Estimating and interpolating a Markov chain from aggregate data

Biometrika

Volumn 89, Issue 1, 2002, Pages 95-110

  Davis, B A ^a   Heathcote, C R ^b   O'Neill, T J ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Interpolation; Longitudinal data; Markov chain; Odds; Vector regression; Weighted least squares

Indexed keywords

EID: 21244456444     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/89.1.95     Document Type: Article

References (23)

1. AGRESTI, A. (1997). A model for repeated measurements of a multivariate binary response. J. Am. Statist. Assoc. 92, 315-21.
2. ANDERSON, T. W. & GOODMAN, L. A. (1957). Statistical inference about Markov chains. Ann. Math. Statist. 28, 89-110.
3. CHIANG, C. L. (1968). Introduction to Stochastic Processes in Biostatistics. New York: Wiley.
4. COX, D. R. (1972). Regression models and life tables (with Discussion). J. R. Statist. Soc. B 34, 187-220.
5. CRIMMINS, E. M., HAYWARD, M. D. & SAITO, Y. (1994). Changing mortality and morbidity rates and the health status and life expectancy of the older population. Demography 31, 159-75.
6. CROWDER, M. (1995). On the use of a working correlation matrix in using generalised linear models for repeated measures. Biometrika 82, 407-10.
7. DAVIS, B. A., HEATHCOTE, C. R. & O'NEILL, T. J. (2001). Estimating cohort health expectancies from cross-sectional surveys of disability. Statist. Med. 20, 1097-111.
8. D'ESPAIGNET, E. T. (1993). Trends in Australian Mortality; Diseases of the Circulatory System 1950-1991. Canberra: Australian Institute of Health and Welfare.
9. GILL, R. D. (1992). Multistate life tables and regression models. Math. Pop. Studies 3, 259-76.
10. GILL, R. D. & KEILMAN, N. (1990). On the estimation of multidimensional demographic models with population registration data. Math. Pop. Studies 2, 119-43.
11. GUILKEY, D. K. & RINDFUSS, R. R. (1987). Logistic regression multivariate lifetables. Social. Meth. Res. 16, 276-300.
12. HEATHCOTE, C. R. & MCDERMID, I. M. (1994). Projection of cohort life expectancy based on weighted least squares methods. In Advances in Health Expectancies, Ed. C. Mathers, J. McCallum and J. M. Robine, pp. 96-114. Canberra: Australian Institute of Health and Welfare.
13. HOEM, J. M. & JENSEN, U. F. (1982). Multistate lifetable methodology: A probabilistic critique. In Multidimensional Mathematical Demography, Ed. K. C. Land and A. Rodgers, pp. 155-264. New York: Academic Press.
14. JORGENSEN, B., LUNDBYE-CHRISTENSEN, S., SONG, P. X.-K. & SUN, L. (1999). A state space model for multivariate longitudinal count data. Biometrika 86, 169-81.
15. KALBFLEISCH, J. D. & LAWLESS, J. F. (1985). The analysis of panel data under a Markov assumption. J. Am. Statist. Assoc. 80, 863-71.
16. LAND, K. C., GURALNIK, J. M. & BLAZER, D. G. (1994). Estimating increment-decrement lifetables with multiple covariates from panel data: the case of active life expectancy. Demography 31, 297-319.
17. LIANG, K. Y. & ZEGER, S. L. (1986). Longitudinal data analysis using generalised linear models. Biometrika 73, 13-22.
18. LIPSITZ, S. R., LAIRD, N. M. & HARRINGTON, D. P. (1991). Generalised estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika 78, 153-60.
19. MAGNUS, J. R. & NEUDECKER, H. (1999). Matrix Differential Calculus, rev. ed. Chichester: Wiley.
20. PRENTICE, R. L. & HSU, L. (1997). Regression on hazard ratios and cross ratios in multivariate failure time analysis. Biometrika 84, 349-63.
21. SUTRADHAR, B. C. & DAS, K. (1999). On the efficiency of regression estimators in generalised linear models for longitudinal data. Biometrika 86, 459-65.
22. ZEGER, S. L. (1988). A regression model for time series of counts. Biometrika 75, 621-9.
23. ZEGER, S. L. & LIANG, K. Y. (1992). An overview of methods for the analysis of longitudinal data. Statist. Med. 11, 1825-39.