9B: Comparing Independent Proportions 5/3/07

9B.1 Smoking cessation trial. A randomized controlled double-blind trial was conducted to see if sustained-release bupropion (a pharmaceutical typically used to treat depression) in combination with a nicotine patch provided benefit over use of the nicotine patch alone in helping people to stop smoking. The  control group (nicotine patch alone) was made up of 244 smokers who wanted to stop smoking. The treatment group (nicotine patch and sustained-release bupropion) was made up of 245 individuals. After one year, 40 individuals in the control group had remained smoke-free. In contrast, 87 in the treatment group remained smoke-free (Jorenby et al., 1999). 

(A) Calculate the success proportions in each of the groups. 

(B) Calculate the difference in proportions (risk difference) in the sample. Interpret this results. What does this mean in plain terms? 
(C) Use the plus-four method to calculate the 95% confidence interval for risk difference parameter p₁ - p₂. Interpret this interval. 

9B.2 Telephone survey response. Telephone surveys typically have high rates of non-response. This can cause sampling bias when survey responses are associated with factors that determine the success of a call attempt. For mail and home surveys, it is known that advanced-warning letters letting respondents know that a survey is on its way can increase the overall response. A study investigated the utility of leaving messages on answering machines as a means of encouraging participation in telephone surveys. A message was left (or not) at random, when an answering machine picked up the first call of a telephone survey. The study showed the following counts of households eventually contacted and those that ultimately agreed to complete the survey:

[Source: Xu et al., 1993: * Values extracted from Table 1; Values extracted from Table 2; *** Value extrapolated from response percents in Table 1.]

(A) Proportion contacted: This part of the analysis will address whether the advanced warning message increased the proportion of households that were contacted. 

• Point estimation: Calculate contact proportions ₁  and ₂ and their difference ₁ - ₂ . [Contact proportion, group i = _i = (no. contacted) / (no. households)].  

• Test: Test the proportions for a significant difference. Show all work.

• Confidence interval: Calculate a 95% confidence interval for the difference in proportions, p1 - p2. 

• Size of the effect /  interpretation: Address whether the size of the increase is important. 

(B) Proportion responding: Does leaving the advanced message increase the proportion of households that ultimately complete the survey?  Perform analyses similar those requested in part A of this problem. [Completion proportion in group i = _i = (no. completing) / (no. households)].  

9B.3 Smoking cessation trial.  Perform a test of significance for the smoking cessation data described in exercise 9B.1. Show all work. Intelligently discuss the results.

9B.4 The "Father of Medical Statistics". Pierre-Charles Alexandre Louis (1787 - 1872) is often referred to as the  "father of  clinical statistics. In 1837 he wrote  "I conceive that without the aid of statistics nothing like real medical science is possible" (Lilienfeld and Lilienfeld, 1978a, p. 522). In perhaps his most famous study, Louis evaluated bloodletting as a treatment for pneumonia. It should be noted that bloodletting was an extremely popular form of therapy at the time. Two forms of bloodletting were practiced: by lancet (cutting a vein) and by placement of leeches on specific parts of the body. (In 1833, France had imported more than 42 million leeches for this purpose.) Louis called into question the effectiveness of bloodletting by carefully monitoring and recording outcomes in various treatment groups. In one analysis, he compared patients who received early bloodletting treatment (within the first 4 days of symptoms) and those who received late treatment, finding that 18 of 41 patients in the early treatment group died, while 9 of 36 patients bled later in the course of their illness died (Louis, 1836).

(A) Determine the risk of death in each group and test the difference for significance.  
(B) Calculate the point estimate (₁  - ₂) and a 95% confidence interval for  p₁ - p₂. Discuss in plain terms what this means.

9B.5 Cytomegalovirus and coronary restenosis. Each year cardiologists surgically repair clogged coronary arteries only to have many of these same arteries once again narrow soon following surgery. A study sponsored by the NIH was conducted to help determine whether infection with a common type of virus, cytomegalovirus  (CMV), was predictive of restenosis. Forty-nine (49) of the subjects showed serological evidence of CMV infection, while 26 showed no such evidence. In the CMV+ group, 21 individuals re-clogged their arteries (Zhou et al., 1996). In the CMV- group, 2 individuals restenosed. Determine the incidence risk difference (₁  - ₂) for this outcome and calculate a 95% confidence interval for  p₁ - p₂. 

