Human Predictions Watertown, Massachusetts, United States
Background: Methods for noncompartmental half-life calculation have not substantially changed in the past 50 years. Briefly, the method is to estimate the initial fit to a multi-exponential curve by selecting the minimum weighted sum of squared residuals by weighted least-squares regression of each set of ≥3 data points including points from the last observed concentration toward the time of maximum concentration. Tobit regression is a method to estimate linear models with censored data. We describe a method for applying Tobit regression to estimate the half-life in data with or without BLQ concentrations. Methods: Pharmacokinetic data were simulated using R (version 4.3.0), mrgsolve (version 1.0.9), and targets (version 1.2.2). A 1-, 2- or 3-compartment PK mamillary model was used for simulation with optional target-mediated drug disposition, and 10, 20, or 40% proportional residual variability were simulated.
Half-life was estimated either with standard methods minimizing the adjusted r-squared value or with Tobit regression minimizing the residual standard error. Results: Due to the inclusion of BLQ which are typically after Tlast, Tobit regression had fewer negative half-life estimates than least-squares regression with 0.3% and 1.4%, respectively. Tobit regression performed better by estimating the half-life closer to the theoretical half-life in most scenarios. Tobit regression performed especially well by not under-estimating the half-life as often as least-squares. Across almost all scenarios, Tobit regression out-performed linear regression. Conclusion: A novel tobit regression method for including BLQ concentrations in half-life calculations has been developed. The tobit regression performs better than standard least-squares regression, especially by preventing under-estimation of half-life when concentrations fall below the limit of quantification prior to tlast.
The tobit regression method has been included as an optional method in the PKNCA package for R and is currently available for use.
