1 Fall 2016 PH W250 Homework Problem Set #5 (50 Points) Please type your answers. When doing calculations, please show your work. Numerical answers must contain units when appropriate. When asked to \"interpret\" an answer, this means that you should state in words the meaning of the result referred to. Note that numbers used in problems are not necessarily representative of real world data. Use a different color font for your answers (e.g., blue) so that questions and answers are clearly distinguished. Problem 1. (14 points total). Consumption of sugar-sweetened beverages (SSBs) is hypothesized to increase the risk for childhood obesity. It is further hypothesized that SSBs increase the risk for obesity only among those with a common genotype (Genotype 1) of the OBCT gene that regulates the metabolism of sugar in the blood, whereas the other common genotype of this gene (Genotype 2) does not cause obesity following consumption of SSBs. a. You conducted a prospective cohort study in which children, non-obese at recruitment, were followed over 10 years. Children in the top 25th percentile of self-reported SSB consumption during the first year of the study were categorized as SSB consumers. All other children were categorized as non-SSB consumers. The following table shows the results you obtained at the end of the 10 years: Obese Not Obese Total a. SSB Consumer 250 250 500 Non-SSB Consumer 500 1000 1500 Total 750 1250 2000 Calculate the risk ratio and risk difference for the crude association between SSB consumption and obesity status. (2 points) b. Blood was drawn from the children at enrollment and all were genotyped. Calculate the risk ratio and risk difference for the association between SSB consumption and obesity status within each genotype stratum shown below. (4 points) Genotype 1: 2 Obese Not obese Total SSB consumer 90 190 280 Non-SSB consumer 217 483 700 Total 673 980 307 Genotype 2: Obese Not obese Total SSB consumer a 170 50 220 Non-SSB consumer 300 500 800 Total 550 1020 470 What do you conclude about the relationship of the genotype to the association between SSB consumption and obesity status? Is there evidence of effect modification on the additive and/or multiplicative scales? (2 points) b. Using the stratified tables above, fill in the table below (3 points total, 0.5 for points each observed value and 1 point for the expected value) Genotype SSB Consumption a Observed cumulative incidence Expected cumulative incidence (show calculation) 1 No --- 2 No --- 1 Yes --- 2 Yes Considering only the data shown in the table, is there evidence of effect modification between genotype and SSB consumption status? Explain. (1 point) 3 c. When you write up the study results, should you report the crude (unadjusted) associations for the association between SSB consumption and obesity, the stratum-specific associations, or calculate and report an adjusted association? Why? (2 points) Problem 2. (6 points total, 2 points each part). Which of either Type I error or Type II error should you be most concerned about with the following results? Explain your answer. a. A study team concludes that hormonal contraceptive use increases the risk of Zika Virus transmission between sexual partners in Brazil (p = 0.04). a. A study concludes that cannabis use is not associated with diabetes among US adults aged 18 years or older (OR = 1.13, 95% CI: 0.97, 1.24). b. A study concludes that benzene exposure among Chinese shoe manufacturing workers is associated with increased risk of chronic lymphocytic leukemia (RR = 2.3, 95% CI: 1.02, 3.45). Problem 3. (6 points total, 1 point each part). A study shows oral contraceptive (OC) use to be associated with an increased risk of stroke. The question arises whether this association could be confounded by age. The data show that oral contraceptive use is inversely associated with age (younger women are more likely to use OCs compared to older women), and that age is positively associated with stroke (older women are more likely to have a stroke compared to younger women). a. Is age associated with the exposure? Is age associated with the outcome? b. Calculate the crude OR Stroke No stroke Total OC use a 258 2049 2307 No OC use 279 2877 3156 Total 4926 5463 537 The following table shows the study data stratified by age. 4 Ages 20-29 Ages 30-39 Ages 40-49 Stroke No stroke Stroke No stroke Stroke No stroke OC Use 39 153 93 903 126 993 No OC Use 138 855 90 1389 51 633 Total 1008 183 2292 177 1626 177 Calculate stratum-specific odds ratios: a Is there evidence that age is an effect modifier in the association between OC use and stroke? Why or why not? c. Is there evidence that age was a confounder in the association between OC use and stroke? Why or why not? d. As the investigator, which overall measure of effect (crude or adjusted for