Statistical power of covariate inclusion in popPK models

From: [email protected] [mailto:[email protected]] On Behalf Of Hammami, Ibtihel /FR Sent: Wednesday, March 24, 2021 5:47 AM To: [email protected] Subject: [NMusers] Statistical power of covariate inclusion in popPK models Hi, Thank you all for your answers. I have two follow-up questions: 1. Is it mandatory to use the matrix R as a variance co-variance matrix to obtain the FIM? In case we have already used other type of variance co-variance matrix, should we rerun the model with matrix R setting? Ken: The Hessian (or R matrix) is the 2nd derivative matrix of -LL which is equivalent to the FIM. However, you don't have to invert the Hessian to obtain the covariance matrix. For example, in NONMEM the default estimator is the sandwich estimator, (R^-1)S(R^-1), where S is the 1st derivative (gradient) cross-product matrix. Note that R^-1 as well as (R^-1)S(R^-1) are consistent estimators of the covariance matrix and thus asymptotically, both should converge to the same result as the sample size increases. However, most nonlinear regression packages invert the Hessian (R matrix) as the default estimate of the covariance matrix of the parameter estimates. 2. How critical is the estimation method for the computed SE? In other words, is it relevant to compare two powers computed based on two standard errors givens by different estimation algorithms? For example, if we used FOCE-INTER to minimize our model, could we compare the power (based on the Wald test) to results given by PFIM which is based on FO ? Ken: The R and S matrices involve taking 1st and 2nd derivatives of the log-likelihood and evaluating them at the final estimates of the parameters. Thus, if you use different approximations of the likelihood (e.g., FOCEI or FOCE or FO) and you get different final estimates of the population parameters you will also get different values for the R and S matrices. Just for a little bit of background to clarify why we are interested in the Wald test. We are working on the comparison of different methods to compute the statistical power of covariate inclusion in popPK models (SSE (gold standard), MCMP, PPE , and Wald test). We have also included the Wald test in our comparison because it is the fastest method and mostly because it used by optimal designs software. R Therefore, the evaluation of the accuracy of the power derived by this method could facilitate the bridging step between model validation and the design of upcoming clinical trials using optimal design software. Ken: Most optimal design software (e.g., D-optimality) I imagine would use the Hessian (R matrix) rather than the sandwich estimator, however, I'm not familiar with what PFIM uses. You may want to follow up with the PFIM developers to find out what they use. Thank you in advance. Cordially. Ibtihel HAMMAMI. -- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus