Proportional Odds

Dear All, I have been coding a Proportional Odds Emax model for some categorical PD data. The model seems to be sensitive to initial estimates of the baseline odds. The SE in the final estimates after a few trials comes to be 30% at worst. Any suggestions on methods to make better guesses for initial values of baseline odds from the given data? Another question would be - is it possible to generate confidence bounds on probabilities using NONMEM for such a model? Thanks, Sathej

Dear Sathej, I will for simplicity assume your Emax model varies with dose of drug. If the Emax model varies with time, concentration of drug or some other covariate this should be easy enough to translate. As a first initial estimate, you can use the empirical probabilities of the observed 1's, 2's, 3's etc. for the population of dose=0. Logit transform these empirical probabilities to get the baseline odds, logit = ln(pr/(1-pr)). If there aren't any observations of dose=0, this might be the reason why your model is so sensitive to initial estimates. Your baseline odds are then estimated based on extrapolation from the observations from the treatment arms. If this is the case and you're interested in the shape of the drug effect, rewrite the Emax model to place the baseline odds at the lowest observed dose and use the empirical probabilities of the lowest dose as the initial estimates. Reversely, use the inverse logit function pr = exp(logit)/(1+exp(logit)) to transform any logit-values to probabilities, to generate for example confidence interval. Remember however that you assume normally distributed logit-values, if you use the estimated typical values +- 2*SE as your confidence bounds. To avoid this assumption of normality you could perform a bootstrap and use those boundaries and transform into probabilities. Hope this was helpful, Mia ____________________________________________ Maria Kjellsson, PhD Pharmacometrics Research Group Uppsala University