One-compartment PK modeling, based only on summary statistics

I’m working on a variability/sensitivity analysis with data from a population PK study, from which I know the mean (and sd) of each of AUC, Cmax, and tmax, but not the underlying PK constants. I’ve recast all the normal one-compartment PK constants (apparent volume v, absorption rate ka, and elimination rate ke) as non-linear formulas for AUC, Cmax, and tmax, see model spec here:

parameters {
  real ka;
  real ke;
  real v;
transformed parameters {
  real cmaxexp = dose/((ka/ke)^(ke/(ka - ke)) * v)
  real tmaxexp = (log(ka) - log(ke))/(ka-ke);
  real aucexp = dose / (ke * v);
model {
  cmaxobs ~ normal(cmaxexp, cmaxerr);
  tmaxobs ~ normal(tmaxexp, tmaxerr);
  aucobs ~ normal(aucexp, aucerr);

And then I provide the summary statistics for *obs and *err values as data. Everything “works”, except that I get lots of warnings about treedepth, divergent transitions, bad Rhat, etc. I believe this is because I haven’t specified any informative priors, and so the sampler is bouncing all over the place. Before I introduce priors, I wanted to check if this is a sane approach. Note that it’s also possible that the observed data are not consistent with a one-compartment model, but I would still expect to get a stable “fit”, though with poor accuracy.

thanks for any advice,

Tagging @wds15, @yizhang and @bbbales2.

This is a classic application of Fisher factorization theorem and sufficient statistics. So yes this is a sound approach to me.

Thanks! Once I further transformed the three constants into log-space everything ran smoothly. -Aaron