An Application of Optimal Design to Dose Selection and Sample Size Determination with a Negative-Binomial Exposure-Response Model for a Phase IIb Study
Gordon Graham
Novartis, Basel, Switzerland
Objectives: Previously, late stage clinical trials had been performed with drug Tx, enabling the development of an exposure-response model for a count endpoint, R. However, the drug exposure range from these studies did not adequately cover the range of concentrations below the IC50. The objective of this work was to determine the doses and sample size per dose for an additional study into drug Tx to better characterise the exposure-response relationship at concentrations below the IC50.
Methods: Doses of Tx were selected based on maximising the determinant of the information matrix, and sample size was based on the estimated relative standard error (RSE) on IC50 being less than 50%. [1] was used for developing the information matrix for the negative binomial exposure-response model. As a sensitivity analysis, doses and sample sizes were also assessed using a Poisson model for the count endpoint, R. The power of testing for a difference between dose groups was also performed based on model simulations.
Results: The selection of doses corresponding to concentrations mostly below the IC50 greatly improved the precision of the IC50 and other exposure-response model parameters. However, the RSE was not less than 50% for doses: 0Tx, 0.25Tx, 0.5Tx and 1Tx, where 1Tx is a reference dose group, and a total sample size of 1750 in a ratio 1:2:2:2. Combining the planned study with previous studies leads to a RSE for IC50 of 49.9% and allows the sample size to be reduced to 650 in a ratio of 1:5:5:2. The power of detecting a difference between 0.5Tx and 1Tx was low, but high power of comparing 0Tx and 1Tx.
Conclusions: Optimal design techniques were useful for assessing dose selection and sample size of this clinical trial.
References:
[1] Jerald F. LAWLESS; Negative binomial and mixed Poisson regression. The Canadian Journal of Statistics, Vol. 15, No. 3, 1987, 209-225