Review exercises_Final Exam_11_30_2022

1 THE UNIVERSITY OF TEXAS HEALTH SCIENCE CENTER AT HOUSTON SCHOOL OF PUBLIC HEALTH PH1700 – INTERMEDIATE BIOSTATISTICS EXERCISES IN PREPARATION FOR FINAL EXAM Please read the problems carefully and identify what question is being asked. Try to identify the variable of interest, possible hypotheses for the question, and which test statistic you would need to evaluate the hypothesis. Write down assumptions you need to investigate prior to choosing the appropriate test. We recommend you use the flow chart in your textbook!!! Focus on developing a strategy for solving the problems. If time allows, you can solve the problems. Otherwise, please solve the questions, bring your answers and questions for the lecture on December 5, 2022. The following is a list of potential test statistics that you should use in the problems. Distribution tables are provided as appendix. List A A. Contingency Chi-square Test / Chi-square test of Heterogeneity / Chi-square test of Independent / Test for RxC Tables B. Analysis of Variance (ANOVA) C. Kruskal-Wallis test D. One sample t-test E. Pearson correlation coefficient F. Spearman correlation coefficient G. Linear regression H. Regression diagnosis I. Logistic regression J. Kaplan Meier Survival analysis K. Odds ratio L. Relative Risk M. Fisher Exact Test N. Test for homogeneity of variance O. McNemar ’s Test P: Test for difference of proportions Q: Log rank test R: Wald test S: Cox proportional hazard model(s) T: Coefficient of determination U: Multiple comparison using the Dunn Test

2 1. Suppose we wish to investigate the familial aggregation of respiratory disease according to the specific type of respiratory disease. 100 families in which the head of household or the spouse has asthma, referred to as type A families, and 200 families in which either the head of household or the spouse has non-asthmatic pulmonary disease, but neither has asthma, referred to as type B families, are identified. Suppose that in 15 of the type A families the first-born child has asthma, whereas in 3 other type A families the first-born child has some non-asthmatic respiratory disease. Furthermore, in 4 of the type B households the first-born child has asthma, whereas in 2 other type B households the first-born child has some non-asthmatic respiratory disease. Test the hypothesis H 0 : P A =P B versus H 1 : P A ≠P B , where P A =Pr(first-born child has asthma in a type A family) P B =Pr(first-born child has asthma in a type B family) Choose the appropriate test from List A (first page). 2. Construct the 2x2 table and compute the expected values in problem 1. Which one of the outputs below you will use after checking the assumptions regarding problem 1? Please compute the p-value by hand. [Note: Please compute the p-value by hand, assume we will give you copies of the distribution tables from the textbook] 3. Compute the prevalence of non-asthmatic respiratory disease in the two types of families. State all hypotheses being tested. What would you conclude from this STATA output? Output A OUPUT B

4 Output C. Output D. Output E. 5. The hypothesis for problem 4 is H 0 : p 1 =p 2 ; H 1 : p 1 ≠p 2, where p1= proportion of people who were ill in the work group, p2= proportion of people who were ill in the “did not work” group. Given a chi square statistic of 7.92 and using the appropriate appendix in your textbook, please estimate the p-value for this test statistic by hand? What conclusion will you reach? 𝜒 49,0.005 2 = 27.25 ; 𝜒 49,0.01 2 = 28.94 ; 𝜒 49,0.025 2 = 31.55 ; 𝜒 49,0.05 2 = 33.93 ; 𝜒 49,0.95 2 = 66.34; 𝜒 49,0.975 2 = 70.22 ; 𝜒 49,0.99 2 = 74.92 ; 𝜒 49,0.995 2 = 78.23 ; 𝜒 49,0.999 2 = 85.35 ; 𝜒 4,0.005 2 = 0.21 ; 𝜒 4,0.01 2 = 0.3 ; 𝜒 4,0.025 2 = 0.48 ; 𝜒 4,0.05 2 = 0.71 ; 𝜒 4,0.95 2 = 9.49; 𝜒 4,0.975 2 = 11.14 ; 𝜒 4,0.99 2 = 13.28 ; 𝜒 4,0.995 2 = 14.86 ; 𝜒 4,0.999 2 = 18.47 ; 𝜒 1,0.005 2 = 0.00 ; 𝜒 1,0.01 2 = 0.00 ; 𝜒 1,0.025 2 = 0.00 ; 𝜒 1,0.05 2 = 0.00 ; 𝜒 1,0.95 2 = 3.84; 𝜒 1,0.975 2 = 5.02 ; 𝜒 1,0.99 2 = 6.63 ; 𝜒 1,0.995 2 = 7.88 ; 𝜒 1,0.999 2 = 10.83) healthstatus 50 0.93567 3.025 2.361 0.00912 Variable Obs W V z Prob>z Shapiro-Wilk W test for normal data . swilk healthstatus 1-sided Fisher's exact = 0.002 Fisher's exact = 0.002 Pearson chi2(1) = 9.9140 Pr = 0.002 12.0 38.0 50.0 Total 12 38 50 6.7 21.3 28.0 2 2 26 28 5.3 16.7 22.0 1 10 12 22 row 1 2 Total col expected frequency frequency Key . tabi 10 12\2 26, chi2 expected exact Pr(Z < z) = 1.0000 Pr(|Z| > |z|) = 0.0000 Pr(Z > z) = 0.0000 Ha: p < 0.07 Ha: p != 0.07 Ha: p > 0.07 Ho: p = 0.07 p = proportion(x) z = 10.5312 x .45 .0703562 .3121043 .5878957 Variable Mean Std. Err. [95% Conf. Interval] One-sample test of proportion x: Number of obs = 50 . prtesti 50 .45 .07

