A gross mating table for a West Indian population

At a sample survey carried out in Trinidad in 1958 data were collected on the participation of women in three union types: “visiting”, “common law” and “married”. It is assumed that the maximum number of changes of union type in which a woman is involved is three. From the survey material the chances of non-East Indian women moving from one type of union to another as they pass through the childbearing span (taken here as 14 to 45) are calculated. These chances are used to construct a table showing the types of unions in which a cohort of 10,000 women are involved between the ages of 14 and 45.

This table makes possible the estimation of the length of time spent by the average woman in the three union types as well as the time spent in the “single” state, the numbers of women participating in these union types at different ages and the stability of these types of union.

This table emphasizes that despite the fact that the “visiting” type is very important at lower ages, there is a progressive concentration in “married” and “common law” types with advance in age, and by age 45 more than half the women are “married” and about one-fifth are in “common law” associations. It also shows that the average woman spends the longest period of childbearing life in the “married” state (9.6 years), the shortest time in “visiting” unions (4.1 years) and 5.9 years in “common law” unions. Stability is strongest in the case of the “married” type and lowest for the “visiting”; this, however, may be viewed not so much as evidence of family disorganisation, but as a progressive shift from a less stable to a more stable union type.     

A two-sex nuptiality-mortality life table

The “problem of the sexes” has been one of trying to reconcile inconsistent male and female demographic rates. The present paper deals with that question in the context of a two-sex nuptiality-mortality life table. A “rectangular” population, with equal numbers of persons in each age-sex group, is introduced as a standard, and a standardization relationship expressed in equation (9) relates changes in rectangular population rates to changes in age-sex composition. The standardization relationship is shown to satisfy a number of desirable properties and produce a realistic two-sex model. The standardization approach is then applied to data from Sweden for 1973, and the results and their implications are discussed. In particular, it is seen that the total number of marriages in a two-sex population neither is nor should be bounded by the total numbers of marriages in the associated male and female one-sex nuptiality-mortality tables.     

A comment on Coale's life table construction

In a recent issue of Population Index, Coale (1984) described a method of deriving a life table for an intercensal period separated by T years from 2 census single-year age distributions of a closed population. This note examines the formula used by Coale and points out that although it works well for all practical purposes, the formula with his new growth rate is an approximation, not an identity as is assumed by Coale. The Coale formula involves more steps than the usual method of estmating mortality and yields less accurate results. Coale's formula is explained. In general, in the case under consideration, if a larger cohort is followed by a smaller cohort, the survival probability calculated by the formula exceeds unity, whereas if a smaller cohort is followed by a larger cohort, the calculated survival probability becomes less than unity. The size of the relative cohorts determines the degree of error in the calculated probability. The formula does not give the survival probability of unity as it should if it were an identity. The formula in the continuous time is an identity. Feeney's alternative method presented in Coale's Computational Appendix 3 produces an exact life table without using any formula. Feeney's method is, however, less accurate than the usual method, given the same data, because it omits some information. The Coale procedure losses its usefulness in that it requires extra data manipulation, only to yield less accurate results.     

Coping with multiple morbidity in a life table

"We present the proportional multi-state life table method, that makes the inclusion of multiple diseases better manageable and allows for comorbidity implicitly, without the need to define additional states. We implement the method for heart disease and stroke [among Dutch males in 1988], and look at the effect of hypothetical but not unrealistic changes in incidence and survival on disease prevalence and comorbidity. Finally we discuss limitations and extensions of the method." (EXCERPT)     

A long period multistate life table using micro data

"The multistate life table (MLT) has been widely used by demographers for the past twenty years. However, the pivotal Markov condition upon which the entire methodology rests is rarely satisfied in practice. We lessen reliance upon the assumption by computing transition probabilities for longer periods of time than was previously practical. An extended Kaplan-Meier estimator accomplishes this task, simultaneously addressing the issue of censoring.... We provide an illustrative example of a 10-year period MLT, with comparison to a 1-year period MLT." The data for California are used as an illustration. (EXCERPT)     

A new look at entropy and the life table

The mathematical derivations described in this paper offer a new look at the entropy of the life table, denoted by H. Contrary to previous claims, it is theoretically possible, and has been observed empirically, for life tables to have entropy values greater than unity. A re-expression of H as a weighted average of life expectancy at different ages relative to life expectancy at birth demonstrates clearly the conditions under which reductions in mortality by a fixed amount at all ages can result in even greater gains in life expectancy.     

