16.1 Induction of labor [similar 9.5.6]. Meconium staining of the fetus during childbirth is a sign of fetal distress. In a randomized trial, 11 pregnant women had elective induction of labor between 39 and 40 weeks of gestation and 117 control women were managed expectantly until 41 weeks of gestation. One case of meconium staining occurred in the treatment group. Thirteen (13) occurred in the control group (Osborn, 1979, p. 37 cites "M. Sc. Social Medicine, September 1975"; individual data records in labor.sav).
(A) Determine the risks of meconium staining in each group.
(B) Express the association between induction and meconium staining as a risk ratio. Explain the meaning of the RR to a lay person.
(C) Calculate a 95% confidence interval for the RR.
16.2 Joseph Lister and antiseptic surgery [similar to 9.5.13]. When Joseph Lister introduced the antiseptic method for surgical operations he demonstrated that postoperative mortality dropped from 16 per 35 procedures to 6 per 40 procedures. Determine the risks of postoperative mortality in each group and determine whether the difference is statistically significant.
16.3 HIV infection among women entering the New York State Correctional System (similar to lab exercise). A study by Smith et al. (1991) determined the prevalence of HIVseropositivity in female prison inmates. Crosstabulated results by intravenous drug use (IVDU) are shown below. Individual records stored online in PRISON.SAV.
IVDU HIV+ HIV
+ 61 75 136
 27 312 339
88 387 475(A) Calculate the prevalence of HIV in each group.
(B) Calculate the prevalence ratio associated with intravenous drug use and then interpret your results in plain terms.
(C) Calculate a 95% confidence interval for the prevalence ratio. Interpret your results.
(D) Use a continuity correct (Yates's) chisquare test to derive a P value for the association. Show all hypothesis testing. Explain why Fisher's test is unnecessary.
(E) Replicate the analysis in SPSS.
(F) Suppose you were to plan a study in a prison population to see if ethnic group is an independent risk factor for HIV. You want to achieve 90% power with alpha = 0.01 (twosided). We will use a equal number of study participants in each ethnic group. Determine the number of study participants needed to detect a twofold difference in prevalence.
(G) Determine the sample size needed to detect a 50% increase in risk.
16.4 Treatment of acute otitis media [Similar to 9.5.15]. A trial on the treatment of otitis media studied clearance of infection within 14 days of treatment in two groups. Group 1 received cefaclor and group 2 received amoxicillin (Mandel et al., 1982; entire article). Crosstabulated data are shown below. Individual records are stored online in the file EAR.SAV.
CLEARANCE
AB 1 2 TOTAL
1 89 61 150
2 56 72 128
TOTAL 145 133 278(A) Calculate the incidence of the clearance of infection in each ear. [This unit of observation in this analysis is each ear, not each patient. This is open to criticism, but let's go with this for now.]
(B) Calculate the incidence proportion ratio associated with cefaclor. Interpret this statistic.
(C) Calculate a 95% confidence interval for the incidence proportion ratio. Interpret your results.
(D) Conduct a chisquare test. Interpret your test results.
(E) You are planning a study of a new antibiotic with cefaclor as your control group. How large a sample is needed to detect a 25% increase in clearance with alpha = 0.01 with 80% power? You are going to use a 1:1 ratio of sample sizes. Be explicit in your assumptions.
16.5 Cytomegalovirus and coronary restenosis [similar to 9.5.5]. Each year cardiologists perform procedures to blocked coronary arteries only to have may of these repaired arteries reclog (restenosis) afterwards. A study sponsored by the NIH Heart, Lung and Blood Institute was performed to determine whether prior infection with cytomegalovirus was predictive of arterial restenosis (Zhou et al., 1996). In 21 of the 49 patients with serologic evidence of cytomegalovirus infection, regrowth of arterial plaque was noted. In contrast, only 2 of the 26 patients seronegative patient had restenosis.
