Abstract
In epidemiologic studies, we compare disease frequencies of two or more groups using a measure of effect. We will describe several types of measures of effect in this chapter. The choice of measure typically depends on the study design being used.
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Doll R, and Hill AB. Smoking and carcinoma of lungs: preliminary report. Br Med J 1950;2:739-48.
Dyer AR, Stamler J, Shekelle RB. Serum cholesterol and mortality from coronary heart disease in young, middle-aged, and older men and women in three Chicago epidemiologic studies. Ann of Epidemiol 1992;2(1-2): 51-7.
Greenberg RS, Daniels SR, Flanders WD, Eley JW, Boring JR. Medical Epidemiology (3rd Ed). Lange Medical Books, New York, 2001.
Hammond EC, Horn D. The relationship between human smoking habits and death rates. JAMA 1958;155:1316-28.
Johansson S, Bergstrand R, Pennert K, Ulvenstam G, Vedin A, Wedel H, Wilhelmsson C, Wilhemsen L, Aberg A. Cessation of smoking after myocardial infarction in women. Effects on mortality and reinfarctions. Am J Epidemiol 1985;121(6): 823-31.
Kleinbaum DG, Kupper LL, Morgenstern H. Epidemiologic Research: Principles and Quantitative Methods. John Wiley and Sons Publishers, New York, 1982.
Spika JS, Dabis F, Hargett-Bean N, Salcedo J, Veillard S, Blake PA. Shigellosis at a Caribbean Resort. Hamburger and North American origin as risk factors. Am J Epidemiol 1987;126 (6): 1173-80.
Steenland K (ed.). Case studies in occupational epidemiology. Oxford University Press, New York, NY: 1993.
Uitterlinden AG, Burger H, Huang Q, Yue F, McGuigan FE, Grant SF, Hofman A, van Leeuwen JP, Pols HA, Ralson SH. Relation of alleles of the collagen type I alpha1 gene to bone density and the risk of osteoporotic fractures in postmenopausal women. N Engl J Med 1998;338(15):1016-21.
Wynder EL, Graham EA. Tobacco smoking as a possible etiologic factor in bronchogenic carcinoma: a study of six hundred and eighty-four proved cases. JAMA 1950;143:329-36.
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Appendices
Homework
1.1 ACE-1. Measures of Effect: Chewing Tobacco vs. Oral Leukoplakia
A study is conducted to investigate the association between chewing tobacco and oral leukoplakia (a precancerous lesion) among currently active professional baseball players in the southeastern United States. A roster of all active players is obtained (n = 500). All potential study subjects agree to participate. Each subject has an interview regarding current use of chewing tobacco and has his mouth examined by a dentist. Of the 500 subjects, 125 subjects chew tobacco and 375 do not chew tobacco. Of the chewers, 25 have evidence of oral leukoplakia. Of the non-chewers, 15 have evidence of oral leukoplakia. All 500 players were followed for a period of 5 years. Of those who had evidence of oral leukoplakia, 18 died of some type of oral cancer.
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a.
Draw a 2 x 2 table demonstrating the relationship between chewing tobacco and oral leukoplakia. In drawing this table, put the exposure variable on the columns and the health outcome variable on the rows.
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b.
Draw a second 2 x 2 table demonstrating the relationship between chewing tobacco and oral leukoplakia, but this time, put the exposure variable on the rows and the health outcome variable on the columns.
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c.
Using the table drawn in part a, compute the prevalence ratio and the prevalence odds ratio of oral leukoplakia for chewers compared to non-chewers. Are these two estimates close to one-another? Why are these prevalence measures and not incidence measures?
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d.
Using the table drawn in part b, compute the prevalence ratio and the prevalence odds ratio of oral leukoplakia for chewers compared to non-chewers. Are these estimates equal to their corresponding estimates computed using the table drawn in part a? Explain.
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e.
Ignoring the issue of statistical inference and the control of other variables, what do these results say about the relationship between chewing tobacco and the presence of oral leukoplakia?
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f.
Calculate the case-fatality rate (actually, a risk) in this study. Why is this a measure of risk?
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g.
Based on the information provided, why can’t you evaluate whether tobacco chewers have a higher case-fatality risk than non-chewers?
1.2 ACE-2. Rate Ratios: Colon Cancer Deaths
The following table shows the number of colon cancer deaths and person-years of risk by the frequency of aspirin for males and females.
