> (observed for example at first interview) (<A
! 807: href="http://euroreves.ined.fr/imach/doc/imach.htm#Health expectancies">see
! 808: below</A>).</P>
! 809: <H5><FONT color=#ec5e5e size=3><B>- Variances of life expectancies by age and
! 810: initial health status</B></FONT><B>: </B><A
! 811: href="http://euroreves.ined.fr/imach/doc/biaspar/vrbiaspar.txt"><B>biaspar/vrbiaspar.txt</B></A></H5>
! 812: <P>For example, the covariances of life expectancies Cov(ei,ej) at age 50 are
! 813: (line 3) </P><PRE> Cov(e1,e1)=0.4776 Cov(e1,e2)=0.0488=Cov(e2,e1) Cov(e2,e2)=0.0424</PRE>
! 814: <H5><FONT color=#ec5e5e size=3><B>-Variances of one-step probabilities
! 815: </B></FONT><B>: </B><A
! 816: href="http://euroreves.ined.fr/imach/doc/biaspar/probrbiaspar.txt"><B>biaspar/probrbiaspar.txt</B></A></H5>
! 817: <P>For example, at age 65</P><PRE> p11=9.960e-001 standard deviation of p11=2.359e-004</PRE>
! 818: <H5><FONT color=#ec5e5e size=3><B>- </B></FONT><A
! 819: name="Health expectancies"><FONT color=#ec5e5e size=3><B>Health
! 820: expectancies</B></FONT></A><FONT color=#ec5e5e size=3><B> with standard errors
! 821: in parentheses</B></FONT><B>: </B><A
! 822: href="http://euroreves.ined.fr/imach/doc/biaspar/trbiaspar.txt"><FONT
! 823: face="Courier New"><B>biaspar/trbiaspar.txt</B></FONT></A></H5><PRE>#Total LEs with variances: e.. (std) e.1 (std) e.2 (std) </PRE><PRE>70 13.26 (0.22) 9.95 (0.20) 3.30 (0.14) </PRE>
! 824: <P>Thus, at age 70 the total life expectancy, e..=13.26 years is the weighted
! 825: mean of e1.=13.46 and e2.=11.35 by the period prevalences at age 70 which are
! 826: 0.90134 in state 1 and 0.09866 in state 2 respectively (the sum is equal to
! 827: one). e.1=9.95 is the Disability-free life expectancy at age 70 (it is again a
! 828: weighted mean of e11 and e21). e.2=3.30 is also the life expectancy at age 70 to
! 829: be spent in the disability state.</P>
! 830: <H5><FONT color=#ec5e5e size=3><B>-Total life expectancy by age and health
! 831: expectancies in states (1=healthy) and (2=disable)</B></FONT><B>: </B><A
! 832: href="Computing Health Expectancies using IMaCh_fichiers/ebiaspar1.png"><B>biaspar/ebiaspar1.png</B></A></H5>
! 833: <P>This figure represents the health expectancies and the total life expectancy
! 834: with a confidence interval (dashed line). </P><PRE> <IMG height=300 src="Computing Health Expectancies using IMaCh_fichiers/ebiaspar1.png" width=400></PRE>
! 835: <P>Standard deviations (obtained from the information matrix of the model) of
! 836: these quantities are very useful. Cross-longitudinal surveys are costly and do
! 837: not involve huge samples, generally a few thousands; therefore it is very
! 838: important to have an idea of the standard deviation of our estimates. It has
! 839: been a big challenge to compute the Health Expectancy standard deviations. Don't
! 840: be confused: life expectancy is, as any expected value, the mean of a
! 841: distribution; but here we are not computing the standard deviation of the
! 842: distribution, but the standard deviation of the estimate of the mean.</P>
! 843: <P>Our health expectancy estimates vary according to the sample size (and the
! 844: standard deviations give confidence intervals of the estimates) but also
! 845: according to the model fitted. We explain this in more detail.</P>
! 846: <P>Choosing a model means at least two kind of choices. First we have to
! 847: decide the number of disability states. And second we have to design, within
! 848: the logit model family, the model itself: variables, covariates, confounding
! 849: factors etc. to be included.</P>
! 850: <P>The more disability states we have, the better is our demographical
! 851: approximation of the disability process, but the smaller the number of
