Computation of Expected Deaths for Prediction and for Long-Term Follow-up Studies

Summary

In this paper we discuss an uncomplicated procedure for computing the expected number of deaths in a heterogeneous study sample without requiring any information about the number or distribution of observed deaths. This procedure can thus be used to compare grouped mortality data to a large reference population and also to make predictions about the number of deaths to be expected in the not too distant future based on current population rates. The estimation procedure is introduced in a simple context and later extended to allow for multiple hazard rates, for right censoring, and for competing causes of death.

In dieser Arbeit wird ein unkomplizierter Verfahren zur Errechnung der erwarteten Anzahl von Todesfällen in einer heterogenen Studienstichprobe erörtert, ohne daß hierbei Informationen über die Anzahl oder Verteilung der beobachteten Todesfälle erforderlich wären. Dieses Verfahren kann angewandt werden, um Gruppen von Mortalitätsdaten mit einer großen Bezugsgruppe zu vergleichen und auch um Vorhersagen über die Anzahl zu erwartender Todesfälle in der nicht zu fernen Zukunft auf der Grundlage gegenwärtiger Bevölkerungsraten anzustellen. Das Schätzverfahren wird in einem einfachen Zusammenhang vorgestellt und später erweitert, um multiple Zukunftsraten, richtige Zensierung und konkurrierende Todesursachen einzuschließen.

Key-Words

Mortality Analysis - Expected Deaths - Prediction - One-Sample Problem - Censored Data - Competing Risks

Schlüssel-Wörter

Mortalitätsanalyse - erwartete Todesfälle - Vorhersage - Ein-Stichproben-Problem - zensierte Daten - konkurrierende Risiken

^* Reprint requests to Dr. Simpson

• REFERENCES

• 1 Berry G. The Analysis of Mortality by the Subject-Years Method. Biometrics 1983; 39: 173-1S4.
• 2 Breslow N. E. Analysis of Survival Data under the Proportional Hazards Model. Int. stat. Rev 1975; 43: 45-58.
• 3 Breslow N. E. Some Statistical Models Useful in the Study of Occupational Mortality. In Whittemore A. S. (Edit.) Environmental Health, Quantitative Methods. Philadelphia: Society for Industrial and Applied Mathematics; 1977: 88-103.
• 4 Decoufle P. Cancer Mortality among Workers Exposed to Cutting Oil Mist. Ann. N. Y. Acad. Sci 1976; 271: 94-101.
• 5 Gail M. H, Ware J. H. Comparing Observed Life Table Data with a Known Survival Curve in the Presence of Random Censorship. Biometrics. 1979; 35: 385-391.
• 6 Gross A. J, Clark V. A. Survival Distributions: Reliability Applications in the Biomedical Sciences. New York: John Wiley; 1975
• 7 Kahn H. A. An Introduction to Epidemiologic Methods. New York: Oxford University Press; 1983
• 8 Oleinick A, Mantel N. Family Studies in Systemic Lupus Erythematosus II. Mortality among Siblings and Offspring of Index Cases with a Statistical Appendix Concerning Life Table Analysis. J. chron. Dis 1970; 22: 617-625.
• 9 Woolson R. E. Rank Tests and a One-Sample Logrank Test for Comparing Observed Survival Data to a Standard Population. Biometrics 1981; 37: 687-696.
• 10 Woolson R. F, Tsuang M. T, Fleming J. A. A Method for Analyzing Mortality Data Collected in Follow-up Studies. Meth. Inf. Med 1978; 17: 116-120.
• 11 Woolson R. F, Tsuang M. T, Fleming J. A. Utility of the Proportional-Hazards Model for Survival Analysis of Psychiatric Data. J. chron. Dis 1980; 33: 183-195.