We consider a logistic regression model with clustered binary responses and a set of covariates which includes variable having a pre-assumed, fixed coefficient. We argue that the model is appropriate for instance when assessing excess mortality in multiple temporal clusters of disease occurrences. An example is given in which the method is applied retrospectively to analyzing temporal pattern of cancer mortality in a cohort of now retired workers from the chemical plant in Louisville, KY. The results are compared with that obtained from standard mortality analysis.