# SPACE Program (Stochastic Population Analysis for Complex Events)

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The SPACE (Stochastic Population Analysis for Complex Events) program is a collection of PC SAS® programs to estimate multi-state life table (MSLT) functions via microsimulation, and their sampling variability via a special bootstrap approach. This program offers a versatile statistical tool for researchers interested in modeling multiple and recurrent events using longitudinal survey data. Its development and applications is described in detail in a recent paper (Cai et al. 2010).

MSLT models describe the changes over time in states of interest (i.e., health, employment, residence, marriage, disease stages, etc.) for members of a population, conditional on member’s select attributes (e.g., age, sex, race/ethnicity, education, etc.). The SPACE program estimates two types of MSLT models: the duration-independent model and the duration-dependent model. Duration-independent model is a first-order Markov chain model that estimates transition probabilities or rates as a function of one’s current age and status, and other attributes (Schoen 1988). Duration-dependent model views the underlying stochastic process as a renewal process (Cox 1962), thus considers the effect of duration in current states as well. Wolf (1988) applied this model to longitudinal data with known duration in current states; Cai, Schenker and Lubitz (2006) extended this model to data without known values of duration by using the stochastic EM (Expectation-Maximization) algorithm.

The SPACE program uses both deterministic and microsimulation approaches to computing MSLT functions. Microsimulation “expresses” the transition probability estimates by generating detailed life paths for each member of the target population, thus offering users much greater flexibility in the characterization of the underlying stochastic process than other deterministic approaches. Simulation permits calculation of a wide variety of summary statistics (e.g., distribution of life years in various states), in addition to average values such as life expectancy.

The SPACE program uses a special bootstrap approach to estimate survey design-adjusted variance for MSLT functions. When the MSLT model was originally developed, life tables were calculated using population-level rates. Increasingly, however, the data source is panel data obtained via survey sampling, making it difficult to test hypotheses about the differences between population subgroups without knowing the sampling variability of MSLT functions. The SPACE program uses a version of the rescaling bootstrap method developed specifically for complex surveys (Korn and Graubard 1999:32-33; Rao and Wu 1988; Sitter 1992), controlling for the survey design elements such as stratification and clustering. The design-adjusted variance estimates are typically larger than other estimates that treat complex survey as simple random survey.

#### References

- Cai, L., M. Hayward, Y. Saito, J. Lubitz, A. Hagedorn, and E. Crimmins. 2010. "Estimation of Multi-State Life Table Functions and Their Variances Using the SPACE Program." Demographic Research 22-6.
- Cai, L.M., N. Schenker, and J. Lubitz. 2006. "Analysis of Functional Status Transitions by Using a Semi-Markov Process model in the Presence of Left-Censored Spells." Journal of the Royal Statistical Society Series C-Applied Statistics 55:477-491.
- Cox, D.R. 1962. Renewal theory. London: Methuen.
- Korn, E.L.and B.I. Graubard. 1999. Analysis of health surveys. New York: Wiley.
- Rao, J.N.K.and C.F.J. Wu. 1988. "Resampling Inference with Complex Survey Data." Journal of the American Statistical Association 83(401):231-241.
- Schoen, R. 1988. "PRACTICAL USES OF MULTISTATE POPULATION-MODELS." Annual Review of Sociology 14:341-361.
- Sitter, R.R. 1992. "Comparing 3 Bootstrap Methods for Survey Data." Canadian Journal of Statistics-Revue Canadienne De Statistique 20(2):135-154.
- Wolf, D.A. 1988. "The multistate life table with duration-dependence." Math Popul Stud 1(3):217-245, 317.

## Documentation and Data Files

- User’s manual [PDF - 55 KB]
- Readme file [TXT - 3 KB]
- Annotated SPACE programs
- Mark Hayward’s SAS macro to compute MSLT function via the deterministic approach [SAS - 37 KB]
- Duration-independent MSLT model with deterministic approach to calculation of MSLT functions
- Duration-independent MSLT model with microsimulation approach to calculation of MSLT functions
- Duration-dependent MSLT model with microsimulation approach to calculation of MSLT functions
- Sample data [SAS7BDAT - 2.1 MB]

## Journal Articles

- Paper details the development and features of the SPACE program
- Paper details the development of the SMP-EM model

Cai, L., N. Schenker, J. Lubitz. 2006. “Analysis of Functional Status Transitions Using a Semi-Markov Process Model in the Presence of Left-Censored Spells.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 55 (4): 477-491