How to set ttk::radiobutton -variable to an object's instance variable?

Given this class:

oo::class create App {
    # ...
    variable ShowState
}

And this method:

oo::define App method make_controls {} {
    # ...
    ttk::radiobutton .controlsFrame.showFrame.asIsRadio \
        -text "Show as-is" -value asis -variable ShowState
    set ShowState asis

The variable given to the radio button and the instance variable
are _different_.

I tried these variations, all of which gave errors:

-variable [my ShowState]
-variable [my $ShowState]
-variable [self ShowState]
-variable [self $ShowState]

For now I'm using a global variable ::ShowState
but I'd really like it to be an instance variable -
if it can be done?