Nick Holford
Dept of Pharmacology & Clinical Pharmacology, University of Auckland, Private Bag 92019, Auckland, New Zealand
Objective: An important challenge for clinical pharmacologists is to be able to describe the time course of disease progression biomarkers and link this to the probability of clinical outcome events. A common event in clinical trials is subject dropout. Hu & Sale (1) described a joint modeling method for describing informative dropout using observations of a disease status biomarker and a subject dropout interval (the exact time of dropout was not known) or censoring time. They used NM-TRAN to construct code for -2 times the log likelihood (-2LL) for each type of observation. The objective of this study is to compare the NM-TRAN method with using a modified CCONTR subroutine to compute the objective function contributions and to evaluate the use of the likelihood ratio test for model discrimination.
Methods: The -2LL method has been compared with the CCONTR method using NM-TRAN to compute the likelihood for dropout and censoring events and the more usual predicted value for the continuous scale disease status. Biomarker status, dropout and censoring event data were simulated with NONMEM. Data was simulated and parameters estimated using a linear time course for the disease status and 3 dropout models (completely at random, random and informative). NONMEM was used to estimate parameters of the joint model. A randomization test was used to generate null distributions for the likelihood ratio (LR) obtained from data simulated with completely random dropout.
Results: The CCONTR method had more successful runs (79% vs 44%) and was 10% faster (100 runs) than the NM-TRAN method. The estimates of slope and parameter variability of the disease status were unbiased for both methods. The CCONTR method estimates of baseline hazard and informative dropout hazard were also unbiased but the NM-TRAN method estimates were significantly biased (+15% and -2% respectively). The root mean square error of all parameters was less than 20%. The null distribution of the LR obtained from random and informative dropout models fitted to completely random dropout data was similar to the chi-square distribution.
Conclusion: NONMEM can be used to estimate hazard function parameters for dropout models with acceptable bias and imprecision. The CCONTR method is preferable to NM-TRAN coding of -2LL for joint models. Model discrimination can be performed by assuming the likelihood ratio is approximately chi-square distributed.
Reference:
[1] Hu C, Sale ME. A joint model for nonlinear longitudinal data with informative dropout. J Pharmacokinet Pharmacodyn 2003;30(1):83-103.
Reference: PAGE 14 (2005) Abstr 722 [www.page-meeting.org/?abstract=722]
Poster: poster