-------------------------------------------------------------------------------
help for lxpct_2
-------------------------------------------------------------------------------

Multistate Life Expectancy Calculator

        lxpct_2 [, i(#) d(#)]

    where i is the total number of states in the model (absorbing states and
    non-absorbing states)

    and d is the number of absorbing states (e.g. death).


Description

    lxpct_2 calculates multistate life expectancies from age-specific
    transition probabilities.  Like a standard life table, the multistate, or
    increment-decrement, life table allows a researcher to calculate expected
    years of life while adjusting for age-related differences in the
    composition of various populations.

        The input file must contain the following variables:

        Variable name    Details

        age               Age 'x' in single years
        pij               Transition probability from state `i' at age `x' to
                            state `j' at age `x+1'


        For example in a model with the states disabled, non-diabled, and
        dead, the total number of states in the model is three (i.e. i(3) )
        and the total number of non-absorbing states is one (i.e. d(1) ).  An
        appropriately structured dataset would take the following shape*:

            age      p11       p12       p13       p21       p22       p23
            10       0.6468    0.3524    0.0008    0.1510    0.8489    0.0001
            11       0.6544    0.3450    0.0006    0.1515    0.8484    0.0001
            12       0.6612    0.3381    0.0007    0.1522    0.8476    0.0001
            13       0.6668    0.3321    0.0011    0.1530    0.8469    0.0001
            14       0.6717    0.3265    0.0018    0.1538    0.8461    0.0002
            15       0.6771    0.3204    0.0026    0.1547    0.8450    0.0003
            .        .         .         .         .         .         .
            .        .         .         .         .         .         .
            .        .         .         .         .         .         .
            60       0.9384    0.0000    0.0616    0.3969    0.5814    0.0217

        Notice that no transition probabilites are needed for transitions
        from absorbing to non-aborbing states and that no transition
        probablities are needed for remaining within an absorbing state (i.e.
        I assume the dead remain dead).  The program automatically sets the
        former to 0 and the later to 1.


Results

    The lxpct_2 command calculates and displays, by age, the life table
    functions which have been stored as matrices. These entail the following:

        li_x     the survival function in state `i' at age `x'
        Li_x     the person-years in state `i' at age `x'
        Ti_x     the reverse-cumulative function of Li_x in state `i' at age
        `x'
        ei_x     the life expectancy in state `i' at age `x'


Example

    A calcuation of multistate life table expectancies using the model and
    dataset described above involves the following syntax :

        . lxpct_2, i(3) d(1)

    The program calculates the matrices l1_x, l2_x, l3_x, L1_x, L2_x, L3_x,
    T1_x, T2_x, T3_x, e1_x, e2_x, and e3_x.  These matrices can be transposed
    into variables using the command svmat.  For example:

        . svmat e2_x, names(col)

    The variables can then be manipulated within Stata using such commands as
    summarize and graph, or they can be exported into another software
    package for manipulation.


References

    For more information about the methods and models, please see the
    following references:

    Laditka, S.B. and Wolf, D.A. (1998) “New methods for analyzing active
        life expectancy”. Journal of Aging and Health. 10, 214-241.
    Schoen, R. (1988) Modeling Multigroup Populations. New York, NY: Plenum
        Press.
    Preston, S.H., Heuveline, P., Guillot, M. (2001) Demography: Measuring
        and Modeling Population Processes. Malden, MA: Blackwell Publishers.

    *The data for this example was abstracted with minor changes from a
    dataset obtained courtesy of Paula Diehr, University of Washington,
    Department of Biostatistics.


Author

    Margaret M. Weden
    Robert Wood Johnson Health & Society Scholar
    University of Wisconsin- Madison
    Department of Population Health Sciences
    Madison, WI  53726
    weden@wisc.edu