There are several ways to do this.
1. Using the Value Display Order column property
Highlight (select) the response column in the data table, then select Columns > Column Info > Value Order from the menu. You can use the Move Up and Move Down buttons to change the order.
2. Using the "Event Level" pull-down list in the launch dialog
The launch dialogs for Bivariate Relationships and Fit Model have a pull-down list for selecting the "level that indicates an event." When you run an analysis, you can perform the same operation by changing the level that is to be the event.
3. Using the Event Level column property
There is also an Event Level column property, which is used when logistic regression is performed on a binary categorical response in Bivariate Relationships or Fit Model. Highlight (select) the response column in the data table, then select Columns -> Column Info -> Event Level from the menu.
To check the settings, please check the output "Estimates are for the log odds of:" displayed in the logistic regression fit report. If it says 0/1, it means that the estimated value is the logarithmic transformation of the odds ratio of level 0 to level 1.
In addition, FAQ #2078 contains related material (methods of calculating odds ratios and hazard ratios (risk ratios) using JMP and points to note).
FAQ # 2086