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a.
Calculate the death rates and the rate ratios for each of the aspirin-use categories in the above table.
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b.
Given the results in this table, what is your conclusion about the association between the use of aspirin and fatal colon cancer?
1.3 ACE-3. Rate Ratios: NSAIDS’s
NSAID’s (i.e., non-steroidal anti-inflammatory drugs) are prescribed or taken over-the-counter for acute and chronic, perceived and diagnosed illnesses. For this reason, the investigators in the study described in question 2 also analyzed the data excluding those individuals with selected illnesses at the start of follow-up. Table 2 shows the number of colon cancer deaths by the frequency of aspirin-use after exclusion of those subjects with selected illnesses.
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a.
Calculate the rates and rate ratios for each of the aspirin-use categories in the above table.
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b.
Given the results in both Table 1 (from question 2) and Table 2, what do you conclude about the association between the use of aspirin and fatal colon cancer?
1.4 ACE-4. Incidence Measures of Effect: Quitting Smoking
The following data come from a study of self-help approaches to quitting smoking. Smokers wanting to quit were randomized into one of four groups (C = control, M = quitting manual, MS = manual + social support brochure, MST = manual + social support brochure + telephone counseling). Smoking status was measured by mailed survey at 8, 16, and 24 months following randomization. These are the 16-month results:
Randomization Group | |||||
---|---|---|---|---|---|
Status | C | M | MS | MST | Total |
Quit | 84 | 71 | 67 | 109 | 331 |
Smoking | 381 | 396 | 404 | 365 | 1546 |
Total | 465 | 467 | 471 | 474 | 1877 |
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a.
The “quit rate” is calculated as the proportion abstinent (quit) at the time of follow-up. What was the overall 16-month quit rate for all subjects? Based upon quit rates, which of the intervention groups was the least successful as of the 16-month follow-up? Justify your answer.
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b.
Is this “quit rate” a cumulative incidence-type measure or an incidence density-type measure? Justify your answer.
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c.
Compare the quit rate for the MST group with that of the control group by calculating both a CIR and an OR. Show your work. Provide an interpretation of the CIR.
1.5 ACE-5. Incidence Density Ratio: Radiotherapy Among Children
In a study of adverse effects of radiotherapy among children in Israel, 10,834 irradiated children were identified from original treatment records and matched to 10,834 non-irradiated comparison subjects selected from the general population. Subjects were followed for a mean of 26 years. Person-years of observation were: irradiated subjects, 279,901 person-years; comparison subjects, 280,561 person-years. During the follow-up period there were 49 deaths from cancer in irradiated subjects, and 44 in the non-irradiated population comparison subjects.
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a.
What are the rates of cancer death (per 105 person-years) in each of the two groups?
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b.
Calculate and interpret the IDR for cancer death comparing irradiated and non-irradiated subjects.
1.6 ACE-6. Odds Ratio: Alcohol Consumption vs. Myocardial Infarction
A case-control study was conducted to assess the relationship of alcohol consumption and myocardial infarction (MI). Cases were men aged 40 to 65 years who had suffered their first MI during the six months prior to recruitment into the study. A group of age-matched men who had never experienced an MI were selected as controls. Data from this study are summarized below:
Exposed | Unexposed | Totals | |
---|---|---|---|
Diseased | 158 | 201 | 359 |
Nondiseased | 252 | 170 | 422 |
Totals | 410 | 371 | 781 |
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a.
What is the odds of exposure among the controls?
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b.
Calculate and interpret the exposure odds ratio for these data.
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c.
Do you think that the OR calculated in part b above is a good estimate of the corresponding risk ratio for the relationship between alcohol and MI? Why or why not?
Answers to Study Questions and Quizzes
2.1 Q5.1
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1.
The five-year risk for continuing smokers is 4½ times greater than the risk for smokers who quit.
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2.
The risk ratio is very close to 1.0, which indicates no meaningful difference between the risks for the two groups.
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3.
Think of an inverse situation.
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4.
You should have the hang of this by now.
2.2 Q5.2
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1.
2
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2.
1
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3.
0.5
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4.
0.0104
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5.
0.0236
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6.
0.44 – In general, the risk ratio that compares two groups is defined to be the risk for one group divided by the risk for the other group. It is important to clearly specify which group is in the numerator and which group is in the denominator. If, for example, the two groups are labeled group 1 and group 0, and the risk for group 1 is in the numerator, then we say the risk ratio compares group 1 to group 0.