5 6. Student’s t test with 40 df was used to analyze the results in the table below. If we want to test H 0 : p 1 =p 2 versus H 1 : p 1 ≠p 2, where p 1 = proportion of hepatitis A in the “ate salad” group and p 2 =proportion of hepatitis A in the “did not eat salad” group . Do you agree that a t-test is the correct test? Why or why not? Suggest an alternative test from the list and conduct the test. Which of the following output(s) help you to determine if there is a difference in the proportion of illness between those who ate salad and those who did not eat salad? Health status Salad Ill Well Total No 3 6 9 Yes 25 8 33 Total 28 14 42 Output A. Output B. Output C. 66.67 33.33 100.00 Total 28 14 42 75.76 24.24 100.00 1 25 8 33 33.33 66.67 100.00 0 3 6 9 salad 0 1 Total health row percentage frequency Key . tab salad health, row

7 7. The authors of the data from problem 6 claim that there is a significant difference between the proportion with hepatitis A among those who did and did not eat salad. Does their claim match the conclusions reached using the following STATA output? 8. The data in the table below are for 27 patients with acute dilated cardiomyopathy. LVEF indicates left ventricular ejection fraction. Researchers are interested in evaluating the linear association of age on the LVEF. Regress Age on left ventricular ejection fraction and check any assumptions associated with linear regression. Please answer the questions below which will help you with the thinking process. 8.1. What will be the parameter of interest? What is your dependent and what is your independent variable if you are interested in the effect of age on LVEF? 8.2. Which one of the outputs help you to answer the question? 8.3. Name two methods for determining the linear association of age and LVEF. 8.4. What is the regression equation evaluating the effect of age on LVEF? 8.5. What would we be our estimate for the average LVEF for a 45-year-old patient with this condition using this regression line? 8.6. Name two methods for determining the linear association of age and LVEF. 8.7. What is your conclusion about the F-statistic? Report the p-value by hand. [Note: Please compute the p-value by hand, assume we will give you copies of the distribution tables from the textbook] 8.8. What is your conclusion about the slope and intercept of the line using the t-statistic? Report the p- value by hand. [Note: Please compute the p-value by hand, assume we will give you copies of the distribution tables from the textbook] 8.9. What are the standard errors of the slope and intercept for the regression line? 8.10. Identify the 95% confidence interval for the slope. 8.11. Identify the 95% confidence interval for the intercept 8.12. What is the coefficient of determination (R 2 ) for the regression line in Exercise 8.4? 8.13. If we want to evaluate the linear association of age and LVEF, would you recommend Pearson or Spearman? The following outputs are for your convenience:

8 Output A. Output B. Output C. Output D. LVEF 27 0.96943 0.899 -0.220 0.58694 Variable Obs W V z Prob>z Shapiro-Wilk W test for normal data . swilk LVEF age 27 0.93805 1.821 1.231 0.10907 Variable Obs W V z Prob>z Shapiro-Wilk W test for normal data . swilk age 0 .01 .02 .03 .04 20 30 40 50 60 70 age 0 2 4 6 0 .1 .2 .3 .4 lvef

10 Output H. Output I. Output J. 9. Suppose that 20 married couples, each in the age group 25-34, have their systolic blood pressures taken, with the data listed below. What statistic from list A would be useful for determining whether male and female SBP are related? _cons 31.10282 9.370703 3.32 0.003 11.8035 50.40215 LVEF 49.12789 39.47203 1.24 0.225 -32.16628 130.4221 age Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 6868.66667 26 264.179487 Root MSE = 16.085 Adj R-squared = 0.0207 Residual 6467.89223 25 258.715689 R-squared = 0.0583 Model 400.774433 1 400.774433 Prob > F = 0.2248 F(1, 25) = 1.55 Source SS df MS Number of obs = 27 . regress age LVEF Couple Male Female Couple Male Female 1 136 110 11 156 135 2 121 112 12 98 115 3 128 128 13 132 125 4 100 106 14 142 130 5 110 127 15 138 132 6 116 100 16 126 146 7 127 98 17 124 127 8 150 142 18 137 128 9 180 143 19 160 135 10 172 150 20 125 110

