Stopping rules for phase I clinical trials with dose expansion cohorts

Many clinical trials incorporate stopping rules to terminate early if the clinical question under study can be answered with a high degree of confidence. While common in later-stage trials, these rules are rarely implemented in dose escalation studies, due in part to the relatively smaller sample size of these designs. However, even with a small sample size, this paper shows that easily implementable stopping rules can terminate dose-escalation early with minimal loss to the accuracy of maximum tolerated dose estimation. These stopping rules are developed when the goal is to identify one or two dose levels, as the maximum tolerated dose and co-maximum tolerated dose. In oncology, this latter goal is frequently considered when the study includes dose-expansion cohorts, which are used to further estimate and compare the safety and efficacy of one or two dose levels. As study protocols do not typically halt accrual between escalation and expansion, early termination is of clinical importance as it either allows for additional patients to be treated as part of the dose expansion cohort to obtain more precise estimates of the study endpoints or allows for an overall reduction in the total sample size

dfpk : An R-package for Bayesian dose-finding designs using Pharmacokinetics (PK) for phase I clinical trials

Background and objective Dose-finding, aiming at finding the maximum tolerated dose, and pharmacokinetics studies are the first in human studies in the development process of a new pharmacological treatment. In the literature, to date only few attempts have been made to combine pharmacokinetics and dose-finding and to our knowledge no software implementation is generally available. In previous papers, we proposed several Bayesian adaptive pharmacokinetics-based dose-finding designs in small populations. The objective of this work is to implement these dose-finding methods in an R package, called dfpk. Methods All methods were developed in a sequential Bayesian setting and Bayesian parameter estimation is carried out using the rstan package. All available pharmacokinetics and toxicity data are used to suggest the dose of the next cohort with a constraint regarding the probability of toxicity. Stopping rules are also considered for each method. The ggplot2 package is used to create summary plots of toxicities or concentration curves. Results For all implemented methods, dfpk provides a function (nextDose) to estimate the probability of efficacy and to suggest the dose to give to the next cohort, and a function to run trial simulations to design a trial (nsim). The sim.data function generates at each dose the toxicity value related to a pharmacokinetic measure of exposure, the AUC, with an underlying pharmacokinetic one compartmental model with linear absorption. It is included as an example since similar data-frames can be generated directly by the user and passed to nsim. Conclusion The developed user-friendly R package dfpk, available on the CRAN repository, supports the design of innovative dose-finding studies using PK information

Boosting the discriminatory power of sparse survival models via optimization of the concordance index and stability selection

Background When constructing new biomarker or gene signature scores for time-to-event outcomes, the underlying aims are to develop a discrimination model that helps to predict whether patients have a poor or good prognosis and to identify the most influential variables for this task. In practice, this is often done fitting Cox models. Those are, however, not necessarily optimal with respect to the resulting discriminatory power and are based on restrictive assumptions. We present a combined approach to automatically select and fit sparse discrimination models for potentially high-dimensional survival data based on boosting a smooth version of the concordance index (C-index). Due to this objective function, the resulting prediction models are optimal with respect to their ability to discriminate between patients with longer and shorter survival times. The gradient boosting algorithm is combined with the stability selection approach to enhance and control its variable selection properties. Results The resulting algorithm fits prediction models based on the rankings of the survival times and automatically selects only the most stable predictors. The performance of the approach, which works best for small numbers of informative predictors, is demonstrated in a large scale simulation study: C-index boosting in combination with stability selection is able to identify a small subset of informative predictors from a much larger set of non-informative ones while controlling the per-family error rate. In an application to discover biomarkers for breast cancer patients based on gene expression data, stability selection yielded sparser models and the resulting discriminatory power was higher than with lasso penalized Cox regression models. Conclusion The combination of stability selection and C-index boosting can be used to select small numbers of informative biomarkers and to derive new prediction rules that are optimal with respect to their discriminatory power. Stability selection controls the per-family error rate which makes the new approach also appealing from an inferential point of view, as it provides an alternative to classical hypothesis tests for single predictor effects. Due to the shrinkage and variable selection properties of statistical boosting algorithms, the latter tests are typically unfeasible for prediction models fitted by boosting