! 852: transitions between each state and the higher the noise in the
! 853: measurement. We have not experimented enough with the various models
! 854: to summarize the advantages and disadvantages, but it is important to
! 855: note that even if we had huge unbiased samples, the total life
! 856: expectancy computed from a cross-longitudinal survey would vary with
! 857: the number of states. If we define only two states, alive or dead, we
! 858: find the usual life expectancy where it is assumed that at each age,
! 859: people are at the same risk of dying. If we are differentiating the
! 860: alive state into healthy and disabled, and as mortality from the
! 861: disabled state is higher than mortality from the healthy state, we are
! 862: introducing heterogeneity in the risk of dying. The total mortality at
! 863: each age is the weighted mean of the mortality from each state by the
! 864: prevalence of each state. Therefore if the proportion of people at each age and
! 865: in each state is different from the period equilibrium, there is no reason to
! 866: find the same total mortality at a particular age. Life expectancy, even if it
! 867: is a very useful tool, has a very strong hypothesis of homogeneity of the
! 868: population. Our main purpose is not to measure differential mortality but to
! 869: measure the expected time in a healthy or disabled state in order to maximise
! 870: the former and minimize the latter. But the differential in mortality
! 871: complicates the measurement.</P>
! 872: <P>Incidences of disability or recovery are not affected by the number of states
! 873: if these states are independent. But incidence estimates are dependent on the
! 874: specification of the model. The more covariates we add in the logit
! 875: model the better
! 876: is the model, but some covariates are not well measured, some are confounding
! 877: factors like in any statistical model. The procedure to "fit the best model' is
! 878: similar to logistic regression which itself is similar to regression analysis.
! 879: We haven't yet been sofar because we also have a severe limitation which is the
! 880: speed of the convergence. On a Pentium III, 500 MHz, even the simplest model,
! 881: estimated by month on 8,000 people may take 4 hours to converge. Also, the IMaCh
! 882: program is not a statistical package, and does not allow sophisticated design
! 883: variables. If you need sophisticated design variable you have to them your self
! 884: and and add them as ordinary variables. IMaCh allows up to 8 variables. The
! 885: current version of this program allows only to add simple variables like age+sex
! 886: or age+sex+ age*sex but will never be general enough. But what is to remember,
! 887: is that incidences or probability of change from one state to another is
! 888: affected by the variables specified into the model.</P>
! 889: <P>Also, the age range of the people interviewed is linked the age range of the
! 890: life expectancy which can be estimated by extrapolation. If your sample ranges
! 891: from age 70 to 95, you can clearly estimate a life expectancy at age 70 and
! 892: trust your confidence interval because it is mostly based on your sample size,
! 893: but if you want to estimate the life expectancy at age 50, you should rely in
! 894: the design of your model. Fitting a logistic model on a age range of 70 to 95
! 895: and estimating probabilties of transition out of this age range, say at age 50,
! 896: is very dangerous. At least you should remember that the confidence interval
! 897: given by the standard deviation of the health expectancies, are under the strong
! 898: assumption that your model is the 'true model', which is probably not the case
