Suppose $T$ is a Bernoulli random variable, such that $T = 1$ with probability $s$, $s$ is not known.
I am interested in checking hypothesis $H_1$ that $s \neq 1/2$ ($H_0$ is that $s = 1/2$). One way to do that is to get some 100K of realizations of $T$, and run the binomial test, check the p-value etc. However, sometimes $s$ is pretty far from $1/2$, and in that case I want to stop my experiment as early as possible once I've got enough evidence to reject $H_0$ (low $s$ means that the experiment participants are 'suffering', and generally I want to avoid that; high $s$ means that I can improve life for everyone and generally I want to do that asap).
My idea was to deploy a sequential testing procedure: I split the experiment in 5 equally sized stages (e.g. 20K realizations each) and after each stage I calculate p-values, compare to the predefined thresholds, and decide to stop the experiment or to continue. This idea is inspired by O'Brien & Fleming procedure (O'Brien & Fleming, Biometrics '79).
There exist quite extensive literature on sequential testing, R package gsDesign, etc. However, as the topic is mostly studied in the medical context, usually a control/test split is assumed. Thus I failed to find a guidance how to design the sequential experiment protocol for my set-up: given pre-fixed values for Type I and II errors, the number of stops, I want to find p-value thresholds (or other stopping criteria) for each of the stops.
Could anyone provide me with a relevant link?