How to give reference to owned boxed struct to other owned struct

I have Engine which owns Worker and I want Engine to provide some API to Worker as a reference to trait. API implementation is allocated using Box and is owned by Engine, so reference to it is stable and valid as long as worker is alive.

But I don't understand how to express it in Rust.

I have read Why can't I store a value and a reference to that value in the same struct? and I understand why I can't pass reference to owned value. However, in my case, I pass reference not to owned value itself, but to boxed value, which won't be moved, so reference to it must be stable.

Here is non-working prototype:

trait EngineApi {
    fn foo(&self);
}

struct Worker<'a> {
    api: &'a EngineApi,
}
impl<'a> Worker<'a> {
    fn new(engine_api: &'a EngineApi) -> Self {
        Worker { api: engine_api }
    }
}

struct Api;
impl EngineApi for Api {
    fn foo(&self) {} 
}

struct Engine<'a> {
    api: Box<Api>,
    worker: Box<Worker<'a>>,
}

impl<'a> Engine<'a> {
    fn new() -> Self {
        let api = Box::new(Api);
        let worker = Box::new(Worker::new(api.as_ref()));
        Engine { api: api, worker: worker }
    }
}

fn main() {
    let engine = Engine::new();
}

Errors:

test.rs:27:37: 27:40 error: `api` does not live long enough
test.rs:27      let worker = Box::new(Worker::new(api.as_ref()));
                                                  ^~~
test.rs:25:19: 29:3 note: reference must be valid for the lifetime 'a as defined on the block at 25:18...
test.rs:25  fn new() -> Self {
test.rs:26      let api = Box::new(Api);
test.rs:27      let worker = Box::new(Worker::new(api.as_ref()));
test.rs:28      Engine { api: api, worker: worker }
test.rs:29  }
test.rs:26:27: 29:3 note: ...but borrowed value is only valid for the block suffix following statement 0 at 26:26
test.rs:26      let api = Box::new(Api);
test.rs:27      let worker = Box::new(Worker::new(api.as_ref()));
test.rs:28      Engine { api: api, worker: worker }
test.rs:29  }
error: aborting due to previous error