! 899: outside the age range of your sample.</P>
! 900: <H5><FONT color=#ec5e5e size=3><B>- Copy of the parameter file</B></FONT><B>:
! 901: </B><A
! 902: href="http://euroreves.ined.fr/imach/doc/orbiaspar.txt"><B>orbiaspar.txt</B></A></H5>
! 903: <P>This copy of the parameter file can be useful to re-run the program while
! 904: saving the old output files. </P>
! 905: <H5><FONT color=#ec5e5e size=3><B>- Prevalence forecasting</B></FONT><B>: </B><A
! 906: href="http://euroreves.ined.fr/imach/doc/biaspar/frbiaspar.txt"><B>biaspar/frbiaspar.txt</B></A></H5>
! 907: <P>First, we have estimated the observed prevalence between 1/1/1984 and
! 908: 1/6/1988 (June, European syntax of dates). The mean date of all interviews
! 909: (weighted average of the interviews performed between 1/1/1984 and 1/6/1988) is
! 910: estimated to be 13/9/1985, as written on the top on the file. Then we forecast
! 911: the probability to be in each state. </P>
! 912: <P>For example on 1/1/1989 : </P><PRE class=MsoNormal># StartingAge FinalAge P.1 P.2 P.3
1.1 brouard 913: # Forecasting at date 1/1/1989
1.5 ! lievre 914: 73 0.807 0.078 0.115</PRE>
! 915: <P>Since the minimum age is 70 on the 13/9/1985, the youngest forecasted age is
! 916: 73. This means that at age a person aged 70 at 13/9/1989 has a probability to
! 917: enter state1 of 0.807 at age 73 on 1/1/1989. Similarly, the probability to be in
! 918: state 2 is 0.078 and the probability to die is 0.115. Then, on the 1/1/1989, the
! 919: prevalence of disability at age 73 is estimated to be 0.088.</P>
! 920: <H5><FONT color=#ec5e5e size=3><B>- Population forecasting</B></FONT><B>: </B><A
! 921: href="http://euroreves.ined.fr/imach/doc/biaspar/poprbiaspar.txt"><B>biaspar/poprbiaspar.txt</B></A></H5><PRE># Age P.1 P.2 P.3 [Population]
1.1 brouard 922: # Forecasting at date 1/1/1989
923: 75 572685.22 83798.08
924: 74 621296.51 79767.99
1.5 ! lievre 925: 73 645857.70 69320.60 </PRE><PRE># Forecasting at date 1/1/19909
1.1 brouard 926: 76 442986.68 92721.14 120775.48
927: 75 487781.02 91367.97 121915.51
1.5 ! lievre 928: 74 512892.07 85003.47 117282.76 </PRE>
! 929: <P>From the population file, we estimate the number of people in each state. At
! 930: age 73, 645857 persons are in state 1 and 69320 are in state 2. One year latter,
! 931: 512892 are still in state 1, 85003 are in state 2 and 117282 died before
! 932: 1/1/1990.</P>
! 933: <HR>
! 934:
! 935: <H2><A name=example></A><FONT color=#00006a>Trying an example</FONT></H2>
! 936: <P>Since you know how to run the program, it is time to test it on your own
! 937: computer. Try for example on a parameter file named <A
! 938: href="http://euroreves.ined.fr/imach/doc/imachpar.imach">imachpar.imach</A>
! 939: which is a copy of <FONT face="Courier New" size=2>mypar.imach</FONT> included
! 940: in the subdirectory of imach, <FONT face="Courier New" size=2>mytry</FONT>. Edit
! 941: it and change the name of the data file to <FONT face="Courier New"
! 942: size=2>mydata.txt</FONT> if you don't want to copy it on the same directory. The
! 943: file <FONT face="Courier New">mydata.txt</FONT> is a smaller file of 3,000
! 944: people but still with 4 waves. </P>
! 945: <P>Right click on the .imach file and a window will popup with the string
! 946: '<STRONG>Enter the parameter file name:'</STRONG></P>
! 947: <TABLE border=1>
! 948: <TBODY>
! 949: <TR>
! 950: <TD width="100%"><STRONG>IMACH, Version 0.97b</STRONG>
! 951: <P><STRONG>Enter the parameter file name:
! 952: imachpar.imach</STRONG></P></TD></TR></TBODY></TABLE>
! 953: <P>Most of the data files or image files generated, will use the 'imachpar'
! 954: string into their name. The running time is about 2-3 minutes on a Pentium III.