9B.6. Induction of labor. Labor can be induced by administering pitocin and other pharmaceuticals to near-term pregnant women. Meconium staining during child birth is considered by some to be a sign of fetal distress. In a randomized trial, 111 women at full-term (39 to 40 weeks) had elective induction of labor, while 117 were managed expectantly until 41 weeks of gestation. One (1) of the 111 labor inductions showed meconium staining, while 13 of the 117 conservatively managed pregnancies experienced meconium staining (Osborn., 1979, p. 37 cites M. Sc. Social Medicine, September 1975 as the source; data are stored online in labor.sav). Calculate a 95% confidence for the risk difference (induced minus non-induced). To what extent does induction increase or decrease the risk of meconium staining? Discuss your results.

9B.7 Women’s Health Initiative. The Women's Health Initiative trial included a trial in which post-menopausal women received estrogen or an identical appearing placebo. The treatment was randomized to study subjects in approximately equal proportion, and the subjects were blind to which treatment they received The estrogen-exposed group included n₁ = 8506 subjects;. The placebo group had n₂ = 8102. After a mean 5.2 years of follow-up, the estrogen-exposed group had 751 incidents of a combined outcome consisting of coronary disease, stroke, pulmonary embolism, breast cancer, endometrial cancer, colorectal cancer, hip fracture, and death due to other causes. The control group had 623 incident cases (WHI, 2002). 

(A) Calculate the incidences proportions of this index outcome in the groups. Interpret this result.
(B) Test the difference for significance. Show all hypothesis testing steps. Discuss your findings.

9B.8 Cytarabine and cerebellar toxicity. The drug cytarabine is used for bone marrow ablation in preparation for a bone marrow transplant. This drug is know to have cerebellar toxic effect, and there is a suspicion that a particular generic form of the drug is particularly hazardous. Of 25 patients treated with the generic form of the drug, 11 experienced cerebellar toxicity. In comparison, 3 or of 34 individuals treated with the brand-name product experienced toxicity (Jolson et al., 1992).Calculate the risk difference and its 95% confidence interval. (Optional: Calculate a two-sided P-value for the problem.) Interpret the results.

9B.9 Framingham Heart Study (men). The Framingham Heart Study changed our understanding of the many interrelated factors that cause and prevent cardiovascular disease and has therefore helped to save millions of lives. The study began in the 1948 in the town of Framingham, Massachusetts and is still ongoing. An early publication from the study (Kannel et al., 1961) showed that of 424 men with serum cholesterol levels of 245 mg per 100 mL or greater, 51 experienced incidences of coronary disease over a 6 year follow-up period. Of the 454 men with cholesterol less than 210 mg per 100 mL, there were 16 such cases. Estimate the risk difference of coronary events associated with the high level of serum cholesterol. Include a 95% confidence interval for the risk difference.

9B.10 Framingham Heart Study (women). This question continues our discussion of the Framingham heart study begun in exercise 9B.10. Of 689 women with serum cholesterol of 245 mg per 100 mL or greater, there were 30 coronary incidents over a 6 year period. Of 445 women with cholesterol levels less than 210 mg per 100 mL, there were 8 incident cases. 

(A) Calculate the risk difference and its 95% confidence interval in these groups.
(B) How do the risks in women compare to the risks in men?

9B.11 Scandinavian Simvastatin Survival Study (4S). In a randomized clinical trial designed to evaluate the effects of a cholesterol lowering agent (simvastatin) on mortality and morbidity in patients with coronary heart disease, the treatment group experienced 111 fatal heart attacks in a cohort of  2,221 individuals over a median 5.4 year follow-up period. The placebo group of 2,223 individuals experienced 189 such incidents (4S Study Group, 1994). (a)    Calculate the fatal heart attack proportions in the groups and test the difference for significance. 

9B.12 Scandinavian Simvastatin Survival Study (4S). The 4S trial introduced in exercise 9B.11 also tallied deaths due to any cause (not just heart attack deaths). The treatment group experienced 182 deaths (in the cohort of 2,221 individuals) and the control group experienced 256 (in the 2,223 control subjects). Compare the mortality risks (proportions) in the two groups. Use analytic methods similar to those requested in exercise 9B.11.

9B.13 Joseph Lister and anti-septic surgery. When Joseph Lister introduced the antiseptic method for surgical operations he demonstrated that post-operative mortality dropped from 16 per 35 procedures to 6 per 40 procedures. Determine the risks of post-operative mortality in each group and determine whether they differ significantly from each other. 

