Qualifying drug dosing regimens in pediatrics using Gaussian processes

Siivola, Eero; Weber, Sebastian; Vehtari, Aki

doi:10.1002/sim.8907

Cited by 5 publications

(5 citation statements)

References 23 publications

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“…For example, there can be gaps in time-series data in which case the expert may provide structural information in a form of a prior distribution that helps to fill gaps in the posterior distribution, or the expert knowledge may help to extrapolate from one group in the data to another (e.g., see Siivola et al, 2021).…”

Section: Bayesian Modelling Workflowmentioning

confidence: 99%

Prior knowledge elicitation: The past, present, and future

Mikkola¹,

Martin²,

Chandramouli³

et al. 2021

Preprint

Self Cite

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Specification of the prior distribution for a Bayesian model is a central part of the Bayesian workflow for data analysis, but it is often difficult even for statistical experts. Prior elicitation transforms domain knowledge of various kinds into well-defined prior distributions, and offers a solution to the prior specification problem, in principle. In practice, however, we are still fairly far from having usable prior elicitation tools that could significantly influence the way we build probabilistic models in academia and industry. We lack elicitation methods that integrate well into the Bayesian workflow and perform elicitation efficiently in terms of costs of time and effort. We even lack a comprehensive theoretical framework for understanding different facets of the prior elicitation problem.Why are we not widely using prior elicitation? We analyze the state of the art by identifying a range of key aspects of prior knowledge elicitation, from properties of the modelling task and the nature of the priors to the form of interaction with the expert. The existing prior elicitation literature is reviewed and categorized in these terms. This allows recognizing under-studied directions in prior elicitation research, finally leading to a proposal of several new avenues to improve prior elicitation methodology.

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Section: Bayesian Modelling Workflowmentioning

confidence: 99%

Prior knowledge elicitation: The past, present, and future

Mikkola¹,

Martin²,

Chandramouli³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…This framework has been used in multiple applications, see e.g. Siivola et al (2021). The optimal design methodology which we consider is, however, different from the one used by O'Hagan (1978).…”

Section: Introductionmentioning

confidence: 99%

Robust optimal designs using a model misspecification term

Tsirpitzi

Miller

Burman

2023

Metrika

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Much of classical optimal design theory relies on specifying a model with only a small number of parameters. In many applications, such models will give reasonable approximations. However, they will often be found not to be entirely correct when enough data are at hand. A property of classical optimal design methodology is that the amount of data does not influence the design when a fixed model is used. However, it is reasonable that a low dimensional model is satisfactory only if limited data is available. With more data available, more aspects of the underlying relationship can be assessed. We consider a simple model that is not thought to be fully correct. The model misspecification, that is, the difference between the true mean and the simple model, is explicitly modeled with a stochastic process. This gives a unified approach to handle situations with both limited and rich data. Our objective is to estimate the combined model, which is the sum of the simple model and the assumed misspecification process. In our situation, the low-dimensional model can be viewed as a fixed effect and the misspecification term as a random effect in a mixed-effects model. Our aim is to predict within this model. We describe how we minimize the prediction error using an optimal design. We compute optimal designs for the full model in different cases. The results confirm that the optimal design depends strongly on the sample size. In low-information situations, traditional optimal designs for models with a small number of parameters are sufficient, while the inclusion of the misspecification term lead to very different designs in data-rich cases.

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“…Various examples utilize splines to capture the form of covariates (Lai, Shih and Wong, 2006), or to describe time-varying parameters in cases where constant models are insufficient (Li et al, 2002). More recently, Gaussian process models were applied to evaluate potentially non-linear maturation effects based on age (Siivola, Weber and Vehtari, 2021). Semiparametric models for primary analysis of concentration-time functions in pharmacokinetics have been presented sporadically, but appear to have received limited attention.…”

Section: Introductionmentioning

confidence: 99%

Applying Hierarchical Generalized Additive Models to Non-Compartmental Analysis of Pharmacokinetic Data

Woodward

2023

Preprint

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Non-compartmental analysis (NCA) is a popular strategy for obtaining estimates of pharmacokinetic parameters, while requiring both minimal structural assumptions, and limited input by the analyst. As typically applied, its scope and depth are constrained by its statistical simplicity. Embedding the NCA within a hierarchical generalized additive model (HGAM) may facilitate the simultaneous analysis of data from multiple subjects, estimation of covariate effects in one stage, and implementation of censored responses, similarly to the capabilities of nonlinear multilevel models as widely applied in pharmacometrics. HGAM is an interesting extension to multilevel linear models that allows the effects of predictors to be implemented as smooth functions, which has been widely implemented in various disciplines to nonlinear trends, including for longitudinal data. This approach extends the capability of previous implementations of spline-based methods applied to NCA, within an accessible workflow in open software. Application of HGAM to two example datasets, one describing oral drug administration, and one describing IV and oral drug administration with categorical covariates and censoring, illustrates the overall approach, including parameter estimation, visualization and model checking, and uncertainty quantification. A Bayesian approach to estimation facilitates interpretable expressions of the uncertainty in individual parameters, population parameters, and functions of parameters such as contrasts.

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Qualifying drug dosing regimens in pediatrics using Gaussian processes

Cited by 5 publications

References 23 publications

Prior knowledge elicitation: The past, present, and future

Prior knowledge elicitation: The past, present, and future

Robust optimal designs using a model misspecification term

Applying Hierarchical Generalized Additive Models to Non-Compartmental Analysis of Pharmacokinetic Data

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