Life tables

The operating schedule of a gas turbine produces a low-frequency thermal fatigue. The number of starts per hours of operating time directly affects the blade life. Table 11-1 shows fewer starts per operating time increases turbine life. 

In the combustor, the only two parameters that can be measured are fuel pressure and evenness of combustion noise. Turbine inlet temperatures are not usually measured due to very high temperatures and limited probe life. Table 19-6 shows the effect of various parameters on important functions of the combustor. 

Failure is one of the ways in which engineered devices attain the end of their useful life. Table 62.1 shows some of the possible ways. 

Bechmann, R.K. 1994. Use of life tables and LC50 tests to evaluate chronic and acute toxicity effects of copper on the marine copepod Tisbe furcata (Baird). Environ. Toxicol. Chem. 13 1509-1517. 

Day, K. and N.K. Kaushik. 1987a. An assessment of the chronic toxicity of the synthetic pyrethroid, fenvalerate, to Daphnia galeata mendotae, using life tables. Environ. Pollut. 44 13-26. 

Direct costs include both medical and nonmedical expenditures for the detection, treatment, and prevention of disease. Direct medical costs reflect resources consumed in the "production" of health care, such as pharmaceutical products and services, physician visits, and hospital care. Direct nonmedical costs reflect expenditures for products and services that are not directly related to disease treatment but are still related to patient care. Examples of direct nonmedical costs include transportation to a pharmacy or physician s office and housekeeping during the illness period. Indirect costs account for changes in productivity of an individual because of illness. The monetary value of lost or altered productivity is typically used as a measure of indirect costs. Intangible costs and consequences are nonmonetary in nature and reflect the impact of disease and its treatment on the individual s social and emotional functioning and quality of life. Table 12.2 provides examples of these types of costs and consequences. 

These methods are essential when there is any significant degree of mortality in a bioassay. They seek to adjust for the differences in periods of risk individual animals undergo. Life table techniques can be used for those data where there are observable or palpable tumors. Specifically, one should use Kaplan-Meier product limit estimates from censored data graphically, Cox-Tarone binary regression (log-rank test), and Gehan-Breslow modification of Kruskal-Wallis tests (Thomas et al., 1977 Portier and Bailer, 1989) on censored data. 

TABLE 9.5. Interpretation of the Analysis of Tumor Incidence and Survival Analysis (Life Table)... 

Tarone, R.E. (1975). Tests for trend in life table analysis, Biometrika 62 679-682. 

Thomas, D.G., Breslow, N. and Gart, J.J. (1977). Trend and homogeneity analyses of proportions and life table data. Comput. Biomed. Res. 10 373-381. 

The idea behind the Log-Rank Test for comparison of two life tables is simple if there were no difference between the groups, the total deaths occurring at any time should split between the two groups at that time. So if the numbers at risk in the first and second groups in (say) the sixth month were 70 and 30, respectively, and 10 deaths occurred in that month we would expect... 

The Log-Rank Test as presented by Peto et al. (1977) uses the product-limit life-table calculations rather than the actuarial estimators shown above. The distinction is unlikely to be of practical importance unless the grouping intervals are very coarse. 

Life tables can be constructed to provide estimates of the event time distributions. Estimates commonly used are known as the Kaplan-Meier estimates. 

The final pair of methods for reduction of dimensionality which will be tackled in this chapter are Fourier analysis and the life table analysis. Fourier analysis seeks to identify cyclic patterns in data and then either analyze the patterns or the residuals after the patterns are taken out. Life table analysis techniques are directed to identifying and quantitating the time course of risks (such as death, or the occurrence of tumors). 

Chronic in vivo toxicity studies are generally the most complex and expensive studies conducted by a toxicologist. Answers to a number of questions are sought in such a study, notably if a material results in a significant increase in mortality or in the incidence of tumors in those animals exposed to it. But we are also interested in the time course of these adverse effects (or risks). The classic approach to assessing these age-specific hazard rates is by the use of life tables (also called survivorship tables). 

Cutler, S.J. and Ederer, F. (1958). Maximum utilization of the life table method in analyzing survival. J. Chron. Dis. 8 699-712. 

Crude percentage calculations. Subset analysis. cEstimated from curves. Endpoint was 5-year life table survival but deaths from complications (2 in control arm and 4 in hydroxyurea arm) did not appear to have been included as events in survival calculations. Favoring the cisplatin-containing arm. 

To compute this value requires survivor functions for relevant time periods as well as values for v(f). The survivor functions were computed from male and female life tables available for 1982 and 1997 from Statistics Canada. Economic values for additional life years were computed based on Murphy and Topel (2005) and converted to Canadian dollars using the average per capita ratios of Canadian to U.S. income for 1994-2003. These income-adjusted life year values were then multiplied by 1.267 the purchasing power parity (PPP) rate between Canada and the United States in 2004, expressed in 2004 dollars. 

Although life expectancy is the best available general measure of health outcomes, no life tables exist by disease. We constructed an alternative measure of disease-specific life expectancy by computing the proportion of deaths that occurred above certain ages, such as 65, using data on deaths by disease category from a time series of mortality data obtained from the Department of Health in Taiwan. ... 

Statistics Canada. 2002. Life Tables, Canada, Provinces and Territories, 1995-1997. Ottawa Minister of Industry. 

Cox DR (1972) Regression models and life tables (with discussion) Journal of the Royal Statistical Society, B, 74, 187-220... 

Gehan FA (1969) Estimating survival functions from the life table Journal of Chronic Diseases, 21, 629-644... 

Keller MB, Hanks DL Course and outcome in panic disorder and depression. J Clin Psychopharmacol Biol Psychiatry 17 551-570, 1993 Keller MB, Shapiro RW Double depression superimposition of acute depressive episodes on chronic depressive disorders. Am J Psychiatry 139 438-442, 1982 Keller MB, Shapiro RW, Lavori PW, et al Recovery in major depressive disorder analysis with the life table and regression models. Arch Gen Psychiatry 39 905-910, 1982a... 

---