Application of Optimal Design for Disease Progression Studies
Stefanie Hennig1, Sebastian Ueckert1,2, Joakim Nyberg1, Andrew Hooker1, Mats O. Karlsson1
1.Department of Pharmaceutical Biosciences, Uppsala University, Sweden. 2. DFG Research Center MATHEON and Freie Universitaet Berlin, Germany
Objectives: Disease progression (DP) studies are performed to obtain information on the effect of drugs for the long term prognosis on a disease. There were two aims of this study: firstly to demonstrate the application of optimal design to optimizing period lengths (delayed start, treatment, wash-out) for DP studies, secondly to characterize drug effects across different mechanisms and magnitudes for model discrimination by using uncertainty on parameter values and the expectation of the determinant (ED) for optimization.
Methods: Three drug effects (protective (P), symptomatic (S) and protective+symptomatic (PS)) were used in combination with a linear natural history model. ED-optimality was performed using PopED v.2 to optimize start and stop time of the treatment during the study. One general study design was chosen for all experiments, which had a total study length of 12 time units and 13 evenly spread fixed observations times. However, study designs without wash-out periods, with more or less samples or observation times were tested, as well as simultaneous optimization on period lengths and sampling times. ED-optimality with a uniform distribution around effect parameters was employed to obtain the power to differentiate between different effects within this distribution by evaluating the 95% parameter estimate confidence ellipses. Furthermore, simulation (n=1000) and re-estimations were performed using NONMEM VI. RMSE and ME were calculated to evaluate the performance of the uniform ED-design on parameter estimations for 9 particular effect combinations.
Results: For the P model an optimal start time was found at time 0 and the stop time at time 5.95; for a drug with S effect the start was at 2.48 time units and the stop at 8.24 and for a drug with a PS effect the optimal start was at 0.32 and the stop at 5.61. An efficiency loss of 10-40% on average per parameter was found if no observations were taken during the wash-out period. Simultaneous optimization on sampling times and treatment period improved the efficiency of the designs by 35-50%. Additionally, the relative merits of extending the study length compared to increasing the number of samples per individual can be shown.
The designs optimized for a uniform distribution of effects showed good performance in comparison with designs optimal for a specific effect. However confidence regions spanning large parts of the parameter range made differentiating between some close effects impossible. The RMSE for 92% of the fixed effect parameters was under 20% for the 9 tested effect combinations.
Conclusions: We believe that the results shown in this study illustrate how DP study designs can benefit from formal optimal design analysis. Additionally we can illustrate how ED-optimality can be used to optimize for a wide range of effects.
 Nyberg J, Karlsson MO, Hooker A. Sequential versus simultaneous optimal experimental design on dose and sample times. PAGE 16 (2007) Abstract 1160 [http://www.page-meeting.org/?abstract=1160].