Evaluation of Ten Events Per Covariate Recommendation for Cox Proportional Hazards Regression Models
by
Mehmet Kocak
St. Jude Children's Research Hospital
Coauthors: Mehmet Kocak, Arzu Onar, Seok P. Wong

Cox proportional hazards (PH) models are commonly utilized in medical research to investigate the associations between covariates and survival-type outcomes. Several authors have recommended that for less than ten events per covariate, these models produce spurious results, and therefore, not recommended. In the context of Phase-I and Phase-II clinical trials, as well as many of retrospective studies, the number of events is generally too small to allow a multivariable Cox PH model based on this recommendation. Our investigations aimed at confirming or challenging the ‘minimum of ten events per covariate’ recommendation for Cox PH models in the case of a single covariate. We conducted an extensive simulation study with various scenarios, where number of events and sample size were varied for a continuous and a dichotomous covariate. Empirical powers from those scenarios were then compared with Schoenfeld’s (6) and Hsieh’s (7) formulae. Our simulations indicated that in univariable models ten events may not be adequate to capture the desired effect. Furthermore we illustrate that the number of events suggested by Schoenfeld’s (6) and Hsieh’s (7) formulae are often too small in these small-sample cases. Imbalance of the number of events at each level of a dichotomous covariate was also fount to affect the empirical power substantially.

Date received: February 22, 2008