2.3 Q5.3
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1.
The odds that a case ate raw hamburger is about two ½ times the odds that a control subject ate raw hamburger.
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2.
Because the odds ratio is so close to being equal to one, this would be considered a null case, meaning that the odds that a case ate raw hamburger is about the same as the odds that a control subject age raw hamburger.
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3.
An odds ratio less than one means that the odds that a case subject ate raw hamburger is less than the odds that a control subject ate raw hamburger.
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4.
You should have the hang of this by now.
2.4 Q5.4
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1.
Not possible, odds ratio – The risk of disease is defined as the proportion of initially disease-free population who develop the disease during a specified period of time. In a case-control study, the risk cannot be determined.
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2.
1350/1357
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3.
1296/1357
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4.
192.86
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5.
21.25
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6.
9.08 – In general, the odds ratio that compares two groups is defined to be the odds for the cases divided by the odds for the controls. The odds for each group can be calculated by the formula P/(1-P), where P is the probability of exposure.
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7.
3
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8.
1
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9.
0.333
2.5 Q5.5
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1.
Of course! It is possible, for example, that mayonnaise actually contained the outbreak-causing bacteria and maybe most of the cases that ate raw hamburger used mayonnaise.
2.6 Q5.6
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1.
683, 86, 0.77
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2.
odds, exposure, less than, odds, controls – If the estimated odds ratio is less than 1, then the odds of exposure for cases is less than the odds of exposure for controls. If the estimated odds ratio is greater than 1, then the odds of exposure for cases is greater than the odds of exposure for controls.
2.7 Q5.7
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1.
2.18
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2.
more likely
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3.
prevalence
2.8 Q5.8
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1.
That depends on the disease being considered and on the time-period of follow-up over which the risk is computed. However, for most chronic diseases and short time periods, a risk of.01 is not rare.
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2.
Yes, because even though the risk may not be rare, it may be small enough so that the ROR and the RR are approximately the same.
2.9 Q5.9
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1.
f = (1 – 0.17) / (1 – 0.36) = 1.30
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2.
No, since for these data, the estimated RR equals 2.1 whereas the estimate ROR equals 2.7.
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3.
f = (1 – 0.085) / (1 – 0.180) = 1.12
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4.
Yes, since the estimated RR is again 2.1, (0.180/0.085), but the estimated ROR is 2.4.
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5.
f = 1.05
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6.
Yes, since the estimated ROR is now 2.2.
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7.
In the context of the quit smoking example, risks below 0.10 for both groups indicate a “rare” disease.
2.10 Q5.10
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1.
The risk ratio in this study is 0.0805 divided by 0.0536, which equals 1.50.
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2.
The risk odds ratio is 47/537 divided by 64/1130 equals 1.54.
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3.
f = (1-0.0536) / (1-0.0805) = 1.03. The ROR = 1.03*RR = 1.03*1.50 = 1.54.
2.11 Q5.11
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1.
9.8
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2.
36.0
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3.
No
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4.
No – The risk ratio that compares two groups is defined to be the risk for one group divided by the risk for the other group. The odds ratio can be calculated by the cross product formula ad/bc. In general, a disease is considered “rare” when the OR closely approximates the RR.
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5.
2.44
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6.
2.49
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7.
Yes
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8.
Yes
2.12 Q5.12
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1.
EOR, RR, bias, controls, incident, prevalent
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2.
9
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3.
9
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4.
Yes – A disease is considered rare when the ROR closely approximates the RR.
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5.
50
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6.
9.00
2.13 Q5.13
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1.
38.7 per 1000 person-years – The mortality rate for diabetics equals 72/1,862.4 person-years = 38.7 per 1000 person-years.
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2.
13.9 per 1000 person-years – The mortality rate for non-diabetics equals 511/36,653.2 person-years = 13.9 per 1000 person-years.
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3.
2.8 – The rate ratio is 38.7 per 1000 person-years/13.9 per 1000 person-years = 2.8.
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4.
C
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Kleinbaum, D.G., Sullivan, K.M., Barker, N.D. (2013). Measures of Effect. In: ActivEpi Companion Textbook. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5428-1_5
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DOI: https://doi.org/10.1007/978-1-4614-5428-1_5
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