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Construction of expanded continuous life tables--a generalization of abridged and complete life tables.

This article extends the recent abridged life-table method of Hsieh. It generalizes the conventional discrete (abridged and complete) life tables into a continuous life table that can produce life-table functions at any age and develops a unified method of life-table construction that simplifies the disparate laborious procedures used in the traditional approach of constructing abridged and complete life tables. A set of precise procedures based on the complete cubic spline for the main body of the table and a mortality law for advanced ages is developed for estimating the basic and nonbasic life-table functions from a given mortality schedule. The proposed method can also produce more life-table functions than other existing methods. The method is illustrated with Canadian data.

Humans

A computer program for multiple decrement life table analyses.

Life table analysis has traditionally been the tool of choice in analyzing distribution of "survival" times when a parametric form for the survival curve could not be reasonably assumed. Chiang, in two papers [1,2] formalized the theory of life table analyses in a Markov chain framework and derived maximum likelihood estimates of the relevant parameters for the analyses. He also discussed how the techniques could be generalized to consider competing risks and follow-up studies. Although various computer programs exist for doing different types of life table analysis [3] to date, there has not been a generally available, well documented computer program to carry out multiple decrement analyses, either by Chiang's or any other method. This paper describes such a program developed by Research Triangle Institute. A user's manual is available at printing costs which supplements the contents of this paper with a discussion of the formula used in the program listing.

Computers

Constructing increment-decrement life tables.

A life table model which can recognize increments (or entrants) as well as decrements has proven to be of considerable value in the analysis of marital status patterns, labor force participation patterns, and other areas of substantive interest. Nonetheless, relatively little work has been done on the methodology of increment-decrement (or combined) life tables. The present paper reviews the general, recursive solution of Schoen and Nelson (1974), develops explicit solutions for three cases of particular interest, and compares alternative approaches to the construction of increment-decrement tables.

Adult

Rehabilitation outcome following initial unilateral hemispheric stroke. Life table analysis approach.

Life table analysis is a powerful statistical tool that has become the preferred technique for studying both the natural history of and the effect of treatment on disease outcome. We have found only one report using life table analysis to study rehabilitation outcome after stroke. We assessed the recovery of both independent ambulation and overall self-care function in 95 consecutive patients with unilateral hemispheric stroke using life table analysis. Our results support the segregation of patients into the following prognostic subgroups at the time of entry into the rehabilitation program (mean +/- SD 5 +/- 3 weeks after stroke): 1) motor deficit only, 2) motor deficit plus somatic sensory deficit, and 3) motor deficit plus somatic sensory deficit plus homonymous visual deficit. The probabilities of reaching independence in ambulation, being able to walk 150 feet with assistance, reaching independence in self-care function, and reaching a point of assisted self care (Barthel Index score of greater than or equal to 60) are highly significantly different among subgroups. The interval after stroke required to reach the plateau phase of recovery is also significantly different among subgroups. We propose that life table analysis can be used 1) to define patient outcome goals, 2) to define the time required to reach such goals, 3) to identify patients with medical or behavioral comorbidity who are functioning below their expected level, and 4) to assess the effect of alternative treatment regimens on both final outcome and time to reach that outcome.

Actuarial Analysis

An improved life table method.

A life table estimates probabilities of surviving and of dying as well as death rates, as these would apply in a stationary population with the same underlying continuous mortality curve as the observed population. We have derived approximations to the probability of surviving that require no iteration, do not depend on graduation or interpolation, and appear to give as precise results as interpolated or iterated tables. On the side of theroy we show that methods due to T.N.E. Greville and to Reed and Merrell are special cases of our formula (3). The new approach is extended to cause-deleted tables and to multiple decrement.

Humans

Long-term treatment of rheumatoid arthritis with sulphasalazine, gold, or penicillamine: a comparison using life-table methods.

Life-table analysis was applied to the records of 317 patients with rheumatoid arthritis (RA) treated with sulphasalazine (SAS), 201 treated with sodium aurothiomalate (gold), and 163 with penicillamine. They comprised all those treated in our department with these drugs between January 1973 and July 1984. Risks of treatment termination for all reasons were similar for each drug at five years (gold 92%, penicillamine 83%, SAS 81%). The risk of treatment termination due to inefficacy was less for gold (29.5%) than for penicillamine (38.1%) or sulphasalazine (41.2%). Adverse effects, however, led to withdrawal of gold in 57%, penicillamine in 41.2%, and SAS in 37%; the most effective drugs appeared most toxic. Serious adverse effects were much more common in association with gold (17.4%) and penicillamine (12.3%) than with SAS (1.6%). Sulphasalazine appears as well tolerated over long periods in RA as gold or penicillamine and is associated with fewer serious adverse effects; of these drugs, it might therefore be considered the agent of first choice.

Actuarial Analysis

Analysis of underlying and multiple-cause mortality data: the life table methods.

The stochastic compartment model concepts are employed to analyse and construct complete and abbreviated total mortality life tables, multiple-decrement life tables for a disease, under the underlying and pattern-of-failure definitions of mortality risk, cause-elimination life tables, cause-elimination effects on saved population through the gain in life expectancy as a consequence of eliminating the mortality risk, cause-delay life tables designed to translate the clinically observed increase in survival time as the population gain in life expectancy that would occur if a treatment protocol was made available to the general population and life tables for disease dependency in multiple-cause data.

Actuarial Analysis

Life tables for clinical scientists.

The life-table, or Cutler-Ederer, method of survival analysis is a simple and efficient means of estimating the probability that the first instance of an event will occur in a given period of time in studies complicated by incomplete patient follow-up. This discussion is designed to acquaint the nonstatistician with the general concepts, assumptions, advantages, and disadvantages of life-table analysis. The arcane nature of the calculations frustrates attempts at simplification. A glossary of statistical terms and sample calculations are provided for interested readers.

