repeated measures mixed effects model with time-varying covariates in r

Question

Assuming that we have longitudinal data on pulmonary fibrosis with some patients undergoing transplant while others received medical treatment. Each patient is represented by many rows depending on the time of assessment of the quality of life (qol) which is our outcome (continuous variable). Among the independent predictors are the following variables and their time of occurrence (as they are time-varying covariates); infarction, transplant, and death.

We decided to categorize each of infarction_time and transplant_time into 3 categories (No, recent event (=< 3 months), and old event (> 3 months)) between the independent predictor and qol_assessment_time_months. Patients who will die will be coded as 0 in qol column at time of death. Consequently, we will run a repeated measures mixed effects model as shown in the code below, which has a fictitious data sample.

Will our model be valid? I saw this link but it seems to be irrelevant to my current data. Any advice will be greatly appreciated.

library(mmrm);library(sjPlot)
data<-structure(list(serial.id = 1:16, PT_ID = c("PT1", "PT1", "PT1", 
"PT1", "PT2", "PT2", "PT2", "PT2", "PT3", "PT3", "PT3", "PT3", 
"PT4", "PT4", "PT4", "PT4"), VISIT_No. = c(1L, 2L, 3L, 4L, 1L, 
2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L), transplant = c(0L, 
1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 1L), 
    transplant_time_months = c(1.1, 1.1, 1.1, 1.1, 2.1, 2.1, 
    2.1, 2.1, 2.5, 2.5, 2.5, 2.5, 5.1, 5.1, 5.1, 5.1), transplant_time = c("no", 
    "recent", "old", "old", "no", "recent", "recent", "recent", 
    "no", "recent", "old", "old", "no", "no", "no", "recent"), 
    qol_transplant.time = c(-0.1, 1.4, 3.4, 5.9, -1.1, -0.1, 
    1, 2.9, -1.5, 1.5, 3.5, 4.5, -4.1, -2.1, -0.1, 1.9), infarction = c(0L, 
    0L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L
    ), infarction_time_months = c(2.6, 2.6, 2.6, 2.6, 2.5, 2.5, 
    2.5, 2.5, 6, 6, 6, 6, 6.5, 6.5, 6.5, 6.5), infarction_time = c("no", 
    "no", "recent", "old", "no", "no", "recent", "old", "no", 
    "no", "no", "recent", "no", "no", "no", "recent"), qol_infarction.time = c(-1.6, 
    -0.1, 1.9, 4.4, -1.5, -0.5, 0.6, 2.5, -5, -2, 0, 1, -5.5, 
    -3.5, -1.5, 0.5), qol_baseline = c(0.252714351, 0.252714351, 
    0.252714351, 0.252714351, 0.45024771, 0.45024771, 0.45024771, 
    0.45024771, 0.435006968, 0.435006968, 0.435006968, 0.435006968, 
    0.316031834, 0.316031834, 0.316031834, 0.316031834), VISITN = c(1L, 
    2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L, 1L, 2L, 3L, 4L
    ), qol = c(0.042509539, 0.041262234, 0.798179128, 0.205693285, 
    0.138904667, 0.268516519, 0.18593854, 0.169571187, 0.127670035, 
    0.213748462, 0.348524093, 0.170447984, 0.307079441, 0.122826554, 
    0.068807874, 0), qol_assessment_time_months = c(1, 2.5, 4.5, 
    7, 1, 2, 3.1, 5, 1, 4, 6, 7, 1, 3, 5, 7), death = c(0L, 0L, 
    0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L), 
    death_time = c("no", "no", "no", "no", "no", "no", "no", 
    "no", "no", "no", "no", "no", "no", "no", "no", "no"), follow_up_time_months = c(10L, 
    10L, 10L, 10L, 15L, 15L, 15L, 15L, 12L, 12L, 12L, 12L, 7L, 
    7L, 7L, 7L)), class = "data.frame", row.names = c(NA, -16L
))

fit <- mmrm(  formula = qol ~ transplant+transplant_time + infarction+infarction_time + death+ death_time+ us(VISIT_No. | PT_ID),  data = data);tab_model(fit)




### A similar data structure without time-varying covariates was present in 
fev_data ## built-in database in mmrm package

Answer 1

These comments were written before I realized that time is not your outcome variable:

I think that times should be in days and not categorized. For example when you have transplant as a time-dependent covariate, the risk sets need to be properly constructed on exact times. You'll also need to check that patient condition measured at original based is always updated at the transplant time if you want to make inference about the effect of transplant.

Are you assuming normality for QOL? That may cause troubles. Consider an ordinal model. A Markov ordinal model allows for time-dependent variables. It's pretty easy if time intervals are regular and time is discrete.