PS9 Spring 2023 solutions(1)

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PH717 Spring 2023 ©Boston University School of Public Health Problem Set 9: Bias Solutions ● Problem set 9 has 5 multipart questions and is worth 100 points. ● Please show your work and include R code where appropriate. ● For most questions, you can provide a full and thoughtful answer in 1-2 short sentences. 1. You have been asked to review a retrospective cohort study in a large HIV Treatment Clinic in South Africa to explore the association between history of use of Tenofovir (an HIV Antiretroviral drug) and risk of kidney disease (kidney disease yes/no) among HIV patients. The study determined Tenofovir use from a review of pharmacy records and kidney disease from clinical records. Over the study period patients using Tenofovir had 1.5 times the risk of kidney disease compared to patients who hadn’t used Tenofovir. The study authors report that while they believe the clinical records would capture all the kidney disease, not all the Tenofovir use would be captured by the pharmacy records and only 80% of the Tenofovir use would be correctly identified. Furthermore, they don’t believe the Tenofovir use classification to differ among those with and without kidney disease. The paper doesn’t address bias due to the recording of Tenofovir use. What type of bias does this study have? What is the direction of the bias? Briefly justify your reasoning. (10 points) Only 80% of the Tenofovir use was correctly identified. This is information bias. Because Tenofovir use is misclassified equally among the outcome groups, then we would have non-differential misclassification of exposure. This misclassification can theoretically lead to bias either towards or away from the null. However, non-differential misclassification of a dichotomous exposure is expected to lead – on average – to bias towards the null. Bias towards the null will on average lead us to underestimate (rather than overestimate) the association between Tenofovir and risk of kidney disease. 2. A case control study was conducted to measure the association between the long-term consumption of sugary beverages sweetened with high fructose corn syrup (HFCS) and the risk of coronary artery disease in persons aged 40 to 49 years old. Cases were recently diagnosed cases of coronary artery disease identified in academic hospitals in the Boston metropolitan area. Controls free from coronary artery disease were aged and neighborhood matched and selected from patients who attended the emergency departments of the same hospitals. The study participants were asked to estimate their daily consumption in ounces of HFCS drinks over the past 20 years and the consumption of HFCS was dichotomized into ≥20 ounces daily (exposed) and <20 ounces daily (unexposed). Unbeknownst to the study investigators the cases with coronary artery disease systematically over- reported their consumption of HFCS drinks. Below are 2x2 contingency tables for the “TRUE” (unobserved or hypothetical) data and the OBSERVED study data.

“TRUE” Data OBSERVED Data ≥20 ounces HFCS Drinks daily <20 ounces HFCS Drinks daily ≥20 ounces HFCS Drinks daily <20 ounces HFCS Drinks daily Coronary Artery Disease + 100 300 Coronary Artery Disease + 150 250 Coronary Artery Disease - 200 600 Coronary Artery Disease - 200 600 a) Do you think that control selection bias is a concern in this study? Why or why not? ( 5 points ) I don’t think control selection bias is a concern in this study. The selection of controls meet the would criterion and they were selected independently of exposure status. (The students could argue the opposite for full credit, but they must identify the would- be criteria and selection based upon exposure status.) b) Calculate the odds ratio for the “TRUE” data by hand. ( 5 points ) OR=(100/300)/(200/600)= 0.333/0.333= 1.0 or OR =(100*600)/(200*300)= (6000/6000) = 1.0 or OR = (100/200)/(300/600) = 0.5/0.5 = 1.0 c) Calculate the OR ratio for the OBSERVED data and the 95% confidence interval using R . Interpret the relative measure of association comparing the odds in the exposed to the odds in the unexposed. ( 10 points ) oddsratio.wald(c(150,200,250,600)) The observed odds ratio is 1.8 (95% CI: 1.39, 2.33). Over a 20 year period of exposure, 40 to 49 year olds who reported that they consumed 20 ounces or more of HFCS drinks daily had 1.8 times the odds of developing Coronary Artery Disease than those who reported drinking less than 20 ounces of HFCS drinks daily. d) Did the misclassification of the exposure to the daily consumption in HFCS drinks lead to bias in the observed study results (include direction of bias)? ( 5 points ) Yes, the observed results (OR = 1.8) had an upward bias from the true results (OR = 1.0). e) What type of misclassification bias could have occurred in this study? Justify your response. ( 5 points )

