Cox Model with Non-proportional Hazards and Its Application to Organization Studies

The Cox proportional hazards model is extensively used to model censored survival data. However, relatively little attention has been paid to potential problems arising from the violation of its fundamental assumption; the proportionality assumption that the hazard rates for different values of covariates are proportional over time. When the proportionality assumption does not hold, however, the estimation of the Cox proportional hazards model would be biased. This paper introduces a way to deal with this problem, showing that a non-proportional hazards model can be obtained simply by including in the Cox model the terms for interaction between a function of time and covariates with non-proportional hazards. Then, the model is applied to both simulation data and real data on the adoption of a quality team strategy by business units within a big multinational bank. The analyses confirm that the inattention to non-proportionality of hazards could result in biased estimation and lead to incorrect theoretical interpretation, especially when unobserved heterogeneity is problematic. The paper suggests that proportionality should be carefully checked, and the model that allows hazard ratios to vary over time should be employed.