! 955: If the execution worked correctly, the outputs files are created in the current
! 956: directory, and should be the same as the mypar files initially included in the
! 957: directory <FONT face="Courier New" size=2>mytry</FONT>.</P>
! 958: <UL>
! 959: <LI><PRE><U>Output on the screen</U> The output screen looks like <A href="http://euroreves.ined.fr/imach/doc/biaspar.log">biaspar.log</A>
1.1 brouard 960: #
1.2 brouard 961: title=MLE datafile=mydaiata.txt lastobs=3000 firstpass=1 lastpass=3
1.5 ! lievre 962: ftol=1.000000e-008 stepm=24 ncovcol=2 nlstate=2 ndeath=1 maxwav=4 mle=1 weight=0</PRE>
! 963: <LI><PRE>Total number of individuals= 2965, Agemin = 70.00, Agemax= 100.92
1.1 brouard 964:
965: Warning, no any valid information for:126 line=126
966: Warning, no any valid information for:2307 line=2307
967: Delay (in months) between two waves Min=21 Max=51 Mean=24.495826
1.5 ! lievre 968: <FONT face="Times New Roman">These lines give some warnings on the data file and also some raw statistics on frequencies of transitions.</FONT>
1.1 brouard 969: Age 70 1.=230 loss[1]=3.5% 2.=16 loss[2]=12.5% 1.=222 prev[1]=94.1% 2.=14
970: prev[2]=5.9% 1-1=8 11=200 12=7 13=15 2-1=2 21=6 22=7 23=1
1.5 ! lievre 971: Age 102 1.=0 loss[1]=NaNQ% 2.=0 loss[2]=NaNQ% 1.=0 prev[1]=NaNQ% 2.=0 </PRE></LI></UL>It
! 972: includes some warnings or errors which are very important for you. Be careful
! 973: with such warnings because your results may be biased if, for example, you have
! 974: people who accepted to be interviewed at first pass but never after. Or if you
! 975: don't have the exact month of death. In such cases IMaCh doesn't take any
! 976: initiative, it does only warn you. It is up to you to decide what to do with
! 977: these people. Excluding them is usually a wrong decision. It is better to decide
! 978: that the month of death is at the mid-interval between the last two waves for
! 979: example.
! 980: <P>If you survey suffers from severe attrition, you have to analyse the
! 981: characteristics of the lost people and overweight people with same
! 982: characteristics for example.
! 983: <P>By default, IMaCH warns and excludes these problematic people, but you have
! 984: to be careful with such results.
! 985: <P> </P>
! 986: <UL>
! 987: <LI>Maximisation with the Powell algorithm. 8 directions are given
! 988: corresponding to the 8 parameters. this can be rather long to get
! 989: convergence.<BR><FONT face="Courier New" size=1><BR>Powell iter=1
! 990: -2*LL=11531.405658264877 1 0.000000000000 2 0.000000000000 3<BR>0.000000000000
! 991: 4 0.000000000000 5 0.000000000000 6 0.000000000000 7 <BR>0.000000000000 8
! 992: 0.000000000000<BR>1..........2.................3..........4.................5.........<BR>6................7........8...............<BR>Powell
! 993: iter=23 -2*LL=6744.954108371555 1 -12.967632334283 <BR>2 0.135136681033 3
! 994: -7.402109728262 4 0.067844593326 <BR>5 -0.673601538129 6 -0.006615504377 7
! 995: -5.051341616718 <BR>8
! 996: 0.051272038506<BR>1..............2...........3..............4...........<BR>5..........6................7...........8.........<BR>#Number
! 997: of iterations = 23, -2 Log likelihood = 6744.954042573691<BR>#
! 998: Parameters<BR>12 -12.966061 0.135117 <BR>13 -7.401109 0.067831 <BR>21
! 999: -0.672648 -0.006627 <BR>23 -5.051297 0.051271 </FONT><BR>
! 1000: <LI><PRE><FONT size=2>Calculation of the hessian matrix. Wait...
1.1 brouard 1001: 12345678.12.13.14.15.16.17.18.23.24.25.26.27.28.34.35.36.37.38.45.46.47.48.56.57.58.67.68.78
1002:
1003: Inverting the hessian to get the covariance matrix. Wait...
