Assignment 1_Biostats

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Indiana University, Purdue University, Indianapolis *

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Medicine

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Feb 20, 2024

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Deborupa Pal 1. A migraine is a particularly painful type of headache, which patients sometimes wish to treat with acupuncture. To determine whether acupuncture relieves migraine pain, researchers conducted a randomized controlled study where 89 females diagnosed with migraine headaches were randomly assigned to one of two groups: treatment or control. 43 patients in the treatment group received acupuncture that is specifically designed to treat migraines. 46 patients in the control group received placebo acupuncture (needle insertion at non-acupoint locations). 24 hours after patients received acupuncture, they were asked if they were pain-free. Results are summarized in the contingency table below. (a) What percent of patients in the treatment group were pain-free 24 hours after receiving acupuncture? (0.5 points) Ans- No. of Pain free patients in treatment group/Total number of Patients in TG * 100 10/43*100 = 23.2% (b) What percent were pain-free in the control group? (0.5 points) Ans- No.of patient pain-free in control group/ Total no.of patients in control group * 100 2/46*100= 4.3% (c) In which group did a higher percentage of patients become pain-free 24 hours after receiving acupuncture? (0.5 points) Ans- The treatment group had a higher percentage of patients who became pain free 24hrs after receiving acupuncture. (d) Your findings so far might suggest that acupuncture is an effective treatment for migraines for all people who suffer from migraines. However, this is not the only possible conclusion that can be drawn based on your findings so far. What is one other possible explanation for the observed difference between the percentages of patients that are pain-free 24 hours after receiving acupuncture in the two groups? (0.5 points) Ans- Another possible conclusion that we can draw from the study is that the medication is not that effective and efficiency is really low. 2. The Buteyko method is a shallow breathing technique developed by Konstantin Buteyko, a Russian doctor, in 1952. Anecdotal evidence suggests that the Buteyko method can reduce asthma symptoms and improve quality of life. In a scientific study to determine the effectiveness of this method, researchers recruited 600 asthma patients aged 18-69

who relied on medication for asthma treatment. These patients were randomly split into two research groups: one practiced the Buteyko method and the other did not. Patients were scored on the quality of life, activity, asthma symptoms, and medication reduction on a scale from 0 to 10. On average, the participants in the Buteyko group experienced a significant. (a) Identify the main research question of the study. (0.5 points) Ans- The main research question of the study is- " Are asthma patients who rely on medicine for treatment able to improve their quality of life and reduce their symptoms with the Buteyko method?" (b) Who are the subjects in this study, and how many are included? (0.5 points) Ans- The subjects in this study are 600 asthma patients aged 18-69 who relied on medication for asthma treatment. There are 600 participants included in this study. (c) What are the variables in the study? Identify each variable as numerical or categorical. If numerical, state whether the variable is discrete or continuous. If categorical, state whether the variable is ordinal. (1 point) Ans- 1. Treatment Group (Categorical) 2. Age (Numerical - Continuous) 3. Quality of Life Score (Numerical - Continuous) 4. Activity Score (Numerical - Continuous) 5. Asthma Symptoms Score (Numerical – Continuous) 6. Medication Reduction Score (Numerical - Continuous) 3. Researchers hypothesized that a particular taste receptor in hummingbirds, T1R1-T1R3, played a primary role in dictating taste behavior; specifically, in determining which compounds hummingbirds detect as sweet. In a series of field tests, hummingbirds were presented simultaneously with two filled containers, one containing test stimuli and a second containing sucrose. The test stimuli included aspartame, erythritol, water, and sucrose. Aspartame is an artificial sweetener that tastes sweet to humans but is not detected by hummingbird T1R1-T1R3, while erythritol is an artificial sweetener known to activate T1R1-T1R3. Data were collected on how long a hummingbird drank from a particular container for a given trial, measured in seconds. For example, in one field test comparing aspartame and sucrose, a hummingbird drank from the aspartame container for 0.54 seconds and from the sucrose container for 3.21 seconds. (a) Which tests are controls? Which tests are treatments? (1 point) Ans- Control Tests- The control tests involve the container with sucrose (establishing the baseline for sweetness) and potentially the container with water (to assess preference over non-sweetness).

