Time-to-Event Modeling of Left- or Right-Censored Toxicity Data in Nonclinical Drug Toxicology

Finding the right hazard function for time-to-event modeling: A tutorial and Shiny application

Parametric time-to-event analysis is an important pharmacometric method to predict the probability of an event up until a certain time as a function of covariates and/or drug exposure. Modeling is performed at the level of the hazard function describing the instantaneous rate of an event occurring at that timepoint. We give an overview of the parametric time-to-event analysis starting with graphical exploration by Kaplan-Meier plotting for the event data including censoring and nonparametric hazard estimators such as the kernel-based visual hazard comparison for the underlying hazard. The most common hazard functions including the exponential, Gompertz, Weibull, log-normal, log-logistic, and circadian functions are described in detail. A Shiny application was developed to graphically guide the modeler which of the most common hazard functions presents a similar shape compared to the data in order to guide which hazard functions to test in the parametric time-to-event analysis. For the chosen hazard function(s), the Shiny application can additionally be used to explore corresponding parameter values to inform on suitable initial estimates for parametric modeling as well as on possible covariate or treatment relationships to certain parameters. Moreover, it can be used for the dissemination of results as well as communication, training, and workshops on time-to-event analysis. By guiding the modeler on which functions and what parameter values to test and compare as well as to assist in dissemination, the Shiny application developed here greatly supports the modeler in complicated parametric time-to-event modeling.

Hi3 + 3: A model-assisted dose-finding design borrowing historical data

BACKGROUND

In phase I clinical trials, historical data may be available through multi-regional programs, reformulation of the same drug, or previous trials for a drug under the same class. Statistical designs that borrow information from historical data can reduce cost, speed up drug development, and maintain safety.

PURPOSE

Based on a hybrid design that partly uses probability models and partly uses algorithmic rules for decision making, we aim to improve the efficiency of the dose-finding trials in the presence of historical data, maintain safety for patients, and achieve a level of simplicity for practical applications.

METHODS

We propose the Hi3 + 3 design, in which the letter "H" represents "historical data". We apply the idea in power prior to borrow historical data and define the effective sample size (ESS) of the prior. Dose-finding decision rules follow the idea in the i3 + 3 design (Liu et al., 2020 [1]) while incorporating the historical data via the power prior and ESS. The proposed Hi3 + 3 design pretabulates the dosing decisions before the trial starts, a desirable feature for ease of application in practice.

RESULTS

In most cases we investigated, the Hi3 + 3 design is superior than the i3 + 3 design due to information borrow from historical data. Even when the historical data is incompatible with the current data, it is capable of maintaining a high level of safety for trial patients and comparable performances without sacrificing the ability to identify the correct MTD too much. Ilustration of this feature are found in the simulation results.

CONCLUSION

With the demonstrated safety, efficiency, and simplicity, the Hi3 + 3 design could be a desirable choice for dose-finding trials borrowing historical data.

Sex-dependent differences for larkspur (Delphinium barbeyi) toxicosis in yearling Angus cattle1

Larkspur (Delphinium spp.) poisoning is a long-term problem for cattle grazing on rangelands of western North America. Results from preliminary experiments have suggested that differences in larkspur toxicity may exist between heifers and bulls. The objective of this study was to compare the physiological responses of yearling Angus heifers, steers, and bulls with a standardized dose of Delphinium barbeyi and to test the hypothesis that the response is sex dependent. Clinical signs of intoxication, including muscle coordination and function, were measured 24 h after oral dosing with larkspur by walking the cattle at a pace of 5 to 6 km h-1 for up to 40 min on an oval dirt track. Due to the experimental methods used, the variation in susceptibility to larkspur was not quantifiable for walking times of 0 or 40 min or more. Larkspur susceptible animals that were not able to walk (0 min; 36% of the animals) or larkspur resistant animals that walked the entire test period of 40 min (9% of the animals) resulted in censored or truncated data. The statistical methods (censReg and lmec) were used to adjust for data truncation or censoring. The heifers were only able to walk -8.9 ± 3.9 min (65.5% censored on the left) compared with 13.2 ± 3.7 min for bulls and 15.9 ± 2.7 min for steers. When heifers were compared with bulls and steers together, heifers walked 23.4 ± 4.5 min less (P < 0.0001). Serum alkaloid concentrations were measured immediately before walking, and deltaline concentrations averaged 266 ± 28, 131 ± 20, and 219 ± 28 ng mL-1 for all heifers, steers, and bulls, respectively, and serum methyllycaconitine concentrations averaged 660 ± 46, 397 ± 32, and 612 ± 34 ng mL-1 for all heifers, steers, and bulls, respectively. The relative risk of a zero walk time for yearling heifers is 330% that of yearling bulls (P = 0.0008). These results suggest that yearling Angus heifers are more susceptible to larkspur intoxication and, when possible, heifers should be kept from grazing larkspur-infested rangelands as a simple management tool to reduce the risk of fatal poisoning.