Recall bias could have occurred here as people were asked to self-report their daily consumption of HFCS drinks. There was a differential bias that occurred as over- reporting among the persons with coronary artery disease. f) What is the purpose of controls in a case-control study? ( 5 points ) The purpose of controls in a case-control study is to provide an estimate of the distribution of exposure in the source population (or, equivalently, the population that gave rise to the cases). 3. An open-label randomized control trial compared the use of oral amoxycillin (exposed) versus injectable penicillin (unexposed) for the treatment of severe pneumonia in children aged 3 to 59 months. The study hypothesis is that children treated with amoxycillin would have better outcomes than children treated with penicillin. After conducting the trial, the observed risk ratio for successful treatment was 1.35. Study personnel were unblinded and aware of the treatment drug and aware of the study hypothesis. It was observed that study personnel found a suspiciously high number of cases of lower chest wall indrawing (a reason to classify the child as a treatment failure) in the final assessment among the children who received penicillin. Lower chest wall indrawing is a subjective diagnosis. a) What type of bias does this describe? Justify your response. ( 5 points ) This is interviewer bias when the interviewers are aware of the study assignment and the study hypothesis and use that information in differentially assessing outcomes based on that information. In this case they identified more of the penicillin treated children with lower chest wall indrawing (a diagnosis that can be subjective). b) Explain whether you expect that there would be bias that is a) upward b) downward c) towards the null, or d) not present. ( 5 points ). Amoxycillin Penicillin Total Treatment Success a b Treatment Failure c d Total I would expect there to be an upward bias as the number of treatment successes in the penicillin group would be lower and the number of treatment failures would be higher. The relative risk would be artificially higher as a result. RR = (a/(a+c))/ (b/(b+d)): if b gets smaller, then RR is larger. Upward bias. 4. A prospective cohort study investigated the association between neighborhood socio-economic status and development of asthma in children in Massachusetts. The study followed enrolled a cohort of 2-year-olds and followed them from 2003 to 2014. Children received regular medical examinations to determine if they had developed asthma. Low neighborhood socio-economic status is the exposed group and high neighborhood socio-economic status is the unexposed group.

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a) In a perfect (hypothetical) study, we would have obtained the data below. Calculate the RR and 95% CI interval using R . Interpret the relative measure of association. ( 10 points ) Asthma No Asthma Low neighborhood socio- economic status 440 950 High neighborhood socio- economic status 90 1300 riskratio.wald(c(1300,90,950,440)) The risk ratio (RR) is 4.89 (95% CI: 3.95, 6.06). Children living in Massachusetts in low socio- economic status neighborhoods had 4.89 times the risk of developing asthma than those living in high socio-economic status neighborhoods from 2003 to 2014. b) What is the main source of bias that you would expect to see in this study? What is the suspected direction of bias? ( 5 points ) One of the main sources of bias for a prospective cohort study is selection bias through loss to follow-up. Since this would be a form of non-differential selection bias, the estimate would be non-biased, but the precision of the estimate would be reduced due to a smaller number of events. c) The observed data are as follows. Calculate the RR and 95% CI interval using R (interpretation not needed). Compare the values for RR and 95% CI that you calculated in part a and part c. ( 10 points ). Asthma No Asthma Low neighborhood socio- economic status 352 760 High neighborhood socio- economic status 72 1040 riskratio.wald(c(1040,72,760,352)) RR 4.89 95% CI (3.85, 6.21) The RR value is the same, but the 95% CI values are wider. In the hypothetical study the 95% CI are (3.95, 6.06).

5. Consider the following statements and indicate whether they are true or false and briefly explain why in one sentence ( 5 points each ). a) Randomized clinical trials are vulnerable to selection bias. True! Selection bias is possible in any study design due to missing data from (for example) loss to follow-up or other forms of attrition. b) Non-differential loss to follow-up (related to exposure status or outcome status, but not both) can still lead to bias. False! Non-differential loss to follow-up will lead to loss of precision (wider confidence intervals) but not otherwise bias the results. c) Non-differential loss to follow-up will increase the precision of your results. False! Non-differential loss to follow-up will decrease the precision of your results. See numerical example in the in-class exercise. d) In a case-control study it is important to sample controls independently of exposure. True! Otherwise, you get a biased selection of controls that don’t reflect the exposures of the source population .

PS9 Spring 2023 solutions(1)

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