Relation of pooled logistic regression to time dependent Cox regression analysis: the Framingham Heart Study

A standard analysis of the Framingham Heart Study data is a generalized person-years approach in which risk factors or covariates are measured every two years with a follow-up between these measurement times to observe the occurrence of events such as cardiovascular disease. Observations over multiple intervals are pooled into a single sample and a logistic regression is employed to relate the risk factors to the occurrence of the event. We show that this pooled logistic regression is close to the time dependent covariate Cox regression analysis. Numerical examples covering a variety of sample sizes and proportions of events display the closeness of this relationship in situations typical of the Framingham Study. A proof of the relationship and the necessary conditions are given in the Appendix.