Treatment Tests- The treatment tests involve the containers with aspartame and erythritol (testing whether these substances are perceived as sweet by hummingbirds). (b) Identify the response variable(s) in the study. Are they numerical or categorical? (0.5 points) Ans- Duration of Drinking (Numerical)- The response variable is the amount of time spent drinking, expressed in seconds. It shows how long a hummingbird consumes liquid from a certain container during a particular trial. This variable is numerical since it can have a value of 0.54 seconds or 3.21 seconds and is measured on a continuous scale. Therefore, the study's response variable is numerical, more precisely continuous. (c) Describe the main research question. (0.5 points) Ans- Hummingbirds appear to prefer eating chemicals that activate the taste receptor T1R1- T1R3 over those that do not, raising the question, "Does this indicate that the taste receptor T1R1-T1R3 plays a primary role in determining which compounds hummingbirds detect as sweet?" 4. Echinacea has been widely used as an herbal remedy for the common cold, but previous studies evaluating its efficacy as a remedy has produced conflicting results. In a new study, researchers randomly assigned 437 volunteers to receive either a placebo or echinacea treatment before being infected with rhinovirus. Healthy young adult volunteers were recruited for the study from the University of Virginia community. (a) Identify the population of interest and the sample in this study. (0.5 points) Ans- Population of Interest- The population of interest is the larger group to which the researchers want to make inferences. In this case, the population of interest would likely be all individuals, regardless of age or health status, who may use echinacea as an herbal remedy for the common cold in real-world situations. Sample- The sample is the subset of the population that is actually included in the study. In this study, the sample consists of the 437 healthy young adult volunteers recruited from the University of Virginia community who were randomly assigned to receive either a placebo or echinacea treatment before being infected with rhinovirus. So, the sample represents a specific group of individuals who participated in this research study. (b) Comment on whether or not the results of the study can be generalized to a larger population. (0.5 points) Ans- Although the study offers insightful information about the effects of echinacea in a particular demographic of people, care should be used when extrapolating the findings to a larger, more diverse population. To draw more thorough conclusions on the effectiveness of

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echinacea as a cold treatment, more study with a more diverse sample and a wider variety of variables is required. (c) Can the findings of the study be used to establish causal relationships? Justify your answer. (0.5 points) Ans- The results of this study can offer insightful information and add to the conversation on echinacea's possible benefits for treating the common cold. However, a number of factors, including the study's limits and methodology, will determine whether the results can prove causal linkages. 5. In order to assess the effectiveness of taking large doses of vitamin C in reducing the duration of the common cold, researchers recruited 400 healthy volunteers from staff and students at a university. A quarter of the patients were randomly assigned a placebo, and the rest were randomly allocated between 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives to be taken at the onset of a cold for the following two days. All tablets had identical appearance and packaging. No significant differences were observed in any measure of cold duration or severity between the four medication groups, and the placebo group had the shortest duration of symptoms. (a) Was this an experiment or an observational study? Why? (0.5 points) Ans- This was an experiment. An experiment involves the deliberate manipulation of one or more variables (in this case, the dosage of vitamin C) to observe its effect on other variables while controlling for potential confounding factors. In this study, researchers assigned participants to different dosage groups (placebo, 1g Vitamin C, 3g Vitamin C, or 3g Vitamin C plus additives) and observed the impact of these treatments on the duration and severity of cold symptoms. The random allocation of participants to these groups and the controlled administration of treatments make it an experimental study. (b) What are the explanatory and response variables in this study? (0.5 points) Ans- In this study, the explanatory variable is the dose of vitamin C and additives given to the participants. Specifically, there are three levels of the explanatory variable: 1. Placebo (no vitamin C) 2. 1g Vitamin C 3. 3g Vitamin C with additives The response variable in this study is the duration and severity of the common cold symptoms. Researchers are assessing how the different doses of vitamin C and the placebo affect the duration and severity of the common cold symptoms in the participants. (c) Participants are ultimately able to choose whether or not to use the pills prescribed to them. We might expect that not all of them will adhere to and take their pills. Does this introduce a confounding variable to the study? Explain your reasoning. (1 point)