Bias in graduated life table functions

Survival proportions and expectations of life estimated directly from observed crude mortality rates are usually unbiased. Estimates of survival proportions and expectations of life obtained from graduated mortality rates at individual ages tend to be positively biased, although the actual bias is small for reasonably large experiences.     

The multistate life table with duration-dependence

"A method for generalizing the multistate, or increment-decrement, life table to include rates which depend upon duration of exposure to risk, as well as upon age, is proposed. The method is built upon the linear approximation, called the linear integration hypothesis, developed mainly by Rogers and his colleagues....It is possible to derive several new summary indices of the life-table cohort's history, such as the mean and median time in current status, at any age. The method is illustrated using a simple four-state marital-status model which has appeared often in the literature; here, rates of divorce and widowhood vary by duration of marriage as well as age." An example is demonstrated using 1984 period data for women in Finland aged 15-50. (SUMMARY IN FRE)     

The four-parameter logit life table system

Summary Brass's model life table system, which is a two parameter system based on the logit transformation of survivorship values, has been widely and successfully used to describe age patterns of mortality in many populations. As more reliable information has become available for populations with mortality patterns which differ in important ways from the assumed standard pattern of mortality, a more flexible model system is needed. This paper shows how Brass's system can be expanded into a four-parameter model, and evaluates the performance of the new system by examining how well it can fit observed life table data.     

Marriage,divorce, and mortality: A life table analysis

The life status table, an analytical model which follows a birth cohort through life and through the never-married, presently married, widowed and divorced statuses, is developed and applied to data from four Western populations. Particular attention is given to recent marriage, remarriage, and divorce trends in California. California data for 1969 imply that 40 percent of all marriages will end in divorce, that each marrying male will marry an average of 12/3 times, and that every woman born can expect to spend 61/2 years in the divorced state. Rising divorce rates may be seen as signaling fundamental changes in both the nature of the American family and the structure of American society.     

The relationship between the life table method and the formula for calculating life expectancy]

The author states that average life expectancy can be determined either by life table methods or by mathematical equations. An attempt is made to prove that the life table method is an approximation of first degree to the equation method. Some inherent contradictions in the concept of average life expectancy are considered.     

Optimal food allocation in a slave economy

We propose a model of food allocation in an economy in which property rights exist in human beings. We assume that a slave-owner allocates food over the slave's lifetime so as to maximise his own wealth. The slave's productive capacity is determined endogenously by food consumption. Food allotment during childhood and adolescence determines productive capacity over the life course. The slave owner chooses optimal time paths of food allotment in light of the contribution food makes to both the level and growth of physical capacity, as a function of the price of food and of the value of the slave's productivity. Though conceived for an economy in which property rights exist in human beings, the model can be modified so as to apply to resource allocation within a household economy in which parents provide both nourishment and schooling for their children, in order to enhance their current or future productivity. Received: 14 April 2000/Accepted: 25 August 2001     

Methodological issues underlying multiple decrement life table analysis

In this paper, the actuarial method of multiple decrement life table analysis of censored, longitudinal data is examined. The discussion is organized in terms of the first segment of usage of an intrauterine device. Weaknesses of the actuarial approach are pointed out, and an alternative approach, based on the classical model of competing risks, is proposed. Finally, the actuarial and the alternative method of analyzing censored data are compared, using data from the Taichung Medical Study on Intrauterine Devices.     

Life table construction on the basis of two enumerations of a closed population

The author demonstrates that an accurate detailed life table that represents average mortality experience between two censuses can be constructed if the censuses provide accurate records of the single-year age distribution of a closed population. This life table can begin at age zero if accurate data on the annual number of births during the inter-censal period are available; otherwise the first age in the life table must equal the duration of time between the censuses. "The estimation technique involves the calculation of the number of persons attaining each age during the period between the censuses and the determination of the average rate of increase in the number at each individual age. The success of the technique comes from the use of interpolation to calculate how many in each cohort attain each exact age the cohort passes through between the censuses." The estimation technique is tested using two alternative methods of interpolation. Some illustrations based on data for Sweden and China are included.     

