Support for competing risks simulation

[adibender]

• basic
• time-varying effects
• time-dependent covariates (concurrent)
• cumulative effects (cumulative)
• integrate into sim_pexp (check if length(RHS(formula)) > 1 -> call sim_pexp_cr internally
• Fix rewrite code that depends on Formula in preparation for CR formulas #88 before deployment

see #105

[pkopper]

We should discuss how the existing simulation may be adapted to facilitate the new functions.

[fabian-s]

@adibender : if I read this correctly you'd suggest a new function sim_pexp_cr that deals with CR complications and that gets called from sim_pexp, which is then simply a wrapper for calling either the new sim_pexp_cr or the "old" sim_pexp (renamed as sim_pexp_single, or similar, see below), depending on the formula structure?

OT: probably need to agree on a global naming scheme rule to differentiate CR functionality from "classic" functionality? suggestion: call one "_cr" and the other "_1r" (one risk)?

[fabian-s]

.. and internallly, sim_pexp_cr will probably just a wrapper around calling (parts of) sim_pexp_single for each of the competing risk processes and then using the minimum of the generated event times as the actualized risk/event type, correct?

[adibender]

Right, I think it would be best to refactor the existing sim_pexp such that

1. there is a function that constructs the linear predictor given specification of the RHS of the input formula (and data)
2. within sim_pexp we calculate one linear predictor/hazard for each part of the RHS of the input formula, i.e. for ~ 0.2 * x1 | 0.1 * x2 we calculate two linear predictors (that requieres to fix rewrite code that depends on Formula in preparation for CR formulas #88 first)
   That could be done by looping through the number of RHS arguments and calling the function from 1.
3. If the List returned in 2. is longer than one, call sim_pexp_cr, otherwise call sim_pexp_1r
   Within sim_pexp_cr it proceeds similar to what I already implemented in the competing-risks branch, but could probably be improved upon.

[pkopper]

Thank you. I think we are on the same page w.r.t. this.