Seems these are related but separate questions. Here are some answers:
- JMP's Cox Proportional Hazard platform does not offer competing risk analysis at the moment.
- Parametric Survival conducts parametric modeling, it is different from the Cox model above. The platform does not produce hazard ratio . You may be able to calculate ratio of two hazard rates from two groups, under comparable conditions, after fitting a model. After fitting a model, you can calculate hazard at any given time. And by definition of hazard ratio, you can calculate a ratio.
- JMP offers a Cumulative Incidence Curves in Competing Cause platform. And it is named as "Subdistributions", which is name in the reliability data analysis context. Take a look at the JMP sample data table "Appliance.jmp". Run the embedded script "Life Distribution", and look for the menu item "Show Subdistributions".
I, however, don't think this is what you are looking for, because you mention Cox model, so you have covariates in your data. For the "Subdistributions" feature, the platform does not support covariates.
If you would like to submit a request, please contact Tech Support at support@jmp.com and we would like to collect necessary information.