Homework 4 (due on Wednesday, April 5)

• Problems will be added until the last class before the due date.
• No electronic submission unless explicitly allowed.
• Use your own words when answering questions. Copying from other sources (including textbooks, handouts, my blog) is strongly discouraged, because it often indicates you don't understand your answer.

1. In a 1985 study of the relationship between contraceptive use and infertility, 89 out of 283 infertile women, compared with 640 out of 3833 control women, had used an IUD at some time in their lives.
   • Carry out a Pearson’s chi-squared test of association between contraceptive use and infertility.
   • Compute a 95% CI for the difference in the proportion of women who have ever used IUDs between the case and control groups.
   • Compute the odds ratio in favor of ever using an IUD for infertile women versus control women. Provide a 95% CI for the true odds ratio corresponding to your answer.
2. The presence of bacteria in the urine (bacteriuria) has been associated with kidney disease. Conflicting results have been reported from several studies concerning the possible role of oral contraceptives (OC) on bacteriuria. The following data were collected in a population-based study of non-pregnant pre-menopausal women below the age of 50. The data are presented on an age-specific basis:

   Age group	OC users		Non-OC users
   	with bacteriuria	total	with bacteriuria	total
   16-19	1	84	9	281
   20-29	16	284	22	552
   30-39	6	96	34	623
   40-49	4	18	13	482

   • Input the data into your statistical software package. Use the software to create tables to make sure the data entered by you reflect the data collected in the study. (You may learn how to input data into Stata from the examples in my Stata Notes.)
   • Perform a significance test to examine the association between OC use and bacteriuria after controlling for age.
   • Estimate the odds ratio in favor of bacteriuria for OC users versus non-OC users after controlling for age. Provide a 95% CI for the odds ratio.
   • Is the association between bacteriuria and OC use comparable among different age groups? Why or why not?
   • Suppose you did not control for age in the preceding analyses. Calculate the crude (unadjusted for age) odds ratio in favor of bacteriuria for OC users versus non_OC users.
   • How do your answers between adjusting and not adjusting for age relate to each other? Explain any differences found.
3. In a study on esophageal cancer, researchers collected data on 975 subjects. The variables collected were age, alcohol and tobacco usage, and esophageal cancer status. The data were tallied into a four-way table with 6 age groups, 4 alcohol usage levels, 4 tobacco usage levels, and 2 cancer status. In the data, the "patients" column has the counts for all four-way combinations. The "heavy" variable is an indicator variable for heavy alcohol consumption. The values and their meanings are:
   age: 1 (25-34), 2 (35-44), 3 (45-54), 4 (55-64), 5 (65-74), 6 (>= 75)
   alcohol: 1 (0-39), 2 (40-79), 3 (80-119), 4 (>= 120)
   tobacco: 1 (0-9), 2 (10-19), 3 (20-29), 4 (>= 30)
   cancer: 0 (No), 1 (Yes)
   heavy: 0 (< 80 gm), 1 (>= 80 gm)
   Cancer is the outcome variable and age group, alcohol usage, and tobacco usage are input variables.
   • Understanding the relationships among the input variables is an important part of statistical analysis. It allows you to gain insight into how the variables correlate with each other and if the results on some variables could be influenced by inclusion of some other variables in the analysis. Explore the relationship among age group, alcohol usage, and tobacco usage.
   • For each input variable, create a two-way table between the input variable and the outcome variable, and carry out logistic regression analysis using the input variable as the only regression variable. Summarize results.
   • Carry out logistic regression analysis using all three input variables. Are the results similar or different from those in the last question? If they are different, why?
   • Explore the interaction effects among the input variables on the risk of esophageal cancer.