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Poisson regression
Polytomous logistic models
Suppose a researcher wants to evaluate the effect of cholesterol on the blood pressure. The following data on serum cholesterol (in mg/dL) and systolic blood pressure (in mm/Hg) were obtained for 15 patients to explore the relationship between cholesterol and blood pressure:
| S. No. | Cholesterol (mg/dL) | SBP (mm/Hg) |
| 1 | 300 | 150 |
| 2 | 410 | 270 |
| 3 | 380 | 210 |
| 4 | 530 | 310 |
| 5 | 570 | 350 |
| 6 | 490 | 310 |
| 7 | 340 | 210 |
| 8 | 320 | 150 |
| 9 | 280 | 110 |
| 10 | 550 | 320 |
| 11 | 340 | 220 |
| 12 | 350 | 170 |
| 13 | 410 | 260 |
| 14 | 390 | 230 |
| 15 | 450 | 270 |
Kaplan and Meier method
Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.
The following data on diagnosis of coronary heart disease (where 0 indicating absence and 1 indicating presence), serum cholesterol (in mg/dl), resting blood pressure (in mmHg) and weight (in kg) were obtained for 80 patients to explore the relationship of coronary heart disease with cholesterol and weight.
| S. No. | Serum Cholesterol (mg/dl) | Weight (kg) | Number of Patients having CHD | Total Number of Patients | |||
| 1 | 420 | 60 | 10 | 20 | |||
| 2 | 450 | 68 | 15 | 30 | |||
| 3 | 400 | 54 | 4 | 15 | |||
| 4 | 510 | 74 | 2 | 10 | |||
| 5 | 480 | 62 | 1 | 5 | |||
(i) Fit a multiple logistic model for the dependence of coronary heart disease on the average serum cholesterol and weight considering and
the initial values of the parameters (solve only for one Iteration).
(ii) Test the significance of the fitted model using Hosmer-Lemeshow test at 5% level of significance.