Calculate the sample size required for detecting at least one rare event

sample.size.for.rare.event.detection <- function(alpha = 0.05, M = 0.01)
{ 
    ## Purpose: Calculate the sample size required for detecting at least one rare event. 
    ## Arguments:
    ##   alpha: Type I Error. Sensitivity = 1 - alpha.
    ##   M: Probability for the rare event. Default to 1%. 
    ## Return: A minimum sample size required for the detection of rare event
    ##         with (1-alpha) probability (aka. confidence). 
    ## Author: Feiming Chen, Date:  8 May 2018, 10:36
    ## ________________________________________________

    N <- ceiling(log(alpha) / log(1 - M))
    N
}
if (F) {                                # Unit Test
    sample.size.for.rare.event.detection() # 299

    ## Detecting 0.5% event with 99% confidence
    sample.size.for.rare.event.detection(alpha = 0.01, M = 0.005) # 919
}

Below is an application example.