I am working with longitudinal MMRMlike Bayesian models for clinical trial data. For each patient, a continuous outcome variable is measured a predetermined n > 2
number of times, and those outcome measurements are treated as multivariate normal for each patient. Outcomes from different patients are assumed independent conditional on the parameters.
It is common for patients to drop out during the study, so there are a lot of missing outcomes. To integrate out the missing outcomes, I am using the technique described at 3.5 Missing multivariate data  Stan Userâ€™s Guide because it works well with ELPD methods like the one by Silva and Zanella (2022). In addition, it easy to generalize to the n
dimensional multivariate case because the marginal of a multivariate normal is multivariate normal on a subset of elements of mean vector \mu and a subset of the rows and columns of covariance matrix \Sigma. Overall, this approach works well. I am very happy with it, and it is much simpler and more computationally efficient than 3.1 Missing data  Stan Userâ€™s Guide in my case.
However, I feel like the way I am coding it is not as efficient as it could be. Each patient uses a different subset of \Sigma, and I code their likelihood in Stan as
y[subset] ~ multi_normal(mu[subset], Sigma[subset, subset])
where:

y
is the patientspecific vector of observations. 
mu
is the patientspecific mean vector. 
Sigma
is the shared covariance matrix among different measurements within a patient. 
subset
is a patientspecificint
array to select only the observed components ofy
.
I want to use multi_normal_cholesky()
, but subset
is different from patient to patient, and I would have to recompute the Cholesky factor of Sigma[subset, subset]
for each patient and each MCMC iteration.
Is there a computational shortcut to compute the Cholesky factor of Sigma[subset, subset]
given an existing Cholesky factorization \Sigma = L L^T of the full covariance matrix? I tried to derive one at linear algebra  Fast shortcut to get the Cholesky factor of a submatrix  Mathematics Stack Exchange, but my answer in that post is wrong because the Choleskylike factor I came up with is not lower triangular.