Problem #3:

You are helping your graduate school advisor put together a grant proposal, and she has specifically asked you to write the section on sample size calculations.There is conflicting evidence about whether vitamin D reduces risk for influenza.Therefore, the proposed study will be a one-year randomized trial to investigate the potential protective effect of vitamin D supplementation on flu incidence.Depending on the specific strains circulating during a given flu season, the cumulative incidence of flu in the adult population can range from 10-20%.Because it will take more than a year to get the study funded and ready for recruitment, you need to budget enough money to enroll a sufficient number of participants regardless of what the flu incidence will be during that particular flu season.Therefore, it is essential that you consider the sample size you will need for a range of potential cumulative incidences (i.e., 10%, 15%, or 20%).Furthermore, while some studies suggest that vitamin D supplementation may be associated with a 40% reduced risk of flu (i.e. a CIR of 0.6), other studies have only found a 20% reduced risk.Your advisor, therefore, hypothesizes that you will observe a 30% reduced risk, which would be a large enough reduction to gain clinical interest in recommending vitamin D as a preventative intervention against flu.You'd like to see how the estimated sample size would change depending on what the true protective effect is (i.e., 20%, 30%, or 40% reduced risk).Finally, you plan to recruit an equal number of participants into the two study arms, allow for the standard alpha of 0.05, and since this is a randomized trial, you would prefer to have 90% power to observe your hypothesized effect size.

Construct the table that you will present to your advisor that satisfies her criteria and assumptions related to sample size.Provide all of the assumptions/inputs used for your calculations in either the table title or in accompanying text. What final sample size would you recommend to her and why did you choose this sample size?

Table X.

Cum. Incidence of Influenza in General Population

Minimum Detectable Cumulative Incidence Ratio