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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

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

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 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

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

Life-table analysis of IUDs: problems and recommendations.

Two major prospective studies of copper-bearing IUDs showed substantial changes in termination rates when calculated at different dates. One of the studies employed the Tietze life-table method and showed progressive increases in termination rates with the passage of time. The other study used the Potter life-table method and showed sharply decreased termination rates at later assessments. In investigating the reasons for these changes, it was noted that the data collected for periodic analyses during the studies violated the assumptions underlying the life-table technique. It was discovered that as a result of these violations the Potter and the Tietze life-table calculations based on the same set of data produced markedly different estimates of IUD termination rates during the course of a study. Underlying these differences, and the reason for the apparent changes in termination rates, was a large set of incomplete observations. Neither of the two life-table methods was able to deal adequately with the biases arising from these incomplete observations. The "anniversary method," devised to overcome the perceived problems of the Potter and Tietze methods, also proved inadequate to deal with the incomplete observations. Only vigorous and active follow-up, together with ample time to complete data collection, editing, coding, and key punching, is likely to reduce the proportion of women with incomplete observations and is likely to minimize the biases attendant upon incomplete or partial observations of acceptors in prospective clinical studies of IUDs.

Evaluation Studies as Topic

The life table. A method for analyzing longitudinal studies.

The life table is presented as the method of choice for analyzing data from longitudinal studies in which the outcome under study occurs randomly and in which patients are followed up varying lengths of time. We discuss the superiority of the life table to methods typically used, the calculation of its entries, and some of the clinical uses that can be made of its results. The method is applied to follow-up data on manic-depressive patients maintained with prophylactic lithium carbonate or with control regimens, and it is shown to disclose mathematical regularities in the parameters of longitudinal course.

Adult

A computer program for life table regression analysis with time dependent covariates.

This paper presents a computer program for analyzing time-dependent covariables in survival studies by the life table regression model described by Holford [3]. Basically, life table regression incorporates the elements of regression and the life table into a single model. Regression parameters are estimated by the method of maximum likelihood using the Newton-Raphson iterative procedure. The program provides two methods for testing hypotheses concerning regression coefficients, namely the standard normal deviate test and a Wald statistic based on the first and second derivatives of the log likelihood. Residual plots are provided to assess the fit of the model to the data.

Actuarial Analysis

A fetal-infant life table based on single births in Norway, 1967--1973.

The study is based on 440,452 single births occurring in Norway, 1967--1973, with known gestational age. The information was collected through a notification system known as "Medical Registration of Births," covering all births occurring in Norway, and the data are made available through the Medical Birth Registry of Norway, which allows for linkage between births and infant deaths. The life table describes the experience of women still pregnant at a gestational age of 16 completed weeks, and states for each subsequent week the number of pregnancy terminations, the outcome, and the number of women still pregnant. Seven outcomes of pregnancy are considered: fetal death prior to labor, fetal death during labor, death within 24 hours, death 1--6 days, death 7--27 days, death 28 days--1 year, and survival of one year or more. The data in the life table provide information on the probability of pregnancy termination in each week of gestation (after 16 completed weeks), and the probabilities of the various outcomes. The fetal-infant life table is considered as an extension of descriptive perinatal statistics and is of value in monitoring health changes and in comparing perinatal mortality between populations. It also provides information on time of pregnancy termination and outcome, which has some clinical applications.

Adult

A modified actuarial life-table approach to the analysis of implantable device performance.

The actuarial life-table method is often used by pacemaker manufacturers and the pacing research community to describe pacemaker and lead performance. Most life-table methods allow for differing lengths of follow-up but assume that all devices were followed from implant. Occasionally, however, devices come under follow-up observation sometime after implant. This presentation describes an extension of the actuarial method to accommodate these kinds of data. The specific example to be considered involves follow-up data collected by CardioCare, a commercial cardiac monitoring service, on the performance of Medtronic polyurethane leads. Patients subscribe to this service, generally at some time after actual device implant. Results showed that of 12,112 patients with Models 4002, 6971, and 6972 leads who were followed by CardioCare, only 85 were followed from implant. If one were to exclude patients not followed since implant, more than 99% of the data would be lost. Using the modified approach with allowance for postimplant, entry resulted in an estimated three-year cumulative survival probability for these leads of 95.7%. Treating all patients as if they were followed since implant, the probability would be 96.9%, an optimistic and biased estimate.

Actuarial Analysis

Robustness of life table methods in large populations--a study by computer simulation.

The robustness of the product life table estimator of the survival function was studied for large populations under perturbations in the age distribution, changing levels of mortality and changing patterns of fertility. A macrosimulation system, based on a class of stochastic population models called generalised age-dependent branching processes, was used to carry out the numerical investigations. Aside from drastic perturbations in the age distribution and changes in levels of mortality, the product life table estimator of the survival function was found to be robust in large populations, under a variety of conditions.

Age Factors

Use of the life table method in determining attrition from treatment.

Life table analysis of attendance at an outpatient clinic indicates levels of attrition similar to those reported by follow-up and other studies of treatment for drug dependence. With appropriate qualifications, rates of attrition may be viewed as measures of treatment outcome.

Actuarial Analysis

New developments in the Life Table Analysis System of the National Institute for Occupational Safety and Health.

In the 1970s, the National Institute for Occupational Safety and Health developed a Life Table Analysis System to analyze occupational cohort studies. We have updated the original system by adding two new features: direct standardization with a test for linear trend, and analyses by lagged exposure (either duration of exposure or cumulative exposure). We have also updated US reference rates through 1989. The updated systems and documentation (version F) are available upon request. In collaboration with the National Cancer Institute, we have also developed multiple cause-of-death rate files, which consider contributory as well as underlying cause. These files (also available upon request) will enable investigators to derive the expected prevalence of diseases at death, which can then be compared with the observed prevalence in an exposed cohort. Work is currently underway to produce a personal computer version of the Life Table Analysis System.

Cause of Death