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United States of America (New York) 61

MATHEMATICAL POPULATION STUDIES

1998 - VOLUME 7, NUMBER 1

99.61.1 - English - Arvind PANDEY, Department of Mathematical Demography and Statistics, International Institute for Population Sciences, Bombay (India), S. N. DWIVEDI, Department of Biostatistic, All India Institute of Medical Sciences, New Delhi (India), and R. N. MISHRA, Department of PSM, Institute of Medical Sciences, B.H.U., Varanasi (India)

A stochastic model for the study of last closed birth interval with some biosocial components (p. 1-27)

We present a stochastic model to describe variation in last closed birth interval for women of a given marriage duration by parity as well as regardless of parity. The model is derived under some simplified assumptions relating to human reproduction process accounting for the non exposure period in the beginning of the reproductive life caused by such biosocial, components as adolescent sterility and temporary separation between the partners called as an inoperative period. We illustrate the model regardless of parity on an observed set of data taken from a rural area of northern India and estimate the risk of conception before and after the first birth. (INDIA, BIRTH INTERVALS, MARRIAGE DURATION, PARITY, RISK OF CONCEPTION, STOCHASTIC MODELS)

99.61.2 - English - Jan J. BARENDREGT, Gerrit J. VAN OORTMARSSEN, Ben A. VAN HOUT, Jacqueline M. VAN DEN BOSCH and Luc BONNEUX, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam (Netherlands)

Coping with multiple morbidity in a life table (p. 29-49)

One of the applications of the multi-state life table is in the field of Public Health, with states defining various levels of health or functional ability. Another approach is to model Public Health by looking at the impact of individual diseases, but, unfortunately, then two practical problems arise: there are many diseases, and due to comorbidity people may be in several diseases states simultaneously. Both problems tend to make the number of states in the life table impractically large. In this paper we introduce the proportional multi-state life table. It is especially designed to cope relatively easily with a large number of diseases simultaneously, while allowing for comorbidity. We provide proof of validity and an example implementation for cardiovascular disease. (PUBLIC HEALTH, MULTI-STATE LIFE TABLES, MORBIDITY, MULTIPLE CAUSES OF DEATH)

99.61.3 - English - Anatoli I. YASHIN, Duke University, Center for Demographic Studies, Box 90408, Durham, NC 27708 (U.S.A.), Ivan A. IACHINE, Kirill F. ANDREEV, Odense University, Medical School, Winslowparken 17.1, DK 5000 Odense C (Denmark), and Ulla LARSEN, Department of Population and International Health, Harvard School of Public Health, Boston, MA 02115 (U.S.A.)

Multistate models of postpartum infecundity, fecundability and sterility by age and parity: Methodological issues (p. 51-78)

How do hidden physiological processes influence estimates of fecundability and sterility? Does unobserved heterogeneity play a role in these estimates? To address these questions mathematical models of the reproductive process are needed. It is not well known how to evaluate characteristics of reproductive models based on observed reproductive history data, and such models may not be identifiable without ancillary information. However, little is known about how to introduce ancillary information into reproductive models. Furthermore, even if such information was involved, the use of standard software packages for maximization of the likelihood function is often not feasible, because the function cannot be represented in an explicit parametric form. In this paper we propose an approach which represents the likelihood function in a form useful for further analysis. This approach is based on multistate: models of the basic physiological processes that influence reproductive outcomes, and it is suitable in applications where ancillary information is given in the form of hazard rates. As an alternative, a competing risks model with incomplete information is discussed. (INFERTILITY, FECUNDABILITY, POST-PARTUM STERILITY, MATHEMATICAL MODELS, MAXIMUM LIKELIHOOD METHOD)

99.61.4 - English - Nicholas B. BARKALOV, DGI Inc., 700 North Fairfax St., Alexandria, VA 22314 (U.S.A.)

On solutions of the cohort parity analysis model (p. 79-107)

The cohort parity analysis (CPA) model of David et al. (1988) is studied formally as a three-state parity-progression table. The general solution is found in a form of convex combination of a finite set of solutions which are described explicitly. A parameterization is suggested for a broad subset of solutions which includes two extreme solutions studied in the original publication and maintains the dimension of the entire set. The CPA solution is also treated as a random variate distributed uniformly on the set of all possible solutions. An algorithm is given for computing the marginal distributions without Monte Carlo simulation. (DEMOGRAPHIC MODELS, COHORT ANALYSIS, PARITY PROGRESSION RATIO)

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