invest_3ed.pdf

# L what is the mean of the simulated lnrelrisk values

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(l) What is the mean of the simulated lnrelrisk values? Why does this value make sense? (m) What is the standard deviation of the lnrelrisk values? (n) Calculate the observed value of ln( p ˆ 1 / p ˆ 2 ) for this study. Where does this value fall (near in the middle or in the tail) of this simulated distribution of lnrelrisk values? Has the empirical p-value changed? (o) If you found the empirical p-value using ln( p ˆ 1 / p ˆ 2 ), it would be identical to the empirical p-value found in (i). Why? What did change about the distribution? [ Hint : What percentage of the simulated ln rel risk values are more extreme than ln(1.28), how does this compare to (h)?]

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Chance/Rossman, 2015 ISCAM III Investigation 3.9 229 Theoretical Result: It can be shown that the standard error of the ln relative risk is approximated by D B B C A A p p SE ² ± ² ² ± ¸ ¸ ¹ · ¨ ¨ © § 1 1 1 1 ˆ ˆ ln 2 1 where A , B , C , and D are the observed counts in the 2 × 2 table of data, with A and B representing the number of “successes” in the two groups. Having this formula allows us to determine the variability from sample to sample without conducting the simulation first. (p) Calculate the value of this standard error of the ln(rel risk) for this study. Interpret this value and compare it to the standard deviation from your simulated lnrelrisk values. (q) You may find this approximate is in the ballpark but not all that close. What assumption is made by the simulation that is not made by this formula? What if you made the same assumption in this formula? [ Hint : Think pooled p ˆ .] (r) Now that you have a statistic (ln rel risk) that has a sampling distribution that is approximately normal, what general formula can we use to determine a confidence interval for the parameter? (s) Calculate the midpoint, 95% margin-of-error, and 95% confidence interval endpoints using the observed value of ln(rel risk) as the statistic and using the standard error calculated in (p). (t) What parameter does the confidence interval in (s) estimate? (u) Exponentiate the endpoints of this interval to obtain a confidence interval for the ratio of the probabilities of developing influenza between these two treatments. Interpret this interval. (v) Is zero in this interval? Do we care? What value is of interest instead? A B C D A+C B+D
Chance/Rossman, 2015 ISCAM III Investigation 3.9 230 (w) Is the midpoint of this confidence interval for the population relative risk equal to the observed value of the sample relative risk? Explain why this makes sense. (x) Suppose you used this method to construct a confidence interval for each of the 1,000 simulated random samples that you generated in (f). Do you expect the value 1 to be in these intervals? All of them? Most of them? What percentage of them? Explain. (y) Compare the confidence interval you just calculated to the one given by the applet if you now check the 95% CI for relative risk box.

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