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Conditional Non-parametric Bootstrap for Non-linear Mixed Effect Models
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DOI：10.1007/s11095-021-03052-6.png)
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Purpose Non-linear mixed effect models are widely used and increasingly integrated into decision-making processes. Propagating uncertainty is an important element of this process, and while standard errors (SE) on pa- rameters are most often computed using asymptotic approaches, alternative methods such as the bootstrap are also available. In this article, we propose a modified residual parametric bootstrap taking into account the different levels of variability involved in these models. Methods The proposed approach uses samples from the individual conditional distribution, and was implemented in R using the saemix algorithm. We performed a simulation study to assess its performance in different scenarios, comparing it to the asymptotic approximation and to standard bootstraps in terms of coverage, also looking at bias in the parameters and their SE. Results Simulations with an Emax model with different designs and sigmoidicity factors showed a similar coverage rate to the parametric bootstrap, while requiring less hypotheses. Bootstrap improved coverage in several scenarios compared to the asymptotic method especially for the variance param-eters. However, all bootstraps were sensitive to estimation bias in the original datasets. Conclusions The conditional bootstrap provided better coverage rate than the traditional residual bootstrap, while preserving the structure of the data generating process.
Keyword:
bootstrap
conditional distribution
non-linear mixed effect models
uncertainty of parameter estimates
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