Exercises

(1) DOLL1950: Smoking and Lung Cancer (Doll & Hill, 1950)

An early case-control study of smoking and lung cancer found that 647 of 649 lung cancer cases were smokers. In contrast, 622 of 649 controls smoked.

(A) Display the data in a 2-by-2 table.
(B) Calculate exposure proportions in cases and controls (p^1 and p^2, respectively).
(C) Using EpiTable (of some other epidemiologic calculator), compute the exposure odds ratio (EOR^) and a 95% confidence interval for the EOR. Interpret your results.
(D) Test the hypothesis of no association. (List the null and alternative hypotheses; set alpha; compute the test statistics and p value, state your conclusion.) Interpret your results.

(2) ESOPH_CA.REC: Esophageal Cancer Study, Tobacco Analysis (Tuyns, 1977; Breslow & Day, 1980)

This is the same data set discussed in the chapter. However, for the current analysis, we'd like to look at tobacco consumption, dichotomized at 20 grams per day (variable TOB2). Data on case status is contained in ESOPH_CA (1=case, 2=control).

(A) Calculate exposure proportion in cases and controls.
(B) Compute the odds ratio and its 95% confidence interval.
(C) Perform a full test of association. (List the null and alternative hypotheses . . .)
(D) Summarize your results in narrative form.

(3) ESOPH_CA.REC: Esophageal Cancer Study, Age Analysis (Tuyns, 1977; Breslow & Day, 1980)

Data are once again from the French case-control study of esophageal cancer and various risk factors. For this analysis, let us dichotomize age at 55 years (variable AGE2). Subjects 55 years of age and above are classified as "older" subjects, whereas other subjects are classified as "younger." Determine the relationship between age and esophageal cancer using an approach similar to the one used above.

(4) BD2.REC: "Breslow & Day 2" (The Oxford Childhood Cancer Survey) (Stewart & Kneale, 1970; Kneale, 1971; Breslow & Day, 1980, p. 238)

Data come from a case-control study of childhood leukemia and lymphoma and in utero exposure to X-rays. Cases are children less than ten years of age in England and Wales that occurred during the period 1954-65 (variable CASE: 1 = yes, 2 = no). For each case, a neighborhood control of the same age and year of birth was selected. Exposure status is based on whether mothers were exposed to X-rays during pregnancy (variable XRAY: 1 = yes, 2 = no). Perform a complete case-control analysis, similar in type to the ones completed above.

(5) IUD: Intrauterine Device Use and Infertility (Cramer et al., 1985; Rosner, 1990, p. 381)

A study of contraceptive use and infertility found prior use of IUDs in 89 out of 283 infertile women, compared with 640 out of 3833 (fertile) control women.

(A) Calculate relevant case-control statistics (p^1, p^2, OR^, 95% confidence interval for OR).
(B) Test H0: EOR = 1. (Report all steps of the hypothesis testing procedure, starting with the statement of H0, finishing with the categorical conclusion to the test.)
(C) Summarize your results.

(6) PROSTATE.REC: Vasectomy and Prostate Cancer (Data source: Zhu et al., 1996)

A case-control study was conducted to help quantify the relationship between vasectomy and prostate cancer. (Comment: Although cases and controls were initially matched based on birth year and membership status, this is ignored in the exercise. Ignoring the match does not materially alter the results.)

(A) Calculate the exposure proportions in cases and controls.
(B) Calculate the odds ratio and its 95% confidence interval.
(C) Test the hypotheses of no association. (Set up the null and alternative hypotheses, set the alpha level, report a p value and state the conclusion.
(D) Summarize your results.
(E) What was the power of this analysis to detect an odds ratio of 1.5? (From the data we note: allocation ratio = 258/175 = 1.47; exposure proportion in controls = 36%; m1 = 175; m2 = 258, alpha = .05),
(F) Calculate the sample size requiremented to uncover the following odds ratios with a power of at least 80%:
EOR = 1.3
EOR = 1.5
EOR = 2.0
EOR = 3.0

(7) ASBESTOS.REC: Asbestos Exposure and Lung Cancer (Hypothetical data)

Data are from an occupation case-control study of lung cancer. The data set includes information on smoking (variable SMOKE: Yes/no), asbestos exposure (ASBESTOS: Yes, no), and whether the subject is a lung cancer case or control (LUNGCA: yes = case, no = control ).

(A) Calculate the odds ratio and a 95% confidence interval for the OR associated with smoking.
(B) Calculate the odds ratio and 95% confidence interval for the OR associated with asbestos exposure.
(C) Interpret the above results.


(8) BRAINTUM: Brain tumor risk electric blanket use / Power Analysis

A study finds no significant association between brain tumors and electric blanket use in children. (Didactic data for the original problem are in BRAINTUM.REC.) Using these data, determine the allocation ratio of controls to cases, let alpha = .05, determine a good estimate for p2, and then calculate the study's power to uncover the following odds ratios:

EOR = 1.1
EOR = 1.2
EOR = 1.3
EOR = 1.4
EOR = 1.5
EOR = 1.6
EOR = 1.7
EOR = 2.0
Combine the above power analyses in the form of a power curve so that the x-axis represents the expected odds ratio and the y-axis represents the study's power. Discuss your power analysis (e.g., At what point does the study's power become adequate? What can be done to improve the study's power? Would you supplement the study with additional information? etc.)