Hi all,
considering longitudinal profiles of a biomarker in a set of patients, I'd
like to compute the conditional probability to observe jointly all the
available measurements up to time t (Yi_t) on a new patient i given that
the single next measurement at t+6months (Yi_t+6) falls below a threshold
X. Formally:
f(Yi_t | 0 <= Yi_t+6 <= X)
This is the last plug-in part I need in a Bayes formula to actually
compute the reverse conditional probability.
A linear mixed model can be fitted to all other patients so that I know
the fixed effects and variance components for the population. For instance
to compute f(Yi_t), I simulated 1000 profiles from the random effects
distribution. This creates 1000 multivariate normal distributions from
which I can compute the probability to observe jointly all the data in
Yi_t. f(Yi_t) is then assumed to be the mean of the 1000 probabilities.
But I don't know how to compute f(Yi_t | 0 <= Yi_t+6 <= X). As far as I
understand, I should only consider profiles that would allow Yi_t+6 <= X
and among these compute f(Yi_t). Is that correct?
Thanks for any input
Aziz
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