msm_frydman: Determine NPMLE for Multi State illness death Markov model...

In icmstate: Interval Censored Multi-State Models

Determine NPMLE for Multi State illness death Markov model using Frydman (1995)

Description

Determine NPMLE for Multi State illness death Markov model using Frydman (1995)

Usage

msm_frydman(data, tol = 1e-08)

Arguments

data

A data.frame containing the columns named: delta: Did a transition from 1 -> 2 occur? (binary: 0 = no, 1 = yes); In the left-truncated case, delta = 2 indicates initially observed in state 2. Delta: Was the transition to state 3 observed? (binary: 0 = no, 1 = yes); L: Left timepoint of interval censored transition to state 2 (numeric); R: Right timepoint of interval censored transition to state 2 (numeric); time: Time of event (transition to 3) or right-censoring in state 2 (numeric); trunc: (optional) Left-truncation time (numeric); Only used for entries with delta = 2.

tol

Tolerance of the EM algorithm. Algorithm will stop when the absolute difference between current mass estimates and new estimates is smaller than the tolerance

Details

For an illness death model (1 = healthy, 2 = ill, 3 = dead) estimate the NPMLE in the following form:

F12:

Cumulative distribution function of 1->2 transition;

F13:

Cumulative distribution function of 1->3 transition;

Lambda23:

Cumulative intensity of 2->3 transition;

Value

A list with the following entries:

data_idx:

A list containing the data used for the fit (matdata), the indices for which group a subject belongs to (GroupX_idx), some computational parameters (see Frydman(1995)) and the unique failure times of the 2->3 and 1->3 transitions respectively in t_n_star and e_k_star;

supportMSM:

A list containing all transition intervals in A and the theoretical support intervals in Q_mat;

z_lambda:

Computational quantities, see Frydman(1995);

cdf:

A list of functions that allow to recover the cdf for the 1->3 (F13) and 1->2 (F12) transition and the cumulative hazard for the 2->3 (Lambda23) transition.;

References

Frydman, H. (1995). Nonparametric Estimation of a Markov 'Illness-Death' Process from Interval- Censored Observations, with Application to Diabetes Survival Data. Biometrika, 82(4), 773-789. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2337344")}

Examples

data <- data.frame(delta = c(0, 0, 1, 1), Delta = c(0, 1, 0, 1),
                   L = c(NA, NA, 1, 1.5), R = c(NA, 3, 2, 3),
                   time = c(4, 5, 6, 7))

mod_frydman <- msm_frydman(data)
visualise_data(data, mod_frydman)

icmstate documentation built on April 3, 2025, 8:06 p.m.