age) would you choose to include in your study report? Problem 4. (6 points total, 1/2 point each). The following table shows crude and stratum-specific odds ratios for six data analyses. Indicate whether there is evidence that effect modification or confounding is present and, under the circumstances, what is the appropriate measure of association to report (options are: unadjusted, stratum-specific, or adjusted). The first example is given for you. ORcrude ORmen ORwomen Effect Modification? (Yes/No) Confounding? Measure Reported (un(Yes/No/Mayb adjusted, adjusted, or e) stratum specific OR) 3.0 3.0 3.0 N N 3.4 2.0 2.0 1.0 4.0 1.75 0.7 1.2 1.1 4.3 5.4 3.5 Unadjusted OR Problem 5. (8 points total, 2 points each part). In 2002, investigators conducted a study to evaluate the influence of obesity on the development of hypertension among South Korean males and 5 females. This study used data collected by a medical system, established in 1991. The subjects were 1,467 men and 944 women aged 20 to 75 years and data were available for the period that they remained in the system. Study subjects were normotensive (had blood pressure measures in the normal range) at the time of their initial examinations from 1990 to 1991 and their blood pressure status could be confirmed by reviewing their medical records accumulated until June 2000. During an average follow-up period of 6.2 yrs, 234 new cases of hypertension were identified. There was no difference in follow-up time across exposure strata. An analysis using the Cox proportional hazards model showed that the rate of developing hypertension increased with increasing age, body mass index, and amount of daily alcohol consumption in men; and with increasing age and body mass index in women. a. What type of study is this? Explain in 1-2 sentences. b. What is the appropriate measure of disease frequency (cumulative incidence or incidence rate)? Why? Calculate the measure for the entire study population. c. The investigators report the incidence rate for hypertension in males as 17.4/1000 personyears and the corresponding incidence rate for females as 13.9/1000 person-years. Based on this information: (1) Is sex confounding the relationship between obesity and hypertension? (2) Is it appropriate for the investigators to calculate the pooled incidence rate from these data, using the Mantel-Haenszel method? Explain your answers. d. Single blood pressure measurements don't necessarily accurately represent a person's actual blood pressure status. The investigators later decided to exclude from their data analysis nineteen subjects who were diagnosed as hypertensive within 1 yr of their initial medical examination, but who had no further follow-up measurements. With respect to bias, what would be an appropriate rationale for this exclusion criterion? Problem 6. (4 points, 1 point each part). Indicate whether the statement is true or false a. In a randomized controlled trial, if participants who were receiving the experimental treatment were more likely to be lost to follow up and had a different health outcome distribution than those remaining in the trial, selection bias would occur. b. In a case-control study of chocolate consumption and coronary heart disease (CHD), the proportion of proxy responders (e.g., spouses) was higher for CHD patients than for the control group. The investigators are concerned that the proxy responders may be more likely to mis- 6 report the chocolate consumption behavior of the CHD patients. This would result in non-differential misclassification of the exposure. c. The Mantel-Haenszel method is used to combine stratum-specific odds ratios when there is effect modification. d. If there is effect modification, there cannot be confounding. Problem 7. (6 points). You are given data from a researcher who conducted a cohort study on food insecurity and obesity over time (where both variables were binary). Of the 300 food insecure individuals, 75 became obese over the one-year study. Among the 300 food secure individuals, 45 became obese. a. If you want cumulative incidence data, what (immediate) Stata code would you use to set up a 2 by 2 table that would have food security status (the exposure) on the top of the table, and obesity status to the left of the 2 by 2 table? Please show your code and copypaste your Stata output. (2 points) a. According to Stata, what is the risk difference between the exposed and the unexposed? Also calculate by hand (show calculation) to confirm Stata didn't make a mistake. (1 point) b. Interpret this risk difference. (1 point) c. Using your Stata output from part a, state and interpret to two decimal places the 95% confidence interval (CI) for the risk difference. (1 point) d. Using your Stata output again, state and interpret the p-value for the chi-square test. (1 point)