Predictor Identification in Time-to-Event Analyses
C. Steven Ernest II and Andrew C. Hooker
Department of Pharmaceutical Biosciences, Uppsala University, Sweden, Eli Lilly and Company, Indianapolis, IN
Objectives: Analysis of time-to-event data can provide valuable insight in designing appropriate dosing regimens to maximize the benefit/risk ratios. When these events occur relatively rapid in comparison to long term therapy, or time of onset is a primary outcome, identification of the appropriate predictors of early exposure are paramount to accurately determining dosing. The aim of the analysis was to examine influence of sample size, between subject variability on oral absorption and range of time-to-event parameter estimates on predictor identification.
Methods: Data were simulated based on a 1-compartment pharmacokinetic model with between subject variability on Ka and Weibull distribution used to describe the time to an event. The sample sizes consisted of 175, 100 and 75 subjects receiving doses of 0-, 0.3-, 3-, 6- and 10-mg in equal proportion. Concentration was used as the predictor for the simulations based on an Emax model to describe drug effect with EC50 as the half maximal response concentration. An alternative model with dose as the predictor and ED50 as the half maximal response dose was used to compare the power of model discrimination and overall performance between the two predictors. Analysis was performed using NONMEM VI and PSN computed the summary statistics between the two different predictors.
Results: Power to correctly identify the true predictor (concentration) improved with increasing levels of between subject variability. However, the power was generally less than 80% with an N of 100 and 50. Estimates for the shape parameter and Emax did not deviate from the true values as much when concentration was used as the predictor as compared to dose. Estimation of the EC50 or ED50 value tended to be considerably over-estimated when simulated EC50 was low relative to the dosing regimen. However, as the simulated EC50 increased, estimation of EC50 was relatively less biased; whereas, estimated ED50 would project a considerably higher dose needed to achieve similar response. Examination of the relative probability density function demonstrated both predictors provided a reasonable concordance to the true model with respect to the median time of event. However, the maximum probability was impacted by changes in the scale, shape and Emax parameter estimates with changes in subject sample size.
Conclusions: Use of the Weibull distribution to describe time-to-event data using dose as the predictor when the true underling effect is driven by concentration can provide a reasonable estimation of the true model when sample sizes are relatively limited; however, doses based on the ED50 will be over-estimated. Examination of concentration as predictor should occur as sample sizes increase providing more power for model discrimination. Further work needs to examine the impact of between subject variability on clearance and volume of distribution in the pharmacokinetic model.