11 10. If this were your STATA output: what would you conclude? Output A. 11. Which is the appropriate test for the correlation coefficient? Output B. Output C. spearman2 male female Number of obs = 20 Spearman's rho = 0.7169 ( 0.1643 ) Test of Ho: male and female are independent t( 18 ) = 4.3623 Prob > |t| = 0.0004 12. Assess whether there is any overall difference in mean fluorescence level by retinopathy grade. Assume that the variable is normal. What test would you use, from list A? 13. A hypothesis has been suggested that a principal benefit of physical activity is to prevent sudden death from heart attack. The following study was designed to test this hypothesis: 100 men who died for a first heart attack and 100 men who survived a first heart attack in the age group 50-59 were identified and their wives were each given a detailed questionnaire con cerning their husbands’ physical activity in the 20 20 0.0010 Female 0.6807 1.0000 20 Male 1.0000 Male Female . pwcorr Male Female, sig obs Retinopathy grade n Mean± sd Nephropathy grade n Mean± sd 0 11 447± 17 0 28 487± 24 1 16 493± 30 1 6 481± 16 2 14 551± 35 2 7 567± 24

13 14. Which STATA output is correct for problem 13? What would you conclude about the Odds Ratio? 15. What formula would you use to compute a 95% CI for the odds ratio for problem 14? 16. An issue of current interest is the effect of delayed childbearing on pregnancy outcome. In a recent paper a population of first deliveries was assessed for low-birthweight deliveries (<2500g) according to the woman’s age and prior pregnancy history . Estimate the odds ratio relating age to the prevalence of low- birthweight deliveries, for both pregnancy history and no history of pregnancy groups. Report both 2x2 tables and both odds ratios and their 95%CI. Below are some outputs that may help you to answer this question. Please select the correct test from the list and the outputs below. OUTPUT A: Age History n Percentage low birthweight ≥ 30 No 225 3.56 ≥ 30 Yes 88 6.82 < 30 No 906 3.31 <30 Yes 153 1.31

14 OUTPUT B: OUTPUT C: OUTPUT D: 1.546753 1.62 0.2035 0.785529 3.045648 Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] Mantel-Haenszel estimate controlling for history 1 1.076498 0.03 0.8556 0.48647 2.38215 0 5.524390 5.27 0.0218 1.06708 28.60031 history Odds Ratio chi2(1) P>chi2 [95% Conf. Interval] by history Comparing bw==1 vs. bw==0 Maximum likelihood estimate of the odds ratio . mhodds age bw, by(history)

16 Output B: OUTPUT C:

17 Output D 19. Suppose we are interested in comparing the effectiveness of two different antibiotics, A and B, in treating gonorrhea. Each person receiving antibiotic A is matched with an equivalent person (age within 5 years, same sex), to whom antibiotic B is given. These people are asked to return to the clinic within 1 week to see if the gonorrhea has been eliminated. Carry out an appropriate test for comparing the relative effectiveness of the two antibiotics. Suppose the results are below. Make sure you know how to create the 2x2 table for analysis: (1) For 40 pairs of people, both antibiotics are successful. (2) For 50 pairs of people, antibiotic A is effective whereas antibiotic B is not. (3) For 25 pairs of people, antibiotic B is effective whereas antibiotic A is not. (4) For 10 pairs of people, neither antibiotic is effective. Which output below is the correct one for this question? Treatment Treatment A effective yes A effective No B effective yes 40 25 B effective No 50 10 Output A

19 Output B 21. A group of researchers published the data regarding the use of three methods to repair a meniscus from different individuals who only needed the repair in a single knee (P. Borden, J. Nyland, D.N.M. Caborn, D. Pienkowski (2003). "Biomechanical Comparison of the FasT-Fix Meniscal Repair Suture System with Vertical Mattress Sutures and Meniscus Arrows," The American Journal of Sports Medicine, Vol. 31, #3, pp. 374-378.). The data was modified, reported below and provided in the dataset MENISCUS. They compared 3 methods for Meniscal Repair (1=Vertical Suture, 2=Meniscus Arrow, 3=FasT-Fix) on 3 Outcome measures as the change before and after the repair: Load at failure (N), Displacement (mm) and Stiffness (N/mm). What assumptions would you check before analysis? Are there statistically significant differences in the mean of the change in the displacement of the knee between these three methods? What test statistic will you use to answer this question and what will you inform these researchers? The data is shown below as well as some outputs that may help you to answer the questions:

20 OUTPUT A: OUTPUT B: OUTPUT C: