Optimal Design for Population PK/PD Models with Serial Sampling
Robert Gagnon and Sergei Leonov
Abstract: In various pharmaceutical applications repeated measurements are taken from each subject, and model parameters are estimated from the collected data. Examples include dose response modeling and PK/PD studies with serial blood sampling, among others. The quality of the information in an experiment is reflected in the precision of estimates of model parameters, which is traditionally measured by their variance-covariance matrix. In this paper we concentrate on the example of a clinical PK study where multiple blood samples are taken for each enrolled patient, which leads to nonlinear mixed effects regression models with multiple responses. The sampling scheme for each patient is considered a multidimensional point in the space of admissible sampling sequences. We demonstrate how to optimize the precision of parameter estimates by finding the best number and allocation of sampling times. It is shown that a reduced number of samples may be taken without significant loss of precision of parameter estimates. Moreover, our approach allows for taking experimental costs into account which leads to a more meaningful comparison of sampling schemes and to potential cost savings.
Optimal Design of Multicentre Clinical Trials with Random Enrolment
Vladimir Anisimov, Valerii Fedorov and Byron Jones
ABSTRACT. Fedorov et al. (2002) gave formulae for the variance of the estimated ECRT (expected combined response to treatment) and the optimal number of centres and total number of patients to use in a multicentre trial in a setting where the number of patients on each treatment arm in each centre was considered fixed. Here we extend these results to the setting where enrolment at each centre is considered random. We show that such randomness inflates the size of the variance of the estimated ECRT and give formulae for amount of inflation. We also show that this inflation factor is increased if the enrolment rates vary over the centres.
The time to complete enrolment is a crucial component in the problem of optimal study design. We consider the time to complete enrolment under three different policies: competitive, balanced and restricted. For the first two of these we give explicit formulae that may be used to calculate the probability density function of the time to complete enrolment. For restricted enrolment we illustrate how the distribution of the time to complete enrolment may be calculated using simulation.
Finally for “pairwise” competitive enrolment we give formulae for the optimal number of centres and total number of patients for the case in which a risk function takes into account randomness in enrolment. For more realistic enrolment scenarios we can apply numerical optimization based on simulation.
Estimation of the Treatment Difference in Multicentre Trials Taking into Account Random Enrolment
Valerii Fedorov, Byron Jones, Matthew Jones and Anatoly Zhigljavsky
ABSTRACT. The three fixed effects estimators of a treatment difference are compared under conditions of random enrolment in a multicentre clinical trial. These comparisons are done assuming five different enrolment schemes. The estimators are compared via simulation using their expected mean squared errors. Unlike previous discussions of these three estimators we take explicit account of the effect of centres that fail to enrol patients to one or both treatment arms.
Within each centre we assume enrolment follows a Poisson process and consider the two situations where the mean rate of this process is the same in every centre and where the mean rates are sampled from a gamma distribution. The effect of patient drop-out is studied as well as the effect of increasing the number of centres.
Simulations show that for many sound scenarios the simpler estimator corresponding to the simplest model works better, even for the cases when data are generated by more complex models.
Comparison of Different Filters in Detection of Weak Signals for Large Size Contingency Tables
Valerii Fedorov, Xiwu Lin, and Rita Patwardhan
Abstract: Detection of weak signals for large size contingency tables is a common task arising from post marketing drug adverse event detection. By using different measures of the strength for the potential signals, different filters may be developed. Traditional statistical methods such as PRR and chi-squared methods targeting the association in contingency tables have been used in such context. Recently a few methods based on Bayesian ideas have been proposed and applied in such kind of application. In this work, we perform statistical comparison of these different methods and investigate the relationships among these different methods. Motivated by the existing methods, we propose a generalized approach which comprises all the discussed methods as its particular cases and offers a way for constructing various alternatives.
