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Approximate Methodologies for Proportional Mortality Analyses in Epidemiologic Studies Involving Competing Risks of Death Regardless of their Covariance Structure
Author(s) -
Rao B. Raja,
Marsh Gary M.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290503
Subject(s) - statistics , confidence interval , covariate , population , mathematics , econometrics , medicine , environmental health
The present paper discusses methodologies for proportional mortality analyses in epidemiologic studies in which an individual is exposed simultaneously to several (say M ) risks of death which compete for his life. A general situation is considered where nothing is known about the dependence or covariance structure among the risks. The available data consist only of the number of deaths in each stratum of the test population, but not the number of individuals at risk. A general class of approximate simultaneous confidence and prediction intervals are developed which provide overall risk assessment of the competing risk factors in many biomedical and epidemiologic studies. Our paper describes how, under reasonable assumptions, asymptotically precise inferences may be based on proportional mortality analyses in order to estimate the indirectly and the externally standardized cause‐specific risk measures RSMR i and RSRR i respectively. The tuberculosis mortality data of Kupper, et al., (1978) and the respiratory cancer mortality data of Enterline and Marsh (1983) are utilized to illustrate the usefulness of our results. Methodologies are presented to construct simultaneous confidence intervals for RSMR i involving SPMR i and simultaneous prediction intervals for RSRR i involving S e PMR i . Both Scheffé‐and Sidak‐Types of simultaneous intervals are constructed for M competing risks of death. As a particular case if M = 1, i.e., if the risks of death may be assumed to be independent, as is usually done in proportional mortality analyses, the Scheffé and Sidak confidence intervals become identical and are narrower than of Kupper et al., (1978). In this sense, our paper generalizes the methodologies of proportional mortality analyses in two directions, first to discuss the situation involving competing risks, and second to obtain narrower confidence intervals.