Optimal designs for clinical trials with second-order polynomial treatment effects

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Modeling

Background:

• Estimating treatment effects efficiently is crucial in clinical trials.
• The impact of intermediate measures on estimation efficiency requires careful consideration.
• Covariance structures and cost functions influence optimal trial design.

Purpose of the Study:

• To evaluate the efficiency of adding intermediate measures for treatment effect estimation.
• To investigate the influence of covariance structures and optimality criteria (Ds- or c-optimality) on design efficiency.
• To compare designs under fixed sample size and fixed budget constraints.

Main Methods:

• Modeling a second-order polynomial treatment effect with equidistant time-points.
• Analyzing various covariance structures (e.g., compound symmetry, auto-regressive).
• Comparing design efficiency under fixed sample size and fixed budget with a linear cost function.

Main Results:

• Efficiency gains from intermediate measures are highly dependent on the covariance structure.
• For a fixed sample size, gains are large for compound symmetry and small for auto-regressive structures.
• Under a fixed budget, three measures per subject are often efficient, but more may be needed if subject costs are high relative to repeated measure costs.

Conclusions:

• The optimal number of measures and time-points depends on the assumed covariance structure and cost parameters.
• Robust designs, such as those based on auto-regressive structures with measurement error, are preferable when the covariance structure is uncertain.
• Equidistant time-points are optimal or highly efficient for a second-order polynomial treatment effect with three repeated measures.