inst/shiny/multiarm/design_dtl_bern_setting.md

In mjg211/multiarm: Design of single- and multi-stage multi-arm clinical trials

The trial will be designed to compare $K$ experimental treatments to a shared control arm. Response $X_{ik}$, from patient $i=1,\dots,n_k$ in arm $k=0,\dots,K$, will be assumed to be distributed as $X_{ik} \sim Bern(\pi_k)$. Then, the hypotheses to be tested will be: $$ H_k : \tau_k = \pi_k - \pi_0 \le 0,\ k=1,\dots,K.$$ The global null hypothesis, $H_G$, will be: $$ \pi_0 = \cdots = \pi_K. $$ The global alternative hypothesis, $H_A$, will be: $$ \pi_1 = \cdots = \pi_K = \pi_0 + \delta_1. $$ The least favourable configuration for experimental arm $k$, $LFC_k$, will be: $$ \pi_k = \pi_0 + \delta_1,\ \pi_1 = \cdots = \pi_{k-1} = \pi_{k+1} = \cdots = \pi_K = \pi_0 + \delta_0. $$ Here, $\delta_1$ and $\delta_0$ are interesting and uninteresting treatment effects respectively.

mjg211/multiarm documentation built on Jan. 19, 2024, 8:21 a.m.