Relation of pooled logistic regression to time dependent cox regression analysis: The framingham heart study

TLDR

The Framingham Heart Study typically uses a generalized person‑years approach, measuring risk factors biennially and following participants to detect cardiovascular events. The authors pool interval observations into one sample and fit a logistic regression linking risk factors to events, with a formal proof of the relationship provided in the appendix. The pooled logistic regression closely approximates time‑dependent Cox regression, as demonstrated by numerical examples across typical Framingham sample sizes and event rates.

Abstract

Abstract 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.