Multiplicative Models and Cohort Analysis

TLDR

The paper discusses tradeoffs between efficiency and bias in choosing cohort analysis methods and practical application issues. The study presents three cohort analysis methods for a multiplicative statistical model of age‑by‑calendar‑year death rates. The authors describe (1) a multiple‑regression approach using known national baseline rates, (2) a Cox proportional‑hazards variant treating baseline rates as nuisance parameters, and (3) a case‑control sampling strategy from Cox risk sets. The methods differ in computational demand, with the case‑control approach being far less intensive, yet all three produce comparable relative‑risk estimates for arsenic exposure in smelter workers.

Abstract

Abstract Three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age × calendar year specific death rates. The first method, which assumes that the baseline rates are known from national vital statistics, is a multiple regression analysis of the standardized mortality ratio. The second method is a variant of Cox's proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters. The third method consists of case-control sampling from the risk sets formed in the course of applying Cox's model. It requires substantially less computation than do the other two. In illustrative analysis of respiratory cancer deaths among a cohort of smelter workers, all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure. The discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis, and on practical issues that arise in applications.