Asymptotic Interval Estimation of Some Cause‐Specific Mortality Risk Measures in Epidemiologic Studies

Abstract

AbstractThe present paper describes the algebraic and statistical relationships between the population‐based mortality risk measures, the Standardized Mortality Ratio (SMR) and the Standardized Risk Ratio (SRR), and their respective proportional mortality‐based counterparts, the internally and externally Standardized Proportional Mortality Ratios (SPMR, SePMR). The paper shows, how under some reasonable assumptions, asymptotically precise inferences about population‐based risk measures can be made from studies of proportional mortality. Through application of the asymptotic multivariate normal approximation to the multinomial distribution, shortest confidence intervals for the relative SMR (RSMR) involving the corresponding SPMR are constructed for any cause of death. This same technique is also used to construct asymptotic prediction intervals about the cause‐specific SePMR which, with high probability, contains the corresponding relative SRR (RSRR).The utility of the proportional mortality measures SPMR and SePMR as estimators of the corresponding cause‐specific risks RSMR and RSRR in occupational epidemiologic research is empirically evaluated using data from two recent occupational cohort studies.Asymptotic Bonferroni type simultaneous inferential techniques are also developed for these measures which facilitate the assessment of overall risk in the presence of several competing factors.