A reducible four-parameter system of model life tables

Abstract In this paper a four-parameter extension of Brass's relational system of model life tables is suggested that (1) matches a wide range of empirical age patterns of mortality, (2) is easy to apply, especially to partial life tables, and (3) contains demographically meaningful parameters. A test of the model on a set of 62 empirical life tables indicates that four parameters are necessary and sufficient for fitting a wide range of mortality patterns. A further test on an historical series of Swedish life tables reveals a consistent pattern of mortality change. Examination of the parameters for a set of geographicallyrelated life tables suggests a way to define families of life tables. Identification of such temporal and spatial relationships allows the model to be reduced to a form with twoor three-parameters for application to incomplete or inaccurate data.     

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)     

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.     

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 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.     

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.     

The multistate life table method: An application to contraceptive switching behavior

In many demographic behaviors (e.g., those relating to marriage, contraception, migration, and health), people change among multiple statuses through time, sometimes leaving and then returning to the same status. Data on such behaviors are often collected in surveys as censored event histories. The multistate life table (MSLT) can be used to properly describe, in a single analysis, these complex transitions among multiple states measured in such data, but MSLT is rarely applied in the demographic literature because practical guidance is lacking on how to compute MSLTs with such data. We provide methods for computing MSLT quantities using censored event-history data: namely, transition intensities and probabilities, "state occupancy" probabilities and standard errors, average time spent in specified states, and average number of visits to specified states. Applying these methods to contraceptive use, we find high levels of switching back and forth, particularly between barrier methods and non-use, resulting in high rates of unintended pregnancy.     

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.     

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 life table for a West Indian slave population

This note comments briefly on the system of slave registration set up in the British colonies, and deals in particular with the data tabulated for the British Guiana slave population in the Parliamentary Papers, 1833. From the age distributions given there a life table has been constructed by a census differencing method. This life table shows the extremely high mortality then being experienced by slave populations in the West Indies.     

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)     

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.     

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.     

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.     

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 behaviour towards malaria care—a multinomial logit approach

This paper attempts to estimate a disease specific demand function to study the determinants of utilisation of the services of a health care provider or a treatment regiment for malaria. The study adapts a multinomial logit framework to look at both facility characteristics and individual patient features on demand for malaria care in Ghana. The individual patient characteristics form a set of social indicators which can be used to discriminate or put into groups patients with respect to their choice of provider.The study confirms the popular use of self-medication as a first choice of action in treating malaria. The choice of malaria care providers is found to be influenced by facility price, travel time, waiting time for treatment, education, age, sex and quality of care measured in terms of drugs availability. We further find that as income increases, the odds are in favour of self-medication when people get malaria.     

The effects of children on divorce and re-marriage: a multivariate analysis of life table probabilities

Summary Using proportional hazards models and multiple decrement life tables to analyse data from the 1973 National Survey of Family Growth, this study tests the hypotheses that, net of the effects of such factors as age at separation or divorce, the probabilities of divorce after separation and of re-marriage after divorce would be lower for women with larger numbers of children or younger children, and that these transitions would take longer than for women with fewer or older children or women who were childless; and that there would be an interaction between number of children and age of youngest child. Results included: (1) the probability that mothers of two or more children would divorce after separation was significantly lower than for childless women, or those with only one child; (2) among whites, mothers of three or more children were at a significant disadvantage regarding their chances of re-marriage, whereas the probability that a black mother of three or more children would re-marry was no smaller than that of a woman with fewer or no children; (3) among whites, the presence of a youngest child aged between two and five years at separation decreased the probability of divorce after separation; (4) there was no interaction effect between number and age of children; and (5) in each category of family size and age of youngest child, the probability that a black woman would divorce after separation or re-marry after divorce was lower than for white women. The results have important implications for the study of divorce and re-marriage, and for understanding of problems of single-parent families.     

The consequences of unobserved heterogeneity in a sequential logit model

Cameron and Heckman (1998) established that a sequential logit model is more sensitive than many other models to the possible biasing influence of unobserved heterogeneity. This article proposes a method which allows researchers to find out how large this potential problem is for their data, their model, and their hypothesis of interest. This is done by proposing a set of scenarios for this unobserved heterogeneity, and showing how to estimate the effects of interest given these scenarios. The set of results from these scenarios give an indication of how sensitive the results are to assumptions regarding unobserved heterogeneity. This sensitivity analysis has been applied to a study of educational attainment in the Netherlands, and it showed that that the finding that the effect of father's education declined over transitions is quite sensitive to the assumptions made about unobserved heterogeneity, but that the finding that the effect of father's education declined over birth cohorts is more robust than is often feared.