Exercise A group of researchers in Baltimore, Maryland, is interested in conducting a study to test the hypothesis that genetic susceptibility to mutagens is related to lung cancer risk. The mutagen sensitivity assay (MSA) is useful for such as study because it provides an overall index of the genetically-based ability of individuals to repair DNA damage. The MSA protocol takes lymphocytes from subjects and cultures them, then exposes them to a dose of a mutagen such as gamma radiation to induce chromosome breaks. After allowing the cells to repair themselves for a short period of time, the number of remaining chromosomal breaks in a random sample of 50 cells from each subject is counted under a microscope. The number of chromosome breaks per cell (b/c) is considered a biomarker of susceptibility to DNA damage: the higher the number of b/c the higher the risk for mutagenic diseases such as tobacco induced lung cancer.The researchers conducted a pilot study and evaluated the MSA in 20 individuals - 10 with lung cancer and 10 without cancer. The mean b/c was 1.1 in the cases and 0.8 in the controls. The pooled standard deviation was 0.5 b/c. Now the researchers need to decide how many subjects should be recruited for the main study, for which 90% power is desired. The statistical inference test will be the student's T test. The sample size (i.e. the number of cases, using 1 control per case) will dictate how much grant money is needed for the study and how it will be spent, so there are many practical as well as scientific consequences to the problem of determining the best sample size. This exercise will show you how to approach this question, and you will see how alpha, power, the effect size, and measurement precision can affect the required sample size.

For this part of the exercise, we want to see the sample size consequences of hypothesizing different effect sizes, i.e. different levels of case-control differences in the mean b/c. Assume that power is 90% and alpha is 0.05, but consider the following effect sizes in the table below, while holding the other factors constant. Use the standard deviation observed in the pilot study. Start by calculating delta, then go to PS software with the appropriate entry numbers for all the other parameters. Enter the required samples sizes below. What trend do you see?

Scenario Two: Effect Size For this part of the exercise. we want to see the sample size consequences of hypothesizing different effect sizes. i.e. different levels of case-control differences in the mean bfc. Assume that power is 90% and alpha is 0.05, but consider the following effect sizes in the table below, while holding the other factors constant. Use the standard deviation obsewed in the pilot study. Start by calculating delta, then go to PS software with the appropriate entry numbers for all the other parameters. Enter the required samples sizes below. What trend do you see? bio in cases 1.1 1.25 1.30 1.50 bio in controls delta sample size Trend