A bibliographic review of non-parametric methods and their application
Emmanuelle Comets (1), Julie Antic (2), Rada Savic (1,3)
(1) Inserm U738, University Paris Diderot Paris 7, Paris, France; (2) UMR 181, Toulouse, France; (3) Uppsala University, Uppsala, Sweden
Objectives: Nonparametric (NP) methodology within non-linear mixed effects framework has been increasingly discussed and evaluated in recent years. Even though it has proven to be precise, accurate and to have several advantages over the parametric methodology, its use has still been limited for various reasons. In order to identify these limiting factors, and to increase the understanding of utilisation of nonparametric methods, we perform a systematic review of all pharmacokinetic (PK) / pharmacodynamic (PD) analyses concerned with nonparametric methods. We also investigate in which instances modellers would utilise the nonparametric methodology as well as different approaches to performing nonparametric model building.
Methods: We selected the articles which matched the keywords "NPEM or NPAG or NPML or ((non-parametric or nonparametric) and mixed and effects and model))" in the PubMed (for biomedical and life sciences articles) or MathScinet (for maths articles) databases. These articles were analysed using a comprehensive data abstraction form (DAF). The DAF, a check list of items, was built to extract all relevant information from the articles. The items focused on the study, the data, the models, the NP estimation methods and software, the model development and evaluation, and the report of NP results.
Results: The PubMed search returned 153 articles. The MathScinet returned 36 articles with 2 already found in the PubMed search. 69 papers were excluded from the analysis: in 21 papers, an abbreviation used in the search was used in a different meaning and the paper did not in fact concern NP methods; in 17 papers, the regression function was non-parametric; in 15 papers, a non-parametric test was used; in 7 papers, a non-parametric bootstrap procedure was used; 5 papers were reviews; 4 papers were written in foreign languages. The final database contained 118 papers.
The number of papers concerning non-parametric methods has increased over the last decade, with 79 papers published since 2000 compared to 36 papers published between 1990 and 1999. Most of the papers were published by academia; about half were classified as primarily methodological, the other half being more concerned with applications of non-parametric methods. There was no significant difference in this trend before or after 2000.
These findings may reflect a lack of diffusion of non-parametric methods; possible reasons include a perceived higher conceptual difficulty, a lack of easily usable software, as well as unsolved issues such as estimation of some parameters, model comparison, or model evaluation. For instance, the estimation of fixed effects such as parameters of the residual error models is generally a challenge for non-parametric methods and these parameters were often fixed in the papers found in this review, although some papers proposed methods to deal with this problem. Another issue found is the lack of estimates of uncertainty.
Conclusions:In this paper, we provide an overview of the development and use of non-parametric methods in the literature. We highlight key issues with these methods and point at unresolved problems which need to be tackled for these methods to become more widespread.
