A comparison of the polytomous logistic regression and joint cox proportional hazards models for evaluating multiple...

Polytomous logistic regression models are commonly used in case-control studies of cancer to directly compare the risks associated with an exposure variable across multiple cancer subtypes. However, the validity, accuracy, and efficiency of this approach for prospective cohort studies have not been formally evaluated.

We investigated the performance of the polytomous logistic regression model and compared it with an alternative approach based on a joint Cox proportional hazards model using simulation studies. We then applied both methods to a prospective cohort study to assess whether the association of breast cancer with body size differs according to estrogen and progesterone receptor-defined subtypes.

Our simulations showed that the polytomous logistic regression model but not the joint Cox regression model yielded biased results in comparing exposure and disease subtype associations when the baseline hazards for different disease subtypes are nonproportional. For this reason, an analysis of a real data set was based on the joint Cox proportional hazards model and showed that body size has a significantly greater association with estrogen- and progesterone-positive breast cancer than with other subtypes.

Because of the limitations of the polytomous logistic regression model for the comparison of exposure-disease associations across disease subtypes, the joint Cox proportional hazards model is recommended over the polytomous logistic regression model in prospective cohort studies.

The article will promote the use of the joint Cox model in a prospective cohort study. Examples of SAS and S-plus programming codes are provided to facilitate use by nonstatisticians.