We must note here that HRs and ORs are different measures of association and have different interpretations. Cox models incorporate the length of time the individuals are followed up and measure whether the risk factor affects the time at which the disease event occurs. Logistic regression assesses whether the risk factor affects the odds of disease, and hence does not take into account the time of disease occurrence. So early and late failures are given the same weight in the analysis. In addition, individuals who are not observed to have the event during the period of follow-up time are treated as controls. This is different from the time-to-event analysis approaches where these individuals are considered to be censored. That is, we assume that all the individuals will have the event at some point but we just do not observe this event over the follow-up period for some individuals. Since these models have different definitions and estimate different parameters, naturally the results from these models will differ, as observed in our work.