Humans

Life-table methods for contraceptive research.

Life-table methods used for the analysis and interpretation of contraceptive follow-up studies differ from those used in other areas of medical research. The historical development of these methods in the contraceptive literature is outlined and the two main methods are discussed, compared and shown to differ mainly in their nomenclature; their results are very similar in practice. The daily life-table method is simpler to apply and interpret, and facilitates analysis using the logrank statistic as well as powerful regression modelling techniques for survival data.

Actuarial Analysis

An antioxidant-induced life table modification and life-span prolongation in Zaprionus paravittiger (Diptera).

An antioxidant, sodium hypophosphite (SHP-1 X 10(3) microM), when added to the diet of Zaprionus paravittiger, induces various shifts in the age-related biochemical parameters. It maintains the viability of protein synthesis and normal energy-yielding processes through longer intervals besides decelerating the rate of loss of nucleic acids (Sharma and Wadhwa, 1986). Reduced body weight which indicates the low level of food restriction, and adaptive changes in amino acids and proteins, could be the important factors for the favourable effect of this antioxidant on life span.

Amino Acids

Life tables for Down syndrome.

Life expectancy in Down syndrome was calculated to 68 years, using data for 1610 Down syndrome liveborn individuals among over 1.5 million consecutive British Columbia livebirths. Overall, although survival is significantly poorer than for the general population, over half of Down syndrome individuals can be expected to survive into their fifties, and 13.5% will still be alive at age 68. The data are presented as a life table, a practical format for the clinician and planner.

Actuarial Analysis

Application of life table methodology in determining dental caries rates.

Probabilities of caries risk over time measured from eruption of first and second molars are illustrated using life table methodology. Life table rates based on 4,365 children in the National Preventive Dentistry Demonstration Program indicate that both fluoridation and sealants are effective in preventing caries on occlusal and buccal/lingual surfaces of molars. Effectiveness would probably have been greater on occlusal surfaces if sealants had been applied closer to the time of eruption. Similarities and differences between conventional DMFS indices and life table probabilities are discussed.

Actuarial Analysis

The parameters of death: a consideration of the quantity of information in a life table using a polynomial representation of the survivorship curve.

How much unique information is contained in any life table? The logarithmic survivorship (lx) columns of 360 empirical life tables were fitted by a weighted fifth degree polynomial, and it is shown that six parameters are adequate to reproduce these curves almost flawlessly. However, these parameters are highly intercorrelated, so that a two-dimensional representation would be adequate to express the similarities and differences among life tables. It is thus concluded that a life table contains but two unique pieces of information, these being the level of mortality in the population which it represents, and the relative shape of the underlying mortality curve.

Actuarial Analysis

Calculating life tables by estimating Chiang's a from observed rates.

A simple, accurate method of life table construction is advanced based upon a new way to estimate Chiang's nax (the average number of years lived in the x to x + n age interval by those dying in the interval). The estimate for nax leads immediately to an expression for lx+n (the survivors to age x + n) in terms of lx and the known mortality rates for the interval x to x+n and the two adjacent intervals. The complete solution for the basic life table is given. The proposed method and five other easily applied methods are then compared against the standard provided by the U.S. life tables for 1969-1971. The results attest to the excellent performance and high degree of accuracy of the proposed method. Finally, extensions of the method to multiple decrement and associated single decrement life tables are briefly described.

Humans

Extension of life-table methodology to allow for left-censoring in survival studies of pacing devices followed by commercial monitoring services.

The actuarial life-table is commonly used to describe lifetime data of living subjects and manufactured products. The life-table method allows subjects to come under observation at different times and, thus, to have differing lengths of follow-up, by assuming all subjects begin their lifetimes relative to the outcome of interest at some common point in time. As time progresses, subjects are withdrawn from the life-table when their period of observation has elapsed. This pattern of follow-up is often termed "right-censoring." An important feature of the classical life table approach is that the time at which the subject is placed at risk is known, and the status relative to the outcome of interest is known for the entire time at risk. Sometimes, however, subjects cannot be observed for some period after the beginning of their lifetimes. The example to be considered involves follow-up data collected by a commercial pacemaker monitoring service, to which patients subscribe, generally at some point following the actual implant of the pacemaker. Since the outcome of interest is device failure after implant, some means of dealing with the lack of information between implant and initiation of follow-up is needed. The extension of the actuarial life-table to accommodate this "left-censoring" will be described in this paper.

Actuarial Analysis

Actuarial contributions to life table analysis.

The correct principles for the construction of life tables and more particularly select life tables were developed by actuaries in England in the first half of the 19th century. Actuaries explored the phenomenon of selection not only between the insured and annuitants but also in the general population, distinguishing among initial temporary selection, antiselection, and class selection. The conclusion was reached early that no such thing as an unselected population exists. Group life insurance experience among the actively employed has been shown to provide a more appropriate standard of expected mortality than general population death rates in studies of medical impairments and occupational hazards at ages under 65 years. Mortality rates derived from the Cancer Prevention Study can serve as a useful standard of expected mortality when the objective is determination of excess mortality compared with ostensibly healthy persons at ages 65 years and older.

Actuarial Analysis

Mathematical hazard models of mortality: an alternative to model life tables.

A five-parameter competing hazard model of the age pattern of mortality is described, and methods of fitting it to survivorship, death rate, and age structure data are developed and presented. The methods are then applied to published life table and census data to construct life tables for a Late Woodland population, a Christian period Nubian population, and the Yanomama. The advantage of this approach over the use of model life tables is that the hazard model facilitates life-table construction without imposing a particular age pattern of mortality on the data. This development makes it possible to use anthropological data to extend the study of human variation in mortality patterns to small populations.

Adolescent