Kaplan and Meier method
The Kaplan-Meier method is a statistical technique used to estimate survival probabilities for individuals or groups over time. It is commonly used in medical research to analyze the survival rates of patients with a particular disease or condition.
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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 | ||
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
as 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.
A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes:
| Workout (in minutes) | Severity of diabetes status | ||||||||
| Low | Moderate | High | |||||||
| 0 −15 | 06 | 27 | 19 | ||||||
| 15 to 30 | 08 | 36 | 17 | ||||||
| 30 to 45 | 21 | 45 | 33 | ||||||
| ≥ 45 | 14 | 18 | 06 | ||||||
State whether the following statements are True or False. Give reason in support of your answer:
(a) The value of sensitivity of the following results of a diagnostic test is 0.85.
| Disease | Test result | Total | |||
| + | – | ||||
| Present | 170 | 30 | 200 | ||
| Absent | 20 | 280 | 300 | ||
| Lung Cancer | No Lung Cancer | Total | ||||||
| Smokers | 100 | 1220 | 1320 | |||||
| Non-smokers | 50 | 2260 | 2310 | |||||
(c) The logit link function is .
(d) We define three indicator/dummy variables for a regressor variable with three categories.
(e) Left censoring occurs whenever the exact time of occurrence of an event is not known.
Explain the assumptions underlying multiple linear regression model.
Polytomous logistic models
Poisson regression