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help for lxpct_2
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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