Two-part mixture model on left-censored biomarker data

Modeling
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1

I am trying to model blood biomarker data collected longitudinally in a sample of patients vs. controls. There are 4 sampling timepoints, with patient data collected either at timepoint 1 or 2 (I have considered combining them into one timepoint, but biologically speaking it is better to keep them separate). The biomarker concentrations are heavily left-censored, with a large proportion of values below assay detection limits (< LOD, or non-detects).

I believe the best modelling strategy is a two-part mixed-effects mixture model, with bernoulli probability for predicting detects vs. non-detects, and a lognormal truncated model for the rest. Please advise if this is wrong, but I originally thought to do a mixed-effects censored Tobit regression, but I found the proportion of non-detects significantly affected parameters too much.

Example code for one biomarker is below

  cyt <- "IL_7"
  resp_censobs  <- paste0(cyt, "_censobs") # All non-detects re-coded to LOD
  resp_detect   <- paste0(cyt, "_detect") # DETECTED? TRUE/FALSE
  lod <- LOD_vals[[cyt]]

  bf_det <- bf(
    as.formula(paste0(resp_detect, " ~ ", "Group_Mixed * timepoint + Sex 
+ Age_centred + (1 | p | Subj_ID)")),
    family = "bernoulli"
  )
  
  bf_pos <- bf(
    as.formula(paste0(resp_censobs, " | trunc(lb = ", lod, ") ~ Group_Mixed * 
timepoint + Sex + Age_centred + (1 | p | Subj_ID)")),
    family = "lognormal"
  )
  
  fit_hurdle <- brm(
    bf_det + bf_pos + set_rescor(FALSE),
    data = df,
    backend = "cmdstanr",
    chains = 4, cores = 8,
    prior = priors,
    iter = 4000,
    warmup = 1000,
    save_pars = save_pars(all = TRUE),
    control = list(adapt_delta = 0.999, max_treedepth = 15),
    init = 0
  )

Please let me know if this is the correct modelling strategy and if there’s any fixes you would recommend