Satoshi Shoji, Akiyuki Suzuki, Shinichi Tsuchiwata, and Yoshiro Tomono
Pharmacometrics group, Clinical Pharmacology, Clinical Research, Development Japan, Pfizer Japan Inc.
Objectives: When a population of interest is small or data in the population is sparse due to practical constraints, it is occasionally difficult to fit a model with the current data alone. Use of prior [1] is one of the ways to analyze such limited data while borrowing information from the prior and stabilizing the parameter estimation. In this work, we evaluate information of prior relative to current data when analyzing data in a small population or sparse data.
Methods: In this work, information of prior relative to current data is defined as how many times the prior has the amount of information in comparison with current data. This idea was based on prior information of Bayes estimator [2]. To measure the relative information, we use following variance of the parameter estimate.
– V+ p[θ] obtained from information of current data + prior
– V+N[θ] obtained from information of current data + N∙current data
where θ represents a parameter estimate obtained from an analysis with a prior. When V+ p[θ] is equal to V+N[θ], information from the prior is considered equivalent to that from the N∙current data. We define the N as a scale for information of the prior. We analyzed simulated data of several examples for dose-response in a small population and sparse PK data using frequentist prior of NONMEM $PRIOR [1] to obtain V+ p[θ]. The N at V+N[θ] equivalent to V+ p[θ] was calculated from fisher information matrix of parameter estimates [3] given the estimate θ and current study design.
Results: When the information of prior was small (e.g. N around 1 – 2), the parameter estimate was governed by the current data as well as the prior. In those cases, even when the prior was misspecified, the parameter estimate was little influenced by the misspecification. In the meanwhile, in extreme cases of large prior information (e.g. N > 30), as expected, the parameter estimate was mostly governed by the prior, resulting in little improvement in the estimation bias when the prior was misspecified.
Conclusion: Parameter estimates obtained by use of the priors could be applied to infer a population of the current data, depending on information of the priors and the current data. Although further investigation and improvement is needed, information of prior relative to current data presented in this work may be used as one of the scales.
References:
[1] Gisleskog PO, Karlsson MO, Beal SL. Use of prior information to stabilize a population data analysis. J Pharmacokinet Pharmacodyn 2002; 29:473-505.
[2] Mori H. Evaluation of Prior Information in Bayesian Inference. J. Japan Statist. Soc. 2010; 40 :1-16.
[3] Retout S, Mentre F, Bruno R. Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics. Statist. Med. 2002; 21:2623-39
Reference: PAGE 23 (2014) Abstr 3140 [www.page-meeting.org/?abstract=3140]
Poster: Methodology - Other topics