The predictive distribution of the residual variability in the linear-fixed effects model for clinical cross-over trials

• Published in: Biometrical journal Vol. 58; no. 4; pp. 797 - 809
• Main Authors: Bertsche, Anja, Nehmiz, Gerhard, Beyersmann, Jan, Grieve, Andrew P.
• Format: Journal Article
• Language: English
• Published: Germany Blackwell Publishing Ltd 01-07-2016; Wiley - VCH Verlag GmbH & Co. KGaA
• Subjects: Bayes Theorem; Bayesian; Cross-over; Cross-Over Studies; Humans; Linear Models; Pharmacokinetics; Precision; Predictive distribution; Probability; Sample Size; Trial planning; Precision; Cross-over; Predictive distribution; Trial planning; Bayesian
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/bimj.201500245

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.