Question

You are conducting a large concurrent cohort study evaluating the association between drinking alcohol and the likelihood of contracting an STD over the course of a year. After data collection has been completed, your 2 x 2 table looks like the table below (these numbers are hypothetical): Original Data Alcohol No alcohol Total STD 295 160 455 No STD 2,116 929 6,045 Total 2,411 4,089 6,500 3. Alcohol and substance abuse are commonly underreported, as are STDs, due to social desirability bias. Imagine for the sake of this example that these numbers were obtained by biomarker for the alcohol consumption and routine screening of all participants for STDs. (Note that both of these have methodological limitations, such as biomarker variability and limits on sensitivity for STD screening challenges with proper intervals and so forth. But for this example we will imagine this is the gold standard, or "truth".) Calculate the RR (truth) for this study. 4. Now imagine that the data were collected by self-report for alcohol consumption and by routine screening for STDs Because of a combination of social desirability bias and impaired recall, participants underestimated their alcohol consumption by 25% for both those with and without STDs. a) What is the RR now? b) Is this new RR biased away from or toward the null? c) Does it underestimate or overestimate the true RR? Accounting for 25% underestimate of alcohol use: STD No STD 2,116 3,929 6,045 Total 1808 4692 6,500 Alcohol 295 No alcohol 160 Total 455

Answer 1

3) We have to test that if there is any association between drinking alcohol and contracting an STD We calculate relative risk here Let given below 2*2 contingency table STD No std Alcohol No alcohol Total a+b c+d a+b+c+d a+c b+d Then Relative riskis given by RR=a/(a+b) c/c+d) In our case a=295 c=160 a+b=2411 c+d=4089 Hence RR given by

RR-a/(a+b)_295/2411 0.1224 c/c+d) 160/4089 0.0391 = 3.13 In this case we have a=295 c=160 a+b=1808 c+d=4692 Then RR given by RR-a/(a+b)_295/1808 c/c+d) 160/4692 = 4.78 0.1632 0.0341 b) Since here null hypothesis is there is no association between drinking alcohol and contracting an STD and for null hypothesis to be true RR should be equal to 1 while here its 4.783 hence RR is biased away from Null as actual RR is 3.13 Since True RR is 3.13 while in this case its 4.783 hence its overestimate the true RR