Package jline.api.mc

Class Smp_stage_cif

java.lang.Object
jline.api.mc.Smp_stage_cif
public final class Smp_stage_cif extends Object
Cumulative incidence functions of the transitions out of one semi-Markov stage, and the stage's holding-time CDF, on ascending instants.

arcs[h] is the law of the transition to h, or null where there is none. probs selects how they combine:

  • null: COMPETING arcs. Each is a latent clock started on entry and the first to ring picks the destination, so the transition intensity of arc h is the hazard of its own law (Asanjarani et al., Approach II) and CIF_h(t) = int_0^t prod_{k!=h} (1 - F_k(s)) dF_h(s), Fhold(t) = 1 - prod_k (1 - F_k(t)).
  • an E-vector: KERNEL arcs. The destination is drawn on entry with probability probs[h] and the sojourn then follows arcs[h] (Approach I), so CIF_h(t) = probs[h] F_h(t) and Fhold(t) = sum_h probs[h] F_h(t).

The competing integral is a Stieltjes sum with the survival of the other clocks at each interval's midpoint; when t[0] > 0 the stretch [0, t[0]] is summed on 200 intervals of its own so that C[h][0] is not a one-interval guess.

Port of MATLAB smp_stage_cif.m. Reference: A. Asanjarani, B. Liquet, Y. Nazarathy, Estimation of semi-Markov multi-state models: a comparison of the sojourn times and transition intensities approaches, arXiv:2005.14462 (2020), Eqs. (7), (9), (12).

  • Method Details

    • smp_stage_cif

      public static Smp_stage_cif.Result smp_stage_cif(Distribution[] arcs, double[] probs, double[] t)

    • linspace

      public static double[] linspace(double d1, double d2, int n)
      MATLAB linspace: d1 + k*(d2-d1)/(n-1), with both ends exact.