Optimal window design of blood pressure time measurements in hypertensive dippers and non-dippers using ABPM: Application of the compound D-optimality approach.
Marion Dehez (1), Kayode Ogungbenro (2), Emmanuelle Foos-Gilbert(3), Stéphanie Ragot (1) and Marylore Chenel (3)
(1) CIC Inserm 802, CHU La milétrie 86021 Poitiers ;(2) Centre for Applied Pharmacokinetic Research, University of Manchester, United Kingdom ; (3) Institut de Recherches Internationales Servier, France.
Objectives: Ambulatory Blood Pressure Monitoring (ABPM) is a non invasive method whose both diagnostic value and prognostic significance have been recognized for many years. The ABPM allowed to distinguish two populations regarding their 24-h BP profiles: the dippers, who experience at night at least a 10% decrease of daytime BP values, and the non-dippers, who have a BP decrease at night less than 10% of daytime values. Their respective BP rhythm has been described by a population modeling approach (1). In clinical trials, ABPM when performed on 24-hour provide about 100 readings. Readings have to meet strong quality criteria and 75% of the recordings have to be present over the 24 h period in order to calculate means and standard deviations. Those which do not meet the quality criteria are rejected resulting in an important loss of information.
Our objective was to show that ABPM analysis by population approach with an optimal window design allows to take benefit of the total information collected during clinical trials and to reduce the number of records needed. Hence, the minimum number and the optimal measurement time windows for 24-h BP cycle model parameter estimation in dippers and non-dippers were determined.
Methods: Models previously developed (1) describing 24-h SBP (Systolic Blood Pressure) variations in dippers and non-dippers were used to determine fixed optimal measurement times (step1) and then optimal windows (step2). This was done simultaneously in dippers and non-dippers using the compound D-optimality approach (3). This approach allows to optimize measurement times for population parameter estimation in a population made of 2 sub-populations (i.e. 2 models). Each model consisted in 7 fixed-effect parameters with interindividual variability and an additive residual error model. The design domain consisted in times over 24 h without any constraints and there was only one group with 100 subjects. The maximization procedure was based on a local exact design optimization performed using the modified Fedorov exchange algorithm (2). Then, optimal time windows were determined using the approach described by Graham and Aarons (4).
For both populations 1000 simulations and estimations were performed using NONMEM to evaluate optimal fixed time designs as well as optimal sampling windows designs.
Results: The best design without duplicated times and a satisfactory level of accuracy for parameter estimation (less than 20% for fixed effect parameters) was with 8 measurement times. The best compromise between a satisfactory level of efficiency and windows wide enough was with 95% level of efficiency giving 3 h-time windows. Optimal windows were: [0:35-2:35 am], [3-5 am], [6-8 am], [9:15-11:15 am], [0:35-2:35 pm], [3:20-5:20 pm], [6:30-8:30 pm] and [9:30-11:30 pm]. Design evaluations showed that the coefficient of variation of standard error (CVSE) for all parameters computed from the population Fisher information matrix were in agreement with those computed empirically from simulations and estimations.
Conclusion: The compound D-optimality approach was particularly adapted to our concern of joint determination of optimal measurement times in 2 sub-populations. Eight optimal 3 h-time windows were found satisfying to estimate model parameters in both dippers and non-dippers.
Thus, the analyse of ABPM by population approach with an optimal design would allow to avoid an important loss of information and the number of records needed to interpret the baseline ABPM during clinical trials could be dramatically reduced. Quality criteria for ABPM during clinical trials should be re-evaluated if data are analysed by population approach.
References:
[1] Dehez Marion, Chenel Marylore, Jochemsen Roeline, Ragot Stéphanie. Population modeling approach of blood pressure circadian variations using ambulatory monitoring in dippers and non-dippers. PAGE 15 (2006) Abstr 989 [www.page-meeting.org/?abstract=989].
[2] Ogungbenro Kayode, Graham Gordon, Gueorguieva Ivelina, Aarons Leon. The use of a modified Fedorov exchange algorithm to optimize sampling times for population pharmacokinetic experiments. Comput Methods Programs Biomed. 2005; 80(2):115-25.
[3] Atkinson AC, Bogacka B. Compound D- and D-s-optimum designs for determining the order of a chemical reaction. Technometrics. 1997; 39: 347-56.
[4] Graham Gordon, Aarons Leon. Optimal blood sampling time windows for parameter estimation in population pharmacokinetic experiments. Statistics in Medicine. 2006; 25: 4004-19.