1004:
1005: #Hessian matrix#
1006: 3.344e+002 2.708e+004 -4.586e+001 -3.806e+003 -1.577e+000 -1.313e+002 3.914e-001 3.166e+001
1007: 2.708e+004 2.204e+006 -3.805e+003 -3.174e+005 -1.303e+002 -1.091e+004 2.967e+001 2.399e+003
1008: -4.586e+001 -3.805e+003 4.044e+002 3.197e+004 2.431e-002 1.995e+000 1.783e-001 1.486e+001
1009: -3.806e+003 -3.174e+005 3.197e+004 2.541e+006 2.436e+000 2.051e+002 1.483e+001 1.244e+003
1010: -1.577e+000 -1.303e+002 2.431e-002 2.436e+000 1.093e+002 8.979e+003 -3.402e+001 -2.843e+003
1011: -1.313e+002 -1.091e+004 1.995e+000 2.051e+002 8.979e+003 7.420e+005 -2.842e+003 -2.388e+005
1012: 3.914e-001 2.967e+001 1.783e-001 1.483e+001 -3.402e+001 -2.842e+003 1.494e+002 1.251e+004
1013: 3.166e+001 2.399e+003 1.486e+001 1.244e+003 -2.843e+003 -2.388e+005 1.251e+004 1.053e+006
1014: # Scales
1015: 12 1.00000e-004 1.00000e-006
1016: 13 1.00000e-004 1.00000e-006
1017: 21 1.00000e-003 1.00000e-005
1018: 23 1.00000e-004 1.00000e-005
1019: # Covariance
1020: 1 5.90661e-001
1021: 2 -7.26732e-003 8.98810e-005
1022: 3 8.80177e-002 -1.12706e-003 5.15824e-001
1023: 4 -1.13082e-003 1.45267e-005 -6.50070e-003 8.23270e-005
1024: 5 9.31265e-003 -1.16106e-004 6.00210e-004 -8.04151e-006 1.75753e+000
1025: 6 -1.15664e-004 1.44850e-006 -7.79995e-006 1.04770e-007 -2.12929e-002 2.59422e-004
1026: 7 1.35103e-003 -1.75392e-005 -6.38237e-004 7.85424e-006 4.02601e-001 -4.86776e-003 1.32682e+000
1027: 8 -1.82421e-005 2.35811e-007 7.75503e-006 -9.58687e-008 -4.86589e-003 5.91641e-005 -1.57767e-002 1.88622e-004
1028: # agemin agemax for lifexpectancy, bage fage (if mle==0 ie no data nor Max likelihood).
1029:
1030:
1031: agemin=70 agemax=100 bage=50 fage=100
1032: Computing prevalence limit: result on file 'plrmypar.txt'
1033: Computing pij: result on file 'pijrmypar.txt'
1034: Computing Health Expectancies: result on file 'ermypar.txt'
1035: Computing Variance-covariance of DFLEs: file 'vrmypar.txt'
1036: Computing Total LEs with variances: file 'trmypar.txt'
1037: Computing Variance-covariance of Prevalence limit: file 'vplrmypar.txt'
1038: End of Imach
1.5 ! lievre 1039: </FONT></PRE></LI></UL>
! 1040: <P><FONT size=3>Once the running is finished, the program requires a
! 1041: character:</FONT></P>
! 1042: <TABLE border=1>
! 1043: <TBODY>
! 1044: <TR>
! 1045: <TD width="100%"><STRONG>Type e to edit output files, g to graph again, c
! 1046: to start again, and q for exiting:</STRONG></TD></TR></TBODY></TABLE>In order to
! 1047: have an idea of the time needed to reach convergence, IMaCh gives an estimation
! 1048: if the convergence needs 10, 20 or 30 iterations. It might be useful.
