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The predictive distribution of the residual variability in the linear‐fixed effects model for clinical cross‐over trials
Author(s) -
Bertsche Anja,
Nehmiz Gerhard,
Beyersmann Jan,
Grieve Andrew P.
Publication year - 2016
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201500245
Subject(s) - residual , statistics , mathematics , bayesian probability , prior probability , population , distribution (mathematics) , sample size determination , scale (ratio) , econometrics , algorithm , medicine , physics , quantum mechanics , mathematical analysis , environmental health
In the linear model for cross‐over trials, with fixed subject effects and normal i.i.d. random errors, the residual variability corresponds to the intraindividual variability. While population variances are in general unknown, an estimate can be derived that follows a gamma distribution, where the scale parameter is based on the true unknown variability. This gamma distribution is often used for the sample size calculation for trial planning with the precision approach, where the aim is to achieve in the next trial a predefined precision with a given probability. But then the imprecision in the estimated residual variability or, from a Bayesian perspective, the uncertainty of the unknown variability is not taken into account. Here, we present the predictive distribution for the residual variability, and we investigate a link to the F distribution. The consequence is that in the precision approach more subjects will be necessary than with the conventional calculation. For values of the intraindividual variability that are typical of human pharmacokinetics, that is a gCV of 17–36%, we would need approximately a sixth more subjects.