9B.14 UGDP. In the early 1970s, the UGDP assessed the efficacy of oral hypoglycemic treatment in comparison with insulin and diet alone in the prevention of vascular complications. It was found that 26 out of 204 patients treated with phenformin died from cardiovascular disease, whereas 2 of 64 control patients died of cardiovascular disease. Calculate the risks of death in each group and test whether the risk difference is significant. Comment on the results of the study. 

9B.15 Treatment of acute otitis media in children. A double-blind randomized trial compared two antibiotics in the treatment of acute otitis media in children. Each subject received a 14-day course of either cefaclor (n₁ = 106) or amoxicillin (n₂ = 97). There was no difference in clinical failure rates: all but four children in each antibiotic group had a good clinical response to treatment. However, by 14 days after entry into the study, 59 of 106 children (55.7%) in the cefaclor group had ears that were effusion-free as compared to 40 of 97 children (41.2%) in the amoxicillin group (Mandel et al., 1982). Determine whether the effusion-free proportions in the groups were significantly different at 14-days after entry. 

[Comment: By 42 days after entry, the percentage of children whose ears were without effusion or improved was equal in both treatment groups -- 68.9% in the cefaclor group and 67.5% in the amoxicillin group. This and other studies suggest no difference in long term failure rates among these antibiotic regimens. For further information see AHRQ 2001, Health Services/Technology Assessment Text (HSTAT) AHRQ Evidence Reports, Number 15. Management of Acute Otitis Media.] 

9B.16. Drug testing student athletes. The Supreme Court of the United States ruled in 2002 that schools could require random drug testing of students who participate in after-school activities. However, it was not known whether random drug testing reduces use of illicit drugs. To address this question, researchers at the Oregon Health and Science University completed a comparative study of two schools. Student athletes at Wahtonka high school were subject to random drug testing, while student athletes at Warrenton high school were not subject to random drug testing. Five (5) of the 95 students athletes  at the Wahtonka school were positive for illicit drugs within the past thirty days, while 12 of 62 student athletes at Warrenton high school were positive (data extracted from Table 3 in Goldberg et al., 2003). Calculate the proportions of students testing positive at each school and the difference for significance. 

9B.17 Hypothetical situation. Consider a hypothetical study of 7,500 subjects with half the subjects in group 1 (n₁ =3,750) and half the subjects in group 2 (n₂ =3,750). Data represents SRSs from their respective populations. Twenty-five percent of the individuals in both populations have a particular risk factor, so p₁ = p₂ = 0.25.

(A) What is the mean and standard deviation (error) of the sampling distribution of the difference in proportions ₁  - ₂ from these population?
(B) Use the Normal approximation to find the probability that ₁  - ₂ will be between -0.02 and 0.02.

9B.18. Prevalence of cigarette use among  racial/ethnic populations. Among U. S. adult ethnic groups in 1999 - 2000, American Indians / Alaska Natives (AI/AN) had the greatest cigarette smoking prevalence (about 40%) and the Chinese-American population had the lowest (about 12%) (MMWR, 2004).Let population 1 be the AI/AN population and let population 2 be the Chinese-American population (p₁ = 0.40 and p₂ = 0.12). You plan on doing a study by taking SRS of 1000 from each of these populations (n₁ = n₂ = 1000). 

(A) Describe the approximate sampling distribution of ₁  - ₂?
(B) Is your sample likely to show a difference as little as 0.26 (i.e., 26%)? 
(C) Is it likely for a sample to show no difference? 

9B.19 Safety of echinacea, risks. A randomized, double-blind, placebo controlled study evaluated the efficacy and safety of the herbal remedy Echinacea purpurea in treating upper respiratory tract infections in 2- to 11-year-old children. Each time a child had an upper respiratory tract infection, treatment with either echinacea or a placebo was given for the duration of the illness. Parents collected information outcomes during the course of treatments. Efficacy data is reported elsewhere (e.g., Exercise 10.10). Here we consider the safety of the product. Occurrence of various types of adverse events were recorded in logbooks kept by the parents of study subjects. Data are tallied in the table below (Taylor et al., 2003 Table 3). Estimate the risk of each outcome in each group. Which outcomes seem to indicate meaningful differences in risk? Calculate P-values for each of comparison. What are the safety concerns for the product? 

 Key to odd-numbered exercises                             Key to even-numbered exercises (may not be posted)