! 1049: <P><FONT size=3>First you should enter <STRONG>e </STRONG>to edit the master
! 1050: file mypar.htm. </FONT></P>
! 1051: <UL>
! 1052: <LI><U>Outputs files</U> <BR><BR>- Copy of the parameter file: <A
! 1053: href="http://euroreves.ined.fr/imach/doc/ormypar.txt">ormypar.txt</A><BR>-
! 1054: Gnuplot file name: <A
! 1055: href="http://euroreves.ined.fr/imach/doc/mypar.gp.txt">mypar.gp.txt</A><BR>-
! 1056: Cross-sectional prevalence in each state: <A
! 1057: href="http://euroreves.ined.fr/imach/doc/prmypar.txt">prmypar.txt</A> <BR>-
! 1058: Period prevalence in each state: <A
! 1059: href="http://euroreves.ined.fr/imach/doc/plrmypar.txt">plrmypar.txt</A> <BR>-
! 1060: Transition probabilities: <A
! 1061: href="http://euroreves.ined.fr/imach/doc/pijrmypar.txt">pijrmypar.txt</A><BR>-
! 1062: Life expectancies by age and initial health status (estepm=24 months): <A
! 1063: href="http://euroreves.ined.fr/imach/doc/ermypar.txt">ermypar.txt</A> <BR>-
! 1064: Parameter file with estimated parameters and the covariance matrix: <A
! 1065: href="http://euroreves.ined.fr/imach/doc/rmypar.txt">rmypar.txt</A> <BR>-
! 1066: Variance of one-step probabilities: <A
! 1067: href="http://euroreves.ined.fr/imach/doc/probrmypar.txt">probrmypar.txt</A>
! 1068: <BR>- Variances of life expectancies by age and initial health status
! 1069: (estepm=24 months): <A
! 1070: href="http://euroreves.ined.fr/imach/doc/vrmypar.txt">vrmypar.txt</A><BR>-
! 1071: Health expectancies with their variances: <A
! 1072: href="http://euroreves.ined.fr/imach/doc/trmypar.txt">trmypar.txt</A> <BR>-
! 1073: Standard deviation of period prevalences: <A
! 1074: href="http://euroreves.ined.fr/imach/doc/vplrmypar.txt">vplrmypar.txt</A>
! 1075: <BR>No population forecast: popforecast = 0 (instead of 1) or stepm = 24
! 1076: (instead of 1) or model=. (instead of .)<BR><BR>
! 1077: <LI><U>Graphs</U> <BR><BR>-<A
! 1078: href="http://euroreves.ined.fr/imach/mytry/pemypar1.gif">One-step transition
! 1079: probabilities</A><BR>-<A
! 1080: href="http://euroreves.ined.fr/imach/mytry/pmypar11.gif">Convergence to the
! 1081: period prevalence</A><BR>-<A
! 1082: href="http://euroreves.ined.fr/imach/mytry/vmypar11.gif">Cross-sectional and
! 1083: period prevalence in state (1) with the confident interval</A> <BR>-<A
! 1084: href="http://euroreves.ined.fr/imach/mytry/vmypar21.gif">Cross-sectional and
! 1085: period prevalence in state (2) with the confident interval</A> <BR>-<A
! 1086: href="http://euroreves.ined.fr/imach/mytry/expmypar11.gif">Health life
! 1087: expectancies by age and initial health state (1)</A> <BR>-<A
! 1088: href="http://euroreves.ined.fr/imach/mytry/expmypar21.gif">Health life
! 1089: expectancies by age and initial health state (2)</A> <BR>-<A
! 1090: href="http://euroreves.ined.fr/imach/mytry/emypar1.gif">Total life expectancy
! 1091: by age and health expectancies in states (1) and (2).</A> </LI></UL>
! 1092: <P>This software have been partly granted by <A
! 1093: href="http://euroreves.ined.fr/">Euro-REVES</A>, a concerted action from the
! 1094: European Union. It will be copyrighted identically to a GNU software product,
! 1095: i.e. program and software can be distributed freely for non commercial use.
! 1096: Sources are not widely distributed today. You can get them by asking us with a
! 1097: simple justification (name, email, institute) <A
! 1098: href="mailto:brouard@ined.fr">mailto:brouard@ined.fr</A> and <A
! 1099: href="mailto:lievre@ined.fr">mailto:lievre@ined.fr</A> .</P>
! 1100: <P>Latest version (0.97b of June 2004) can be accessed at <A
! 1101: href="http://euroreves.ined.fr/imach">http://euroreves.ined.fr/imach</A><BR></P></BODY></HTML>
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