A clinical trial testing a drug for its anti-cancer effect enrolled 663 patients

Question

A clinical trial testing a drug for its anti-cancer effect enrolled 663 patients, including 321 patients were given placebos, and the rest were on experimental arm. After the treatments, there were 2 patients, who were taken placebos, were reported with undetected lymph nodes metastasis. While for the patients, who were given the drug, sixty-five had undetected lymph nodes metastasis.

1) By typing R command lines, using modified Wald method, calculate the CI of proportion at 95% confidence level for both the placebo-treated group and the drug-treated group.

2) Use R package (PropCIs) to find the CIs (exact CI, Wald method, and modified Wald method) of proportion for both groups. Copy & paste your command lines and results.

3) For which group, you can take a shortcut and estimate the result by using either Rule of Three, Rule of Five, or Rule of Seven? Which rule would apply? What is the result of using this rule? Show your calculations. Is it the same as what you got from using R?

Explanation / Answer

The rule of three is a writing principle that suggests that events or characters introduced in threes are more humorous, satisfying, or effective in execution of the story and engaging the reader.[1]The reader or audience of this form of text is also thereby more likely to remember the information conveyed. This is because having three entities combines both brevity and rhythm with having the smallest amount of information to create a pattern.[2][3] It makes the author or speaker appear knowledgeable while being both simple and catchy.

Slogans, film titles and a variety of other things have been structured in threes, a tradition that grew out of oral storytelling.[4] Examples include the Three Little Pigs, Three Billy Goats Gruff, and the Three Musketeers. Similarly, adjectives are often grouped in threes to emphasize an idea.

The Latin phrase "omne trium perfectum" (everything that comes in threes is perfect, or, every set of three is complete) conveys the same idea as the rule of three.

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