Combining Model‐Based Clinical Trial Simulation, Pharmacoeconomics, and Value of Information to Optimize Trial Design

The Bayesian decision‐analytic approach to trial design uses prior distributions for treatment effects, updated with likelihoods for proposed trial data. Prior distributions for treatment effects based on previous trial results risks sample selection bias and difficulties when a proposed trial differs in terms of patient characteristics, medication adherence, or treatment doses and regimens. The aim of this study was to demonstrate the utility of using pharmacometric‐based clinical trial simulation (CTS) to generate prior distributions for use in Bayesian decision‐theoretic trial design. The methods consisted of four principal stages: a CTS to predict the distribution of treatment response for a range of trial designs; Bayesian updating for a proposed sample size; a pharmacoeconomic model to represent the perspective of a reimbursement authority in which price is contingent on trial outcome; and a model of the pharmaceutical company return on investment linking drug prices to sales revenue. We used a case study of febuxostat versus allopurinol for the treatment of hyperuricemia in patients with gout. Trial design scenarios studied included alternative treatment doses, inclusion criteria, input uncertainty, and sample size. Optimal trial sample sizes varied depending on the uncertainty of model inputs, trial inclusion criteria, and treatment doses. This interdisciplinary framework for trial design and sample size calculation may have value in supporting decisions during later phases of drug development and in identifying costly sources of uncertainty, and thus inform future research and development strategies.


Pharmacokinetic Models
Allopurinol used a one-compartment pharmacokinetic (PK) model with first-order absorption and elimination. There are covariate sub-models for clearance and volume of distribution and are inter-individual variability models for clearance and absorption. Parameter values and covariate model equations are given in Sections 2.2 and 3.2.
Febuxostat used a two-compartment PK model with first-order absorption and elimination. There are covariate sub-models for clearance and inter-individual variability models for clearance and absorption. Parameter values and covariate model equations are given in Sections 2.2 and 3.2.

System Model
The rate of change in each of the four pharmacodynamic model compartments: = 0 * 2 − 1 * 1 * − 2 * 1 * = 1 * 1 * * − 3 * = 2 * 1 * = 3 * and are the total time varying amounts of xanthine and uric acid in serum respectively; and are the total time-varying amounts of xanthine and uric acid in urine respectively; 0 , 1 , 2 and 3 are the rate parameters for the production of xanthine, xanthine to uric acid conversion, removal of xanthine to urine and removal of uric acid to urine, respectively. r is the ratio of uric acid to xanthine molar masses.
The pharmacodynamic model rate contsants can be calculated at steady-state according to: Where is the baseline amount of uric acid; is the baseline amount of xanthine; is the renal clearance of uric acid; is the renal clearance of xanthine; is the volume of uric acid distribution; is the volume of xanthine distribution; and are the molar masses of uric acid and xanthine respectively.

Trial Conduct Inputs
Subject specific attribute calculated according to:

Pharmacokinetic Inputs
Population typical values for parameters are first sampled using the column CV% according to (e.g. ):

Pharmacoeconomic Inputs
The sub-models for S(H) and trial costs are presentenced in the supplementary material. Drawing on the work of Hoyle 1 and Willan 2 , we predicted the number of patients who will receive febuxostat as a function of the annual disease incidence , the market share and a depreciation factor used to model real pharmaceutical price deflation according to: ( ) = ∑ ℎ=1 ℎ where ℎ = 1/(1 + ) ℎ and is the deflation index. The time horizon (H) was taken to be the number of years of patent protection (or market exclusivity) remaining when the drug reaches the market, which we have assumed to be 10 years. The values assumed for these inputs are given in Table   2. Finally, the cost of the trial was decomposed into fixed and variable elements, with the latter being proportional to the number of patients recruited. The separation of trial costs is shown below, where 1 and 2 are the numbers of patients recruited to the allopurinol and febuxostat trial arms respectively.