length of life-and of population life expectancy are made by demographers, biologists, and actuaries. Despite the significance of a life expectancy limit for private and public pension programs, the Social Security Trust Fund in the United States (Preston, 1991) and comparable funds in other aging, industrial societies, and for private and public acute and long-term health insurance, there is little consensus on the value at which the limit is set. Perspectives on the issue can be roughly divided into three groups. The "traditionalists" suggest that the limit is not significantly greater than current life expectancy, namely about 85 years (Olshansky, Carnes, and Cassel, 1990; Fries, 1990). The limit is viewed as due to biological senescence, which is not affected by changing the mortality of specific causes. A "visionary" perspective suggests that, while life expectancy limits are due to senescence, advances in biomedical research will raise those limits in the future (in some 25 to 50 years). Since senescence itself is thereby modified, life expectancies of 100 to 125 years (Strehler, 1975) or more (150 to 200 years, Rosenberg et al., 1973; Walford, 1983) might be achievable. It is suggested that altering senescence has implications for age-dependent diseases (Strehler, 1975: Figure 2). An "empiricist" perspective contends that we are not currently near a life expectancy limit, because mortality is declining and progress is being made in the treatment and management of the chronic diseases and disabilities that dominate mortality at later ages. It is observed that, if recent mortality declines of about 2 percent per year continued, life expectancies POPULATION AND DEVELOPMENT REVIEW 17, NO. 4 (DECEMBER 1991) 603

Consideration is made of the problems involved in determining the effects of a chronic disease process, such as stomach cancer, on the observed mortality of the U.S. population. Specifically, since the time of initiation of tumor growth is unknown and the tumor becomes clinically manifest only after reaching considerable size, the early rate and pattern of tumor growth is unobserved. As a possible solution to the analysis of such problems, it is proposed to use stochastic compartment modelling techniques which deal with the problems of estimating the transition probabilities of a partially observed stochastic process. Implementation of the stochastic compartment techniques in this case depends on the selection of certain mathematical expressions from theories of carcinogenesis, epidemiologic studies and animal studies which allow the calculation of transition probabilities to unobserved states by making them explicit functions of time or age. Though the selection of the specific functions might be subject to debate, the general strategy of explicitly selecting such functions, and thereby exposing them for review in terms of biologic reasonableness and consistency with the data, seems to be a valid and useful methodology. Furthermore, various ways of viewing the model results (say from its internal behavior, e.g., from implied distributions of waiting times in various disease states) yield different insights into the various factors in carcinogenesis. The model, with parameters representing tumor incidence, time to tumor death given onset, genetic susceptibility to tumor growth and the effects of competing forces of mortality, is fitted to data on deaths due to stomach cancer for male U.S. residents age 25 and over in 1969. Two basic forms of the model, one with a waiting time distribution for occupants of the latent state and another with a single latency time, achieved excellent fits to the data. Examination of parameter estimates and compartment waiting time distributions are consistent with theoretical expectations and intuition. It is concluded that such strategies, involving the integration of clinical, experimental and vital statistics data into a comprehensive model of population carcinogenesis, are potentially powerful tools for investigation of the temporal dimensions of disease development in a human population.

No abstract

A well-known method of estimation for the density of bacteria in a sample solution is the most probable number (MPN) procedure. This paper considers the change in density through time of bacteria populations which are undergoing extinction. The MPN with its estimated variance for a fixed time point is a basic module of these investigations and is treated as a general implicit function of the cell proportions in linear categorical data analysis. These quantities are then used to fit exponential decay models over time by weighted least squares. When such models are supported by the data, comparisons of decay rates between populations under possibly different experimental conditions can be undertaken. This methodology is illustrated with an example pertaining to the survival experience of Leptospira autumnalis.

No abstract