Hi everyone! I am new to this forum so hopefully I am following the appropriate etiquette.

I have a dataset of N = 134 subjects. 21 of these will have an event by the end of the longitudinal follow-up period. The time to event is measured in months from the baseline visit, coded by the variable *months_from_baseline*.

The prognosis is usually computed at the baseline visit using a score (integer, 0 to 6, higher score = worse prognosis), here coded in the variable *prognostic_baseline_score*. It makes sense to predict the event in the event submodel through an univariable Cox regression using *prognostic_baseline_score* as sole predictor. The median *prognostic_baseline_score* is 1 (IQR: 0-6).

In this study, a biomarker score (coded by the variable *biomarker_score* is measured at the baseline visit and every 3 months after the baseline visit. *biomarker_score* is a continuous variable scaled in such way that a 1-unit increase in *biomarker_score* corresponds to a clinically meaningful change in the underlying biomarker. The mean *biomarker_score* across longitudinal visit is 1.32 in those who will have an event and 0.52 in those who will not (SD = 1.2).

Here a dataset summary at the baseline visit:

The hypothesis is that a high biomarker score worsen the prognosis of the subject independent of the *prognostic_baseline_score*.

I used the following joint model with a current association structure:

```
mod1 <- stan_jm(
#Longitudinal submodel: biomarker score depends on 2-knot spline subject-specific intercept & slope + global intercept & slope
formulaLong = biomarker_score ~ 1 + months_from_baseline_visit + (1 + ns(months_from_baseline_visit,2) | subject_id),
dataLong = df.toy,
#Event submodel: a 3-B splines approximation of the survival function depends on the baseline_prognostic_score
formulaEvent = survival::Surv(months_to_event, event) ~ baseline_prognostic_score,
dataEvent = df.toy.baseline,
family = gaussian,
basehaz = "bs",
basehaz_ops = list(df = 3),
#Current association structure
assoc = c("etavalue"),
id_var = "subject_id",
time_var = "months_from_baseline_visit",
chains = 3,
cores = 3,
refresh = 200,
iter = 5000,
seed = seed)
```

The summary ouput of this model is:

```
summary(mod1, probs = c(.025,.975))
```

My question is - is it correct to interpret that **each 1-unit increase in a biomarker score observed during follow-up is associated with a HR = exp(0.477) = 1.61 independent of the baseline_prognostic_score** and with a 95% credible interval between exp(0.096) = 1.10 and exp(0.828) = 2.29?

I am using R version 4.3.2 (2023-10-31) with rstanarm_2.32.1

Thank you so much for your help!