Dear Paul, thanks for your comments and for the paper shared. Your question about to adjust for a post-baseline covariate is so interesting. One of the problems to do this is the possibility to produce bias results if this covariate is a mediator of the relationship among the intervention (treatment) and the outcome. Adjusting for a time varying mediator covariate produces the effect of treatment waned down with time. Advantages of Joint model is that you could evaluate post-baseline time-varying covariates (i.e SBP) as and outcome and not as a covariate. In addition, the random part of the linear mixed model could include others time varying covariates (i.e SAEs) as latent variables. Let me give to you an example with my paper:
Our interest was to evaluate if the efficacy of systolic blood pressure (SBP) intensive treatment over SPRINT primary outcome could be affected by cumulative SBP, SBP intra-individual variability and serious adverse events (SAEs) produced during follow-up. In our case, we build a cumulative joint model that include a linear mixed model (LMM) + a traditional Cox proportional hazard model. In the LMM the outcome was SBP repeated measurements over time, adjusted by time, treatment and interaction among time:treatment. No others covariates because both groups were balanced by randomized at baseline. The fixed part of this model include SBP variability between interventions groups and the random part of this model include intra-individual SBP variability and other time varying covariates as latent variables (i.e SAEs). Please see graph below.
In the case that we want to evaluate the impact that SAEs has over SPRINT primary outcome, we used other approach: We created an interaction term between SAEs: treatment into cJM. This interaction was statistical significant (p<0.0001), so we decided do a stratify analysis comparing two groups: people with and without SAEs under cJM. Please see graph below
We found that SBP intensive treatment reduce its beneficial effect in people who suffer SAEs than people without SAEs (HR is less protective 3 times). In addition, this beneficial effect is loss early in participants with SAEs (loss effect at 3.4 years) compared with participants w/o SAEs (4.2 years).