RARtrials is designed for simulating some popular response-adaptive randomization methods in the literature with comparisons of each treatment group to a control group under no delay and delayed (time between treatment and outcome availability) scenarios. All the designs are based on one-sided tests with a choice from values of 'upper' and 'lower'. The general assumption is that binary outcomes follow Binomial distributions, while continuous outcomes follow normal distributions. Additionally, the number of patients accrued in the population follows a Poisson process and users can specify the enrollment rate of patients enrolled in the trial.

Install RARtrials from CRAN with:

install.packages('RARtrials')

Alternatively, install the RARtrials package from github with:

#install.packages('devtools')
devtools::install_github("yayayaoyaoyao/RARtrials")

There are two main groups of functions: those for simulating trials, which begin with sim_, and other functions that constitute the code for sim_ with varying names. Functions included in this R package are as follows:

• sim_RPTW for the Randomized Play-the-Winner rule with binary outcomes in two-armed trials (Wei and Durham, 1978);

• sim_dabcd_small_var for the doubly adaptive biased coin design targeting Neyman allocation and RSIHR allocation using minimal variance strategy with binary outcomes in trials with up to five arms (Biswas and Mandal, 2004; Atkinson and Biswas, 2013) and dabcd_small_var calculates the allocation probabilities with available data using this method;

• sim_dabcd_max_power for the doubly adaptive biased coin design targeting Neyman allocation and RSIHR allocation using maximal power strategy with binary outcomes in trials with up to five arms and up to three arms respectively (Tymofyeyev, Rosenberger, and Hu, 2007; Jeon and Hu, 2010; Bello and Sabo, 2016) and dabcd_max_power calculates the allocation probabilities with available data using this method;

• sim_A_optimal_known_var, sim_A_optimal_unknown_var, sim_Aa_optimal_known_var, sim_Aa_optimal_unknown_var, sim_RSIHR_optimal_known_var and sim_RSIHR_optimal_unknown_var for Neyman allocation ($A_a$-optimal allocation and $A$-optimal allocation) and generalized RSIHR allocation subject to constraints for continuous outcomes with known and unknown variances in trials with up to five arms (Sverdlov and Rosenberger, 2013; Biswas and Mandal, 2004; Atkinson and Biswas, 2013);

• sim_brar_binary, sim_brar_known_var and sim_brar_unknown_var for Bayesian response-adaptive randomization using the Thall & Wathen method for binary outcomes, continuous outcomes with known and unknown variances in trials with up to five arms (Thall and Wathen, 2007); brar_select_au_binary, brar_select_au_known_var and brar_select_au_unknown_var can select appropriate $a_U$ using this method under null hypotheses; Functions start with pgreater_ calculate the posterior probability of stopping a treatment group due to futility around $1%$; Functions start with pmax_ calculate the posterior probability that a particular arm is the best in a trial; convert_gamma_to_chisq, convert_chisq_to_gamma and update_par_nichisq are particular set-up for continuous outcomes with unknown variances;

• sim_flgi_binary, sim_flgi_known_var and sim_flgi_unknown_var for the forward-looking Gittins index rule and the controlled forward-looking Gittins index rule for binary outcomes and continuous outcomes with known and unknown variances in trials with up to five arms (Villar, Wason, and Bowden, 2015; Williamson and Villar, 2019); flgi_cut_off_binary, flgi_cut_off_flgi_known_var and flgi_cut_off_flgi_unknown_var can select cut-off values at the final stage for statistical inference; Gittins provides Gittins indices for binary reward processes and normal reward processes with known and unknown variance for certain discount factors.