(A) Calculate the risk ratio of restenosis associated with CMV infection. Include a 95% confidence interval. (Always pause to interpret results.)
(B) Conduct a chisquare test of H_{0}: RR = 1.
16.6 UGDP [similar to 9.5.14]. The University Group Diabetes Program assessed the efficacy of various oral hypoglycemic^{ }treatments, insulin, and diet in the prevention^{ }of vascular complications in diabetics. Unexpectedly, it was found that 26 (13%) out of 204 patients treated with an oral hypoglycemic called phenformin died from cardiovascular disease. In contrast, 2 (3%) of 64 control patients in this arm of the trial died of cardiovascular disease.
(A) Is an exact procedure (e.g., Fisher's) necessary to test these data, or can you use a chisquare test? Explain your reasoning.
(B) Calculate a P value for the problem and comment on your findings.
16.7 Oral contraceptives and myocardial infarction [new]. A study was conducted to determine the effect of oral contractive use on heart disease risk in 40 to 44year old women (fictitious data). This study found 13 new cases among 5000 OC users over 3years of followup. In contrast, among 10,000 nonusers, 7 developed a first myocardial infarct. [Data are fictitious but realistic.]
(A) Show data in 2by2 crosstabular form.
(B) Calculate the risk ratio. Include a 95% confidence interval. Show all work, and interpret your results.
(C) Conduct a statistical hypothesis test of association and discuss your results.
16.8 OSWEGO: An outbreak of gastroenteritis illness following a church supper. Data in the file oswego.sav are from a a food borne disease outbreak case study used by CDC (1992). Briefly, the study involves the investigation of a local health officer in the village of Lycoming, Oswego County, New York. An outbreak of acute gastrointestinal illness involved 46 cases all of which had attended a church supper is reported. Interview about the church supper were completed on 75 of the 80 persons known to be present at the church supper (including the 46 cases). [Optional: A full description of the case study can be downloaded by clicking here.] Download the dataset oswego.sav [rightclick > Save as] and then open it in SPSS. Crosstabulate the data by case status (variable ILL: 1 = yes, 2 = no) for each of the food item variables in the table below. Calculate risk ratio and Pvalue for each association, and tally the results in this table:
Food  Ate Food  Did Not Eat Food  Risk Ratio  95% CI for RR  P*  
Ill  Total  %  Ill  Total  %  
Baked Ham  29  46  63.0%  17  29  58.6%  1.1  0.7  1.6  0.70 
Spinach  26  43  ___  20  32  ___  ___  ___  ___ 
Mashed P.  23  37  ___  23  37  ___  ___  ___  ___ 
Cabbage Sal.  18  28  ___  28  47  ___  ___  ___  ___ 
JellO  16  23  ___  30  52  ___  ___  ___  ___ 
Rolls  21  37  ___  25  38  ___  ___  ___  ___ 
Brown bread  18  27  ___  28  48  ___  ___  ___  ___ 
Milk  2  4  ___  44  71  ___  ___  ___  ___ 
Coffee  19  31  ___  27  44  ___  ___  ___  ___ 
Water  13  24  ___  33  51  ___  ___  ___  ___ 
Cakes  27  40  ___  19  35  ___  ___  ___  ___ 
Van. ice cr.  43  54  ___  3  21  ___  ___  ___  ___ 
Choc. ice cr.  25  47  ___  20  27  ___  ___  ___  ___ 
Fruit salad  4  6  ___  42  69  ___  ___  ___  ___ 
* Pearson uncorrected chisquare test.
16.9 Kayexelate and colonic necrosis. Data from the Kayexelate and colonic necrosis study as described in the StatPrimer notes are shown below and can be downloaded by clicking HERE.
Necrosis +  Necrosis   
Generic + 
2  115 
Generic  
0  862 
(A) Determine the incidence of colonic necrosis in the groups
(B) Calculate expected cell counts. Which test would you use with these data?
(C) Calculate and report an appropriate P value.
16.10 Yates, 1934 (2by2). The following data from Hellman are reported in the classical article by Contingency tables involving small numbers and the c^{2}^{ }test published in Journal of the Royal Statistical Society Suppl., 1, 1934, 217235 by Frank Yates (p. 230). The frequency of dental malocclusion in infants is crosstabulated by whether the infant was or wasn't breastfed. Four of 20 in the breastfed group (20%) had normal teeth while only 1 of 22 (4.5%) of the nonbreastfed group had normal teeth:
Normal teeth 
Malocclusion 

