Jixian Wang
Department of Medical Statistics, De Montfort University, U.K.
The two-stage procedure for nonlinear mixed model fitting is extended to fit pharmacokinetic/pharmacodynamic (PK/PD) data in cross-over trials. Two approaches are proposed and they differ mainly at the first stage. One approach fits a nonlinear model for each subject in each period. Another re-parameterises the model with sequence by period effects and fits a single re-parameterised model for each subject. At the second stage the effects such as treatment differences are estimated by least square or generalised least square procedures. We compare the two procedures in terms of their asymptotic properties and by simulation. Under some technical conditions the two procedures are asymptotically equivalent. In the simulations we found that under some parameter settings the second procedure had slightly smaller mean square errors than the first one. The two procedures were compared using a real data set with very small sample size and the results were quite different. In this paper we emphasis two issues which are specially important in two stage procedures.
(i) The bias of the estimated parameters in the first stage may be large and can not be reduced in the second stage.
(ii) The variance of the estimated parameters depends on the subject effects. We show that the bias should not be ignored (compared to the variance) when the number of subjects is comparable with the number of repeated measures within a subject.
The dependence of the variance makes the use of generalised least squares and the maximum likelihood procedures difficult. We suggest, as an alternative, to use the least squares and robust procedures for hypothesis tests and estimation of confidence intervals.
Reference: PAGE 6 (1997) Abstr 587 [www.page-meeting.org/?abstract=587]
Poster: oral presentation