Ans- Yes, the fact that participants have the choice to adhere to or not take the pills prescribed to them can introduce a confounding variable to the study. This introduces the issue of non- compliance or non-adherence, which can significantly impact the interpretation of the study's results. The reason’s being- 1. Selection Bias- If some participants in the treatment groups decide not to take their pills as instructed while others do, this can lead to differences in the exposure to vitamin C among participants within those groups. Those who adhere to the regimen may have different characteristics or motivations than those who do not. For example, individuals who are more health-conscious or believe strongly in the benefits of vitamin C may be more likely to adhere to the treatment. This can introduce selection bias, where the two groups (adherent and non- adherent) differ in ways other than just the treatment, making it difficult to attribute any observed effects solely to vitamin C. 2. Dilution of Treatment Effect- If a significant proportion of participants in the treatment groups do not take their pills, the average exposure to vitamin C in those groups will be lower than intended. This can dilute the potential treatment effect and make it harder to detect any benefits of vitamin C in reducing the duration of the common cold. 3. Misclassification of Exposure- Non-adherence can lead to misclassification of exposure status. In this case, participants who were assigned to receive vitamin C may effectively become part of the control group if they don't take their pills. This misclassification can lead to erroneous conclusions about the effectiveness of vitamin C. 4. Reduced Statistical Power- Non-adherence reduces the effective sample size for the treatment groups. With fewer participants actually taking the treatment as prescribed, the study may have reduced statistical power, making it more challenging to detect significant differences even if vitamin C does have an effect on cold duration. To mitigate the impact of non-adherence, researchers typically employ strategies such as monitoring participants' compliance, using intention-to-treat analysis (where participants are analyzed according to their assigned treatment group regardless of actual adherence), or providing incentives or reminders to encourage adherence. Failure to address non-adherence can indeed introduce a confounding variable and weaken the validity of the study's conclusions. 6. A researcher is interested in the effects of exercise on mental health and he proposes the following study: Use stratified random sampling to recruit 18-30, 31-40, and 41-55- year-olds from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results. (a) What type of study is this? (0.5 points) Ans- This study is an experimental study. (b) What are the treatment and control groups in this study? (0.5 points) Ans- In this study: - The treatment group consists of subjects who are assigned to exercise twice a week. - The control group consists of subjects who are instructed not to exercise.

(c) Does this study make use of blocking? If so, what is the blocking variable? (0.5 points) Ans- Yes, this study makes use of blocking. The blocking variable is age. The researcher is stratifying the sample into three age groups (18-30, 31-40, and 41-55) and then randomly assigning half of the subjects from each age group to the exercise group and the other half to the control group. This helps ensure that each age group is represented in both the treatment and control groups, which can help control for potential confounding variables related to age. (c) Comment on whether or not the results of the study can be used to establish a causal relationship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large. (0.5 points) Ans- The results of this study can provide evidence for a causal relationship between exercise and mental health, but causation cannot be definitively established based solely on this study. Generalization to the population at large is a concern. The study population is limited to those aged 18-55, so the results may not be directly applicable to other age groups or populations with different characteristics. (d) Suppose you are given the task of determining if this proposed study should get funding. Would you have any reservations about the study proposal? (0.5 points) Ans- When evaluating whether this proposed study should receive funding, there are several considerations: - The research design appears sound, with random assignment and blocking by age, which can help control for potential biases. - It's important to assess the feasibility of conducting such a study, including recruitment of participants, retention, and conducting mental health exams. - The proposed sample size should be evaluated to ensure it is adequate for detecting meaningful effects. - Budget considerations and ethical considerations related to informed consent, participant safety, and data handling should be assessed. - The potential benefits of the research in terms of advancing knowledge about the relationship between exercise and mental health should be weighed against the costs and resources required for the study. Overall, while there may be some reservations and practical considerations, the proposal appears to have merit for further evaluation and funding if it addresses these issues appropriately. 7. For each part, compare distributions (1) and (2) based on their means and standard deviations. You do not need to calculate these statistics; simply state how the means and the standard deviations compare. Make sure to explain your reasoning. Hint: It may be useful to sketch dot plots of the distributions.

