Hi Emily, A few months ago you posted a reply to an enhancement suggestion regarding Monte Carlo simulations and pred check (see below). I have a question regarding point “a) First Monte Carlo step” in your reply below. How does Phoenix NLME perform this step when the non-parametric engine is selected, since in this case no assumptions are made regarding the distribution of random effects. Thanks Dora ecolby wrote: [quote]Dear Tony, Phoenix NLME currently performs a Monte Carlo simulation when Pred. Check is selected in the Run Options tab. I’ve copy/pasted some information pertaining to this. Best regards, Emily Colby Simulations in Pred. Check Suppose you have N subjects and we want to do a predictive check with 500 simulations, so each subject is simulated 500 times. First, we’ll describe what is done for subject 1. We freeze all the theta, Omega, and Eps parameter values for all the simulations (presumably to the values that were found by a fit to the original data). These values apply to all subjects. We also freeze any covariate values such as weight, age, sex, and the time points at which samples were taken for subject 1 to the values in the original data for subject 1 (similarly, subject 2 is always simulated with the original covariates, dosing, and sampling times for subject 2, etc.). So if subject 1 was male, weighed 187 lbs, and had 17 observations at 17 different time points, all 500 data sets for subjects 1 will correspond to a 187 pound male with samples at the same 17 time points. The same dosing scheme will be used as was used for the original ‘real’ subject 1. Each data set is simulated by the following steps. a) First Monte Carlo step: draw a set of random effect (eta) values from a N(0, Omega) distribution. We then calculate the a predicted value vector, pred(i), i=1, 2, …, 17, since we now know all the information (thetas, Omegas, etas, covariates, and dosing) necessary to do that. Essentially we create new copies of subject 1 that correspond EXACTLY to the original subject in covariates, dosing, and sampling times, but differ in random effect values. b) Suppose the residual error model is proportional, so observation = pred + pred*Eps, where Eps is a normally distributed random variable corresponding to residual error with mean 0 and std deviation Stdev (where Stdev was estimated from the original data, i.e. Eps has a N(0, Stdev^2) distribution) Second Monte Carlo step: draw a set of 17 independent random residual errors, Eps(i), i=1,…,17, from a Normal distribution with mean 0 and standard deviation Stdev. then set observatiion(i) = pred(i) + pred(i)*Eps(i) These are the simulated observations for the first subject, first new data set. We then repeat a) and b) until we get a total of 500 simulated data sets for subject 1. Note each new data set for subject 1 has its own new set of random etas and Eps values. We then go back and repeat the whole procedure for each of the remaining subjects.[/quote]
Dear Dora, When Nonparametric is checked, the predictive check simulation will still use the Omega worksheet (not the nonparametric Omega worksheet) for drawing random values of etas, using the parametric assumption that the etas have a multivariate normal distribution with variance Omega. Therefore, having Nonparametric checked has no effect on the simulation or the predictive check. Best regards, Emily