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I’m analysing an adult cohort where each participant contributes a different number of BMI readings taken at different ages (some are better characterized, other worse). The goal is to quantify in the different groups how much time it takes for a group (stratified according to a specific condition) to reach "obesity" (IMC =>30), in this context, I thought joint models may be useful due to my repeated measures over time. My thought after considering serveral approachas was to build a joint model in JMbayes2 that links repeated BMI measurements to the time at which someone becomes obese (30 kg/m2). My study:

  • ~14 000 adults, BMI measured up to ten times (1990-2024)
  • Baseline covariates: age, sex, smoking, education, diabetes, hypertension
  • I want the event to be “BMI ≥ 30”, but people can cross that line more than once.

1. Handling a reversible obesity threshold (BMI ≥ 30 kg m²) My first instinct is to use the first time BMI hits 30 as the event (I create a variable called event(0,1)) and ignore later reversions, but I’m not sure that’s fully correct. Is there a standard way to treat a threshold that can be crossed, reversed, and crossed again?

  • Some participants cross 30 once and stay obese.
  • Others bounce above and below 30 over time.

2. Non-linear time in the longitudinal sub-model

The BMI curve is clearly non-linear (inverted-U). Can I just plug a spline term in the joint model? —e.g.with sex and group interactions.

enter image description here

The following code is one of the tested models accounting for interactions and non-linear components of time

# mixed-effects model
mod_gam2 <- lme(variable ~ bs(seg, df=4)*group*sexo + 
    fumador + diabetes + hipercol + hta + educ  + 
    cohort , random = ~ 1 | id2, 
    correlation = corCAR1(form = ~seg | id2), 
    control = lmeControl(opt="optim"), data=xxx, 
    method='REML', na.action=na.exclude)

# survival model
coxfit <- coxph(coxph(Surv(years, event) ~ group*sexo + 
    fumador + diabetes + hipercol+hta + educ  + cohort, 
    data = xxx))

Does the joint model support this? Is able to capture non-linear interactions?

# Joint model
jmodel <- jm(mod_gam2, coxfit,  timeVar   = "seg")

3 Do both sub-models need identical covariates? Regarding the prior syntax. Is there a principled rule about adjusting for the same covariates in the mixed-model and the survival one?

Any thoughts, pointers would be really appreciated.

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I have serious reservations about using crossings of BMI at 30 as an "event" (resp. "reversion") in this situation. Those crossings are likely to be highly influenced by minor fluctuations in body weight, particularly for those already near that arbitrary cutoff.

There also are serious reservations about using BMI as a measure of obesity. See this page, for example.

Lets put aside the objections to BMI per se, as you probably don't have much other choice with this data set. You already have what seems to be a pretty comprehensive model for BMI as a function of time.* Why not just use that to evaluate how modeled trajectories of BMI over time differ among groups, after controlling for the other covariates? That continuous estimation will probably be much more interesting than an arbitrary choice of BMI cutoff.

With a continuous outcome like BMI, you might do even better with a generalized least squares model. That provides marginal estimates over groups. That's in keeping with your goal to "quantify in the different groups." A generalized least squares model (gls() in the R nlme package) allows you to specify a within-individual correlation structure, as you did for your lme() model.

Then you no longer need a joint model.

*It might be instructive to add the initial BMI as a predictor and only model later times, so that you can evaluate whether trajectories change (beyond the obvious baseline shift) as a function of the initial BMI. Chapter 7 of Frank Harrell's Regression Modeling Strategies covers longitudinal data modeling, including the importance of using initial values as predictors and with an emphasis on generalized least squares.

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