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(a) (1) 3, 5, 5, 5, 8, 11, 11, 11, 13 (2) 3, 5, 5, 5, 8, 11, 11, 11, 20 The SD is higher for the second distribution as the last value is greater which means it is more spread out from the first distribution. (b) (1) -20, 0, 0, 0, 15, 25, 30, 30 (2) -40, 0, 0, 0, 15, 25, 30, 30 There is an outlier in the second distribution which increases the SD which implies spreading out from the mean even though the mean is same for both the distributions. (c) (1) 0, 2, 4, 6, 8, 10 (2) 20, 22, 24, 26, 28, 30 The SD deviation is same for both the distributions which indicate that the values are evenly spread out from the mean even though the mean is different for both the distributions. (d) (1) 100, 200, 300, 400, 500 (2) 0, 50, 300, 550, 600 In both distributions, the means is the same. However, the standard deviation in second distribution is higher than in first distribution, indicating that the values in second distribution are more spread out from the mean Despite having the same mean, second distribution has more variability. 8. 910 randomly sampled registered voters from Tampa, FL were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guests workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below. (a) What percent of these Tampa, FL voters identify themselves as conservatives? Ans- 372/910*100= 40.87% (b) What percent of these Tampa, FL voters are in favor of the citizenship option? Ans- 278/910*100= 30.54 (c) What percent of these Tampa, FL voters identify themselves as conservatives and are in favor of the citizenship option? Ans- 57/372*100= 15.32%

(d) What percent of these Tampa, FL voters who identify themselves as conservatives are also in favor of the citizenship option? What percent of moderates share this view? What percent of liberals share this view? Ans- 57/372*100= 15.32% 120/363*100= 33.05% 101/175*100= 57.71% 9. Daily air quality is measured by the air quality index (AQI) reported by the Environmental Protection Agency. This index reports the pollution level and what associated health effects might be a concern. The index is calculated for five major air pollutants regulated by the Clean Air Act and takes values from 0 to 300, where a higher value indicates lower air quality. AQI was reported for a sample of 91 days in 2011 in Durham, NC. The relative frequency histogram below shows the distribution of the AQI values on these days. (a) Based on the histogram, describe the distribution of daily AQI. (1 point) Ans- The histogram is described as "skewed right," which means it has a positively skewed distribution. In a positively skewed distribution, most of the data is concentrated on the lower end of the scale, with a tail extending towards higher values. In this context, it suggests that there were more days with lower AQI values, indicating better air quality, and relatively fewer days with higher AQI values, indicating poorer air quality. (b) Estimate the median AQI value of this sample. (0.5 points) Ans- The median is approximately 30. (c) Would you expect the mean AQI value of this sample to be higher or lower than the median? Explain your reasoning. (0.5 points) Ans- Since the distribution is skewed right, the mean will be influenced by the higher values, resulting in a higher mean than median. 10. Indicate which of the plots shows a (a) positive association. (0.5 points) Ans- 1 & 3 have positive association. (b) negative association. (0.5 points) Ans- 4 th one has negative association. (c) no association. (0.5 points) Ans- 2 has no association.

Also, determine if the positive and negative associations are linear or nonlinear. Each part may refer to more than one plot. 1 is approximately linear. Graphs 3 and 4 are linear.

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