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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-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

Dental restoration longevity: a critique of the life table method of analysis.

The use of the life table method for assessing the longevity of dental restorations is growing. One reason for this is the availability of statistical computer packages which can be used by the non-expert, and this is tending to lead to an uncritical approach to the methodology. Although much can be learnt regarding the durability of restorations by using life table analysis, there are many inherent problems related to its use in dental studies. The survival pattern of many restorations is such that long-term studies are required to obtain valid assessments of durability. Results reported after only a few years of study contain many restorations not followed to failure. The ways in which data on these restorations are handled can greatly affect the estimates of longevity. These considerations have not, to date, received sufficient attention.

Actuarial Analysis

Life table method for analyzing relationship between smoking and hypertension.

The life table method is introduced for describing the relationship of smoking amount to prevalence rate of hypertension. The smoking level at different sex groups are collected and grouped according to their cumulative smoking amount. Using the total number of peasants, and the number of hypertensives in each group, one is able to calculate the probability of occurrence of hypertension for each dose group as well as for each cumulative dose group, which indicated that there was a dose-effect curve in estimating the relationship between the cumulative smoking and the probability of hypertension, and females presented a significantly higher probability of hypertension than males in same smoking level.

Adult

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

Life table methods applied to use of medical care and of prescription drugs in early childhood.

Life table methods were applied to analyses of longitudinal data on the use of medical care during the first 5 years of life among all 1701 children born in a Swedish semirural municipality. Cumulative proportions of the children who had used particular types of medical care or prescription drugs at least once by certain ages were estimated. By the fifth birthday, 98% had made at least one visit to any physician and 82% at least one visit to a paediatrician. By the fifth birthday at least one prescription for antibiotics had been purchased at a pharmacy by 82%; and 33% had been admitted to inpatient hospital care at least once (excluding immediate postnatal care). Acute conditions and more chronic diseases were also studied using these methods. At least one visit to a physician at a primary health care centre had been made for acute otitis media in 65% of 5 year olds and for atopic dermatitis in 8%.

Child Health Services

[Cumulative incidence rate of divorces for birth cohort estimated by the life-table method].

The trend of divorces has been usually evaluated by the divorce rate. However, it is difficult to make detailed analyses of the trend of or relevant factors concerning divorces by the divorce rate, because the denominator of this index is not a population at risk of divorces. The application of the life-table method to calculation of cumulative incidence rate of divorces for a birth cohort based on vital statistics data was introduced and its problems were discussed. This method was able to give a precise incidence rate of divorces and made it possible to examine the relationship of marital durations, generation of cohorts or age at marriage to the incidence of divorces. The results obtained were as follows: 1. The cumulative incidence rate of divorces increased and the marital duration-specific incidence rate of divorces decreased with continuation of marriages. 2. The cumulative incidence rate of divorces was higher in younger birth cohorts than in older cohorts. 3. The cumulative incidence rate of divorces was the lowest in the cohort married when the husband was 23 to 32 years of age than in the cohorts with other ages at marriage in all the birth cohorts examined.

Age Factors

Estimating the age-at-onset function using life-table methods.

In the analysis of dominantly inherited diseases, the age-at-onset function is often estimated from the observed age-at-onset distribution of cases. This estimate is confounded with the age distribution of the population from which the cases were sampled and is accurate only if there are no competing causes of death. In this paper, we present a straightforward method for calculating a more accurate age-at-onset function under etiologic heterogeneity. We use the life-table approach and survival analysis methods. This method is illustrated using data on first-degree relatives of probands from two sets of families with high cancer incidence: one with breast/ovarian cancer and the other with colon cancer. A comparison of the estimated age-at-onset function obtained by the two methods is presented. In both cases, colon cancer as well as breast/ovarian cancer, the estimates of onset probabilities based on proportion of cases, are consistently higher than those obtained by the life-table method. For breast/ovarian cancer, this difference is not as striking as it is in the case of colon cancer; nevertheless, the method using proportion of cases tends to give a lower estimate of the age-at-onset function (higher probability of being affected at lower age) than the life-table approach.

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

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-table methods for detecting age-risk factor interactions in long-term follow-up studies.

Methodological investigation has suggested that age-risk factor interactions should be more evident in age of experience life tables than in follow-up time tables due to the mixing of ages of experience over follow-up time in groups defined by age at initial examination. To illustrate the two approaches, age modification of the effect of total cholesterol on ischemic heart disease mortality in two long-term follow-up studies was investigated. Follow-up time life table analysis of 116 deaths over 20 years in one study was more consistent with a uniform relative risk due to cholesterol, while age of experience life table analysis was more consistent with a monotonic negative age interaction. In a second follow-up study (160 deaths over 24 years), there was no evidence of a monotonic negative age-cholesterol interaction by either method. It was concluded that age-specific life table analysis should be used when age-risk factor interactions are considered, but that both approaches yield almost identical results in absence of age interaction. The identification of the more appropriate life-table analysis should be ultimately guided by the nature of the age or time phenomena of scientific interest.

Actuarial Analysis

Comparison of risk estimates using life-table methods.

Risk estimates promulgated by various radiation protection authorities in recent years have become increasingly more complex. Early "integral" estimates in the form of health effects per 0.01 person-Gy (per person-rad) or per 10(4) person-Gy (per 10(6) person-rad) have tended to be replaced by "differential" estimates which are age- and sex-dependent and specify both minimum induction (latency) and duration of risk expression (plateau) periods. These latter types of risk estimate must be used in conjunction with a life table in order to reduce them to integral form. In this paper, the life table has been used to effect a comparison of the organ and tissue risk estimates derived in several recent reports. In addition, a brief review of life-table methodology is presented and some features of the models used in deriving differential coefficients are discussed. While the great number of permutations possible with dose-response models, detailed risk estimates and proposed projection models precludes any unique result, the reduced integral coefficients are required to conform to the linear, absolute-risk model recommended for use with the integral risk estimates reviewed.

Actuarial Analysis