Magnus Åstrand(1)
(1) AstraZeneca Research & Development, Clinical Pharmacology Science
Objectives: Wald type of confidence intervals are easily computed but relies on approximately normal distribution of estimators. Log likelihood profile intervals require more computation but, in contrast to Wald type of confidence intervals, they are invariant to any monotonic transformation of the parameter under investigation and are valid under less strict assumptions. This abstract presents a comparison of confidence intervals for the ED50 parameter of the 3-parameter Emax model.
Methods: Wald confidence intervals was computed for ED50 with and without using a log-transformation and was compared to log likelihood profile intervals. Data was simulated with a fixed set of doses but for a wide range of true values for ED50. Confidence intervals were computed and the coverage probability was estimated based on 10000 replicated data sets. All evaluations was performed in R. The nls function was used to compute Wald confidence intervals whereas a linear search based on the lm and logLik function was used to compute profile intervals.
Results: Maximum likelihood estimation of the Emax model requires iterative estimation techniques, but conditional on ED50 the 3-parameter Emax model is linear in the remaining 2 parameters and hence profiling can be done within the framework of linear regression models. With respect to total coverage probability Wald intervals without log transformation performed as good, or better, than those computed with a log transformation. However a much larger difference in favor of intervals with a transformation was seen on coverage probability of the lower and upper bound respectively. Lower bounds without the log transformation were consistently too optimistic whereas the upper was consistently too conservative. The reverse bias was seen for Wald intervals with a log transformation but only at lower or upper end of the studied values for ED50. The log likelihood profile upper and lower bounds overall hade coverage probability closest to the nominal level and hence further improved on the Wald intervals.
Conclusions: Although log likelihood profile intervals for the ED50 parameter of the 3-parameter Emax model are slightly more computational intensive a numerical stable algorithm is easily implemented in high level languages such as R. Compared to Wald type of confidence intervals log likelihood profile intervals have overall coverage probabilities closest to the nominal level.
Reference: PAGE 21 (2012) Abstr 2654 [www.page-meeting.org/?abstract=2654]
Poster: Model evaluation