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Advanced Biostatistical Methods Prof. DM Steinberg Homework Number 1 1. Zivin and Waud (Stroke, 1992) describe an experiment to study the drug MK801. The drug was designed to limit the negative impact of stroke. The experimenters caused ischemic events in experimental animals and then assessed the animals for neurological damage. The "dose" in this experiment is the length (in minutes) of the ischemic event. Most of the animals were in a control group that did not receive MK-801. If the drug is effective, the experimental group that received MK-801 should have lower probability of neurological damage. The following table gives the results of the experiment. Duration of Ischemia (min) 20 25 30 35 40 45 50 55 60 Control Group No Damage Damage 3 0 8 5 7 8 4 8 0 3 0 1 0 1 0 0 0 4 MK-801 Group No Damage Damage 1 0 1 0 1 0 2 0 1 0 1 1 2 0 0 1 0 1 1.1 Analyze each group separately by logistic regression. For each group, state a 95% confidence interval for the slope, estimate the LD50 (no need for a confidence interval) and estimate the probability of neurological damage if the ischemia lasts 40 minutes (again no CI). 1.2 Analyze the data from both groups together. Is there convincing evidence that MK-801 reduces the risk of neurological damage from ischemia? Fit appropriate logistic regression models and summarize the results, focusing on the above question. 2. The relationship between hypertension and coronary artery disease (CAD) was examined. Subjects with, and without, CAD were tested for hypertension. The subjects were also classified by age into two groups, 35-49 and 65 +. The data for the two age groups were as follows: For subjects aged 35-49: Hypertension Yes No Total CAD Yes 552 941 1493 Total No 212 495 707 764 1436 2200 For subjects aged 65 +: Hypertension Yes No Total CAD Yes 1102 1018 2120 Total No 87 106 193 1189 1124 2313 2.1 In both age groups, compute the odds ratio for suffering from CAD, for individuals with hypertension as opposed to individuals without hypertension. Compute a 95% confidence interval for each group-specific odds ratio. 2.2 Analyze the data by logistic regression. Fit appropriate models. (Note: as in class, you can often fit these different models as separate "blocks" in the analysis.) For each model that you fit, state first why that model is of interest (i.e. what substantive question you can answer by fitting the model), then present the results and finally summarize the important points in the output in a few words. For each model, compute a 95% confidence interval for the odds ratio relating CAD to hypertension. 3. A study in a mixed rural and urban district near Newcastle, UK, examined the relationship between smoking and 20-year survival. The original survey, conducted in 1972-1974, was a random sample of 1/6 of the residents. Twenty years later a follow-up survey was conducted to examine survival. The data here are a subset from the survey and include all women who were classified as current smokers or as never having smoked at the time of the original survey. Subjects are classified on the basis of smoking status and whether or not they were still alive at the time of the follow-up survey. In addition, the data are broken down by the age of the subject at the time of the original survey. The data are listed below. Age Group 18 - 24 25 - 34 35 - 44 45 - 54 55 - 64 65 - 74 75 - Non-smokers Alive Dead 61 1 152 5 114 7 66 12 81 40 28 101 0 64 Smokers Alive Dead 53 2 121 3 95 14 103 27 64 51 7 29 0 13 3.1 Analyze the data by logistic regression, treating age as a categorical variable. Summarize the relationship between smoking and 20-year survival. 3.2 Analyze the data by logistic regression, treating age as a numerical variable, with continuous dependence of the log odds for death on initial age. Summarize the relationship between smoking and 20-year survival. Use this model to estimating the probability of death, within 20 years, as a function of age, for both smokers and non-smokers; include a graph showing the estimated probability of death vs. age for each group.