BE 614 Biostatistics Assignment 1 PDF

BE 614 Biostatistics Assignment 1 Deadline: Friday, 20th September 2024 Instructions: You should write each step of your calculations by hand on your answer sheets and include the measurement units with your quantitative answers. Note t...

BE 614 Biostatistics Assignment 1 Deadline: Friday, 20th September 2024 Instructions: You should write each step of your calculations by hand on your answer sheets and include the measurement units with your quantitative answers. Note that MATLAB is not needed for this homework. You may use a calculator. Submit hand-written answer sheets. Do not submit in the Google Classroom. Partial credit will be given. Total points (pts): 25 Submission Details: You can submit your homework on 20th September between 6 to 7 pm to TA Kajal (AB6/327). Alternatively, if you'd like to submit earlier, you may do so on 18th September at the beginning or end of the class. Question 1 (3 pts): In a clinical trial, patients with diabetes were randomly assigned to receive either Drug A or Drug B for blood sugar control. After a year, the number of adverse events (heart attacks) was recorded for each group. The table below shows the results: Intervention Number per group Person-years of Number of heart attacks exposure Drug A 3000 1500 10 Drug B 3000 1500 3 (a) What is the absolute difference in the incidence rates of heart attacks between the groups that took Drug A and Drug B? Calculate it as the number of events per 1000 person- years and round to the nearest tenth decimal place. (b) What is the absolute difference in the risks of heart attacks between the two groups? Report it as a percentage rounded to the nearest hundredth decimal place. (c) What is the risk ratio of heart attacks comparing Drug A to Drug B? Round to the nearest tenth decimal place. Question 2 (2 pt): The risk of a new experimental therapy for skin cancer causing severe side effects is 0.004%, while the risk of a standard therapy is 0.002%. Based on the absolute difference in risks and the risk ratio, should patients be concerned about the experimental therapy? Explain why or why not. Question 3 (4 pts): Suppose 12% of the population in a certain region was exposed to a pollutant. People who were not exposed have a lifetime risk of lung cancer of 0.005, while people who were exposed have a lifetime risk of 0.03. Answer the following, expressing your answer as a percentage rounded to the nearest tenth. (a) What is the probability that a random person from this region has been exposed to the pollutant and develops lung cancer? (b) What is the probability that a random person from this region will develop lung cancer? (c) What percentage of the population will not develop lung cancer? (d) If someone develops lung cancer, what is the probability that they were exposed to the pollutant? Question 4 (3 pts): In a population of 10,000 people, 2% are carriers of a certain gene mutation. A genetic test correctly identifies 90% of carriers and 95% of non-carriers. Answer the following questions:  (a) What is the probability that a randomly selected person from this population will test positive for the mutation? (b) What is the probability that a person who tests positive is actually a carrier? (c) What is the probability that a person who tests negative is actually not a carrier? Question 5 (2 pt): On an exam, the average score in a class was 75 with a standard deviation of 12. If the teacher wants to give A’s to the top 10% of the class, what is the lowest score a student could get to receive an A? Question 6 (1 pt): A hospital has a success rate of 95% for a particular surgery. What is the probability that exactly 3 out of the next 5 surgeries will be successful? Question 7 (5 pt): A rapid antigen test was administered to a group of 500 people to detect COVID- 19 infection. Of these 500 people, 150 were known to be infected based on a highly accurate PCR test (considered the gold standard). The results of the antigen test are summarized in the following table: Test Result COVID-19 Positive (by PCR) COVID-19 Negative (by PCR) Positive 135 45 Negative 15 305 (a) Calculate the sensitivity of the antigen test. Express your answer as a percentage rounded to the nearest tenth decimal place. (b) Calculate the specificity of the antigen test. Express your answer as a percentage rounded to the nearest tenth decimal place. (c) Calculate the positive predictive value (PPV) of the antigen test. Express your answer as a percentage rounded to the nearest tenth decimal place. (d) Calculate the negative predictive value (NPV) of the antigen test. Express your answer as a percentage rounded to the nearest tenth decimal place. (e) Interpret the results of the test in terms of its usefulness in detecting COVID-19. Consider how high or low sensitivity, specificity, PPV, and NPV affect the reliability of the test. Question 8 (2 pt): For a population of adult males who participated in a national nutrition survey, the distribution of cholesterol levels (mg/dL) is known to have a mean μ=210\mu = 210μ=210 mg/dL and a standard deviation σ=35\sigma = 35σ=35 mg/dL. (a) If repeated samples of 50 men are selected from this population, what is the standard error of the mean cholesterol levels? Round your answer to the nearest hundredth decimal place. (b) What is the probability that a randomly selected sample of 50 men will have a mean cholesterol level between 200 mg/dL and 220 mg/dL? Use the Z-score formula and round your final answer to the nearest thousandth decimal place. Question 9 (3 pt): The following measurements represent the tensile strength (in MPa) of a metallic alloy obtained from a random sample of test specimens: X = [72.3,71.9,72.5,72.0,72.6,72.1,72.4,71.8,75.2] Assume that the tensile strength of the alloy is normally distributed, and the population standard deviation σ is known to be 1.5 MPa. (a) Calculate sample mean, standard error of mean and, find the 95% confidence interval for the population mean μ. Use the formula for confidence intervals based on the Z-distribution. Round your final answers to the nearest hundredth decimal place. Hints: Margin of Error = Z-critical value (Z* ) × standard error of sample mean (SE𝒙 ̅) Confidence interval (CI) = 𝒙 ̅ ± Margin of Error