Estimation of a Common Effect Parameter from Follow-Up Data When There Is No Mechanistic Interaction

In a stratified analysis, the results from different strata if homogeneity assumption is met are pooled together to obtain a single summary estimate for the common effect parameter. However, the effect can appear homogeneous across strata using one measure but heterogeneous using another. Consequently, two researchers analyzing the same data can arrive at conflicting conclusions if they use different effect measures. In this paper, the author draws on the sufficient component cause model to develop a stratified-analysis method regarding a particular effect measure, the ‘peril ratio’. When there is no mechanistic interaction between the exposure under study and the stratifying variable (i.e., when they do not work together to complete any sufficient cause), the peril ratio is constant across strata. The author presents formulas for the estimation of such a common peril ratio. Three real data are re-analyzed for illustration. When the data is consistent with peril-ratio homogeneity in a stratified analysis, researchers can use the formulas in this paper to pool the strata.