Introduction to Biostatistics (ZJU)
W. Fu Sept-Oct. 2008
Homework Assignment 3. Chapters 6,11,12 [ due on Oct 23]
1. (10.13) A study was performed in 1985 relating the duration of IUD use to infertility. A group performed in 1985 relating the duration of IUD use to infertility. A group of 89 infertile IUD users were identified,. The women were subdivided by the duration of IUD use with the data presented in the following table. Duration of IUD use (months) __________________________________________ <3 [3, 18) [18, 36] >36 10 23 20 36 53 200 168 219
Cases Controls
Perform a test for heterogeneity of the proportions of cases in the four groups and interpret your result.
2. (10.21) Suppose we are interested in comparing the effectiveness of two different antibiotics, A and B, in treating gonorrhea. Each person receiving antibiotics A is matched with an equivalent person (age within 5 years, same sex), to whom antibiotics B is given. These people are asked to return to the clinic within 1 week to see if the gonorrhea has been eliminated. Suppose the results are as follows: (1). For 40 pairs of people, antibiotics are successful. (2). For 20 pairs of people, antibiotic A is effective whereas antibiotic B is not. (3). For 16 pairs of people, antibiotic B is effective whereas antibiotic A is not. (4). For 3 pairs of people, neither antibiotic is effective. Test for the relative effectiveness of the two antibiotics.
3. A study group of 576 working women 30-49 years old who took phenacetincontaining analgesics and a control group of 533 comparably aged women without such intake were identified in 1968 and followed for mortality and morbidity outcomes. One hypothesis to be tested was that phenacetin intake may influence renal (kidney) function and hence have an effect on specific indices of renal morbidity and mortality. The mortality status of these women was determined from 1968 to 1987. It was found that 16 of the women in the study group and 1 of the women in the control group died, where at least one of the cases of death was deemed to be renal. To test for the differences in renal mortality between the two groups in either direction, what statistical test should be used? Carry out this test and report the result.
4. A study was performed to estimate the decline in ischemic heart disease (IHD) mortality from 1965 to 1974 and to identify the causes behind it. A special group of patients aged 40 years and older were identified with heart trouble at the beginning of each studies (1965 study and 1974 study). The people who suffered IHD in each study and the total number of people who were at risk of IHD were reported by age group for each study were listed in the table below. Compute the Odds Ratio (OR) for IHD mortality from year 1974 to 1965 by fitting a multiple logistic regression model. Note: please see the revised lecture note for the definition of odds. Report of people who suffered at risk of IHD with percentage (%) and total number of people who were at risk in these two studies (1965 and 1974) 1965 study Sex and age Males < 60 60-69 70+ Female <60 60-69 70+ 0.0 23.4 25.8 32 47 62 0.0 12.9 11.1 26 31 45 % 11.6 38.5 47.1 Number at risk 43 39 34 1974 study % 7.3 4.2 25.0 Number at risk 41 24 12
5. (13.58, 13.60 and 13.61) Sudden death is an important, lethal cardiovascular endpint. Most previous studies of risk factors for sudden death have focused on men. Looking at this issue for women is important as well. For this purpose, data were used from the Framingham Heart Study. Several potential risk factors, such as age, blood pressure, and cigarette smoking, are of interest and need to be controlled for simultaneously. Therefore a multiple logistic regression model were fitted to these data as shown in the following table. Question 1. (13.58) Use the Wald Chi-squares method (df = 1) to assess the individual risk factors by Chi-squares X2 = [ b / se(b)]2. Question 2. (13.60) Compute the odds ratio (OR) relating the additional risk of sudden death per 100-centiliter decrease in vital capacity after adjustment for the other risk factors. Question 3. (13.61) Provide a 95% confidence interval for the above OR.
Multiple logistic regression model relating 2-year incidence of sudden death in females without prior coronary heart disease to several risk factors. Risk factor regression coefficient b se (b) Intercept Systolic blood pressure (mmHg) 0.0019 0.0070 Framingham relative weight -0.0060 0.0100 (%) Cholesterol 0.0056 0.0029 (mg/100 ml) Glucose 0.0066 0.0038 (mg/100 ml) Cigarette Smoking 0.0069 0.0199 (cigarette / day) Hematocrit (%) 0.111 0.049 Vital Capacity -0.0098 0.0036 (centiliters) Age (years) 0.0686 0.0225 _________________________________________________________________
6. In a loglinear model below with a offset accounting for the number of subjects at risk in different sub-group of subjects by risk factors, some people suggest to remove the offset term by simply taking the ratio of the number of cases to the number of subjects at risk. Please comment on this suggestion and justify why or why not you believe this should be done. Log (Expected number of incidence) = log (number of people at risk) + intercept + Xb