On the human survivorship function and life table construction

The construction of life tables is often marred by one or more of the following restrictions: (1) assumptions that are either unjustifiable or of questionable generality; (2) rough approximations; (3) exacting data requirements. This paper recommends instead a simple method which regards the force of mortality as constant within each age interval. The reasoning is readily comprehensible and all life table functions are easily calculated from the age-specific death rates without any need for further assumptions, approximations, or data. Furthermore, this method produces numerical results that are close to those obtained by other methods.     

Effects of dependency among causes of death for cause elimination life table strategies

A study is made of the effects of associated causes of death, and of dependency among causes of death, by observing the relative importance of one cause of death when another is eliminated under various competing risk models. Two disease pairs, cancer and infectious disease and stroke and ischemic heart disease, are selected for analysis because they represent different types of disease dependence. Crude probabilities of death for each disease are calculated for the U.S. white male population in 1969. Next, the effects of the complementary disease in a pair are hypothetically eliminated in one of three ways: (a) a standard competing risk adjustment for cause elimination when deaths are singly caused (Chiang, 1968), (b) lethal defect-pattern of failure computations for multiply caused death when no causal order is inferred (Manton et al., 1976), and (c) relative susceptibility, computations for multiply caused deaths when causes are ordered (Wong, 1977). The paper closes with a discussion of the relative merits of the three types of adjustments.     

Family and fertility careers of Polish females: a semi-parametric and life table approach

"In this paper an evaluation has been made using the semi-parametric analysis and life table method of changes in the process of formation and dissolution of families in Poland, and changes in fertility careers by cohorts. An answer was sought to the following questions: What are the factors significantly determining the process studied? What differences appear between cohorts?"     

On the efficiency of the estimates of life table functions

Expected values and variances of several life table functions have been obtained by converting the sample estimates of age-specific mortality rates to probabilities of dying by Reed-Merrell’s approximation. The expressions also permit the development of a procedure that will enable the researcher, constrained usually by his limited resources, to maximize the efficiency of his sampling technique. Needless to say, these results will be particularly useful for countries where national vital statistics are not adequate for construction of life tables, and also for countries where such tables are usually obtained by comparing age distributions of successive censuses.     

Application of life table techniques to measurement of contraceptive effectiveness

Two problems are associated with the analysis of use-effectiveness of contraception. First, couples belonging to a sample of contraceptors typically vary in their monthly chances of contraceptive failure. Second, one does not observe for many, and perhaps a majority of the couples, how long they can remain protected with the contraceptive, because either they are stopping contraception to plan a pregnancy or else observation of them is being interrrupted by lost contact, by discontinuation of contraception for other reasons, or by the end of the study. It is argued that because of these two problems-namely, sample heterogeneity and incomplete histories-the Pearl pregnancy rate, which has been traditionally used to measure contraceptive effectiveness, is inadequate.A life table method is described that permits one to combine incomplete histories with complete ones for purposes of estimating the proportions of the sample that might have remained protected for specified periods if all members had remained under observation for these periods. The versatility of the techniques is illustrated in relation toa retrospective survey. A detailed account of procedure is given. Finally, it is shown that only under specialized conditions that are rarely met in practice is it possible to estimate the results of the new technique from knowledge of Pearl pregnancy rates alone.     

Analysis of oral contraceptive use through multiple decrement life table techniques

Multiple decrement life table technique is used to analyze the oral contraceptive use in a sample of once married women in Metropolitan Toronto. The overall pattern in the Canadian data is found to be essentially similar to that found in the U. S. Continuation rates show differences by cause of decrement. Two types of rates, net and absolute, are presented, and the relationship between single decrement continuation rates and total continuation rates is examined. Some problems of clinical versus retrospective sample survey data in studies of contraceptive effectiveness are commented on.