+ 
4  16 
 
1  21 
(A) Can you use a chisquare or z test with these data? Explain
(B) Use WinPepi, www.OpenEpi.com, or some other software utility to calculate an exact test for these data. Is the difference in malocclusions statistically significant?
16.11 Yates, 1934 (3by2). The data considered in the prior exercise also considered a third category: breast and bottle fed. The data for the 3by2 table are shown below.
(A) Can you use a chisquare test of association on these data? Explain.
(B) Use WinPepi > Compare2.exe > Program F1 to calculate a Fisher's or midP exact Pvalue for the data.
Normal teeth 
Malocclusion 

4  16  
Bottle fed  1  21 
Brst +bottle 
3  47 
16.12 Binge drinking on campus by gender (similar to Ex. 9.14). It has been estimated that, overall, 19.4% of students at 4year U.S. colleges engage in frequent binge drinking (Wechsler et al., 1994), when "frequent binge drinking" is defined as having five or more drinks in a row three or more times the prior two week period. Data for men and women separately are:
Freq. binge + 
Freq. binge  

Men 
1630  5550 
Women 
1684  8232 
(A) Calculate the prevalence ratio ("RR") of binge drinking for males relative to females. Then, fill in this blank: Male have a ____% greater prevalence of binge drinking than females.
(B) Under what conditions will the prevalence ratio approximate the risk ratio?
(C) Calculate a 95% confidence interval for the prevalence ratio.
16.13 Don't sweat the small stuff or P = 0.05. Consider a study in which 40 of 320 individuals (12.5%) in the treatment group experiences an outcome. In contrast, 26 of 336 (7.7%) of the control group experience the outcome. (Data are shown below.) Calculate chisquare statistics and P values for this problem using both Pearson's and the continuitycorrected (Yates') methods. You may use a software utility such as WinPepi or www.OpenEpi.com for your calculations. Discuss the results of each test. Is it reasonable to derive different conclusions with the different tests?

Adverse event 



Yes 
No 
Total 
Treatment 
40  280  320 
Control 
26  310  336 
Total 
66  590  656 
16.14. Tobacco use in high school students. Refer back to Exercise 10.1. (This exercise compared salivary cotinine levels in male and female students.)
(A) Calculate the RR of smoking for males. Include a 95% confidence interval.
(B) Interpret your results and say how these results relate to the chisquare test produced for Exercise 10.1.
16.15 Do seatbelt laws prevent injury? Refer back to Exercise 10.3. Reclassify the response to either "no injury" or "injury." Display the data in a 2by2 table and compare the incidence of "no injury" to injury" in the form of a risk ratio and interpret these results. Include a 95% confidence interval.
16.16.Efficancy of echinacea (reducing the severity of symptoms). Refer back to exercise 10.10. Merge the moderate and severe responses. Then compare the incidence of mild symptoms to moderate/severe symptoms in the form of a risk ratio. Calculate a 95% confidence interval for the RR, and interpret your results.
16.17 Anger and heart disease (hard outcome, hypertensives). Refer back to Exercise 10.12. Calculate risk ratios for
(A) moderateanger vs. lowanger
(B) highanger vs. lowanger.
(C) Does a doseresponse pattern emerge?
16.18 Helicopter evacuation and survival following trauma. Accident victims may be transported to the hospital by helicopters or, more typically, by road ambulance. Does the use of helicopters actually save lives? This exercise compares survival rates in victims by evacuation method.
(A) The table that follows crosstabulates data for all accidents. Calculate the crude relative risk of death associated with helicopter evacuation.
Table A: All accidents 


Died 
Survived 
Total 
Helicopter 
64 
136 
200 
Road 
260 
840 
1100 
(B) Data stratified by the seriousness of the accident are reported. Calculate these strataspecific relative risks.
Table B: Serious accident 


Died 
Survived 
Total 
Helicopter 
48 
52 
100 
Road 
60 
40 
100 
Table C: Less serious accidents 


Died 
Survived 
Total 
Helicopter 
16 
84 
100 
Road 
200 
800 
1000 
(C) How do you explain the discrepancy between the crude results and strataspecific results?
(D) Calculate the MantelHaenszel adjusted summary relative risk for helicopter evaluation and death while adjusting for the seriousness of the accident.
Key to Odd Numbered Problems Key to Even Numbered Problems (may not be posted)