Bayesian Response-Adaptive Design Analysis with BRADA
In brada: Bayesian Response-Adaptive Design Analysis

wzxhzdk:0 # Introduction The getting started vignette illustrated the basic features of the `brada` package. In this vignette, we illustrate how to monitor a running trial with the `brada` package. Note that there are more vignettes which illustrate

- how to apply and calibrate the predictive evidence value design with the `brada` package. This vignette is hosted at the Open Science Foundation. - how to monitor a running clinical trial with a binary endpoint by means of the `brada` package

# Monitoring a trial To apply the package, first, load the \code{brada} package: wzxhzdk:1 Monitoring a trial with the `brada` package is straightforward through the `monitor` function. Suppose we have analyzed and calibrated a design according to our requirements, and end up with the following design: wzxhzdk:2 Now, suppose the trial is performed and the first ten patients show the response pattern $(0,1,0,0,0,0,0,1,0,0)$, where $1$ encodes a response and $0$ no response. Thus, there are $2$ responses out of `nInit=10` observations. To check whether the trial can be stopped for futility or efficacy based on `theta_L=0.1` and `theta_U=1`, we run the `monitor` function as follows: wzxhzdk:3 Thus, the results indicate that we should stop for efficacy. This is intuitively in agreement with the notion that $2$ responses out of $10$ observations are quite unlikely if $H_1:p>0.4$ would hold. Note that it is not important which value the `p_true` or `nsim` arguments had in the `brada` call which returned the object `design`. We could also have simulated data under `p_true=0.2` and `nsim=3000` or some other values, the monitor function only takes the `brada` object and applies the design specified in the `method` argument of the object, in this case, the predictive probability design. All necessary arguments are identified by the `monitor` function automatically. The predictive evidence value design can be monitored analogue, for details on the design and its calibration see the Open Science Foundation. *** wzxhzdk:4 ## References Berry, S. M. (2011). Bayesian Adaptive Methods for Clinical Trials. CRC Press. Kelter, R. (2022). The Evidence Interval and the Bayesian Evidence Value - On a unified theory for Bayesian hypothesis testing and interval estimation. British Journal of Mathematical and Statistical Psychology (2022). https://doi.org/10.1111/bmsp.12267 Kelter, R. (2021b). Bayesian Hodges-Lehmann tests for statistical equivalence in the two-sample setting: Power analysis, type I error rates and equivalence boundary selection in biomedical research. BMC Medical Research Methodology, 21(171). https://doi.org/10.1186/s12874-021-01341-7 Kelter, R. (2021a). fbst: An R package for the Full Bayesian Significance Test for testing a sharp null hypothesis against its alternative via the e-value. Behav Res (2021). https://doi.org/10.3758/s13428-021-01613-6 Kelter, R. (2020). Analysis of Bayesian posterior significance and effect size indices for the two-sample t-test to support reproducible medical research. BMC Medical Research Methodology, 20(88). https://doi.org/https://doi.org/10.1186/s12874-020-00968-2 Morris, T. P., White, I. R., & Crowther, M. J. (2019). Using simulation studies to evaluate statistical methods. Statistics in Medicine, 38(11), 2074–2102. https://doi.org/10.1002/SIM.8086 Pereira, C. A. d. B., & Stern, J. M. (2020). The e-value: a fully Bayesian significance measure for precise statistical hypotheses and its research program. São Paulo Journal of Mathematical Sciences, 1–19. https://doi.org/10.1007/s40863-020-00171-7 Rosner, G. L. (2021). Bayesian Thinking in Biostatistics. Chapman and Hall/CRC. Rosner, G. L. (2020). Bayesian Adaptive Designs in Drug Development. In E. Lesaffre, G. Baio, & B. Boulanger (Eds.), Bayesian Methods in Pharmaceutical Research (pp. 161–184). CRC Press. Rouder, Jeffrey N., Paul L. Speckman, Dongchu Sun, Richard D. Morey, and Geoffrey Iverson. 2009. “Bayesian t tests for accepting and rejecting the null hypothesis.” Psychonomic Bulletin and Review 16 (2): 225–37. https://doi.org/10.3758/PBR.16.2.225