Kaplan and Meier method
The Kaplan-Meier method, also known as the product-limit method, is a non-parametric statistic used to estimate the survival function from lifetime data. It is commonly employed in medical research, particularly in studying the time it takes for events like death or disease progression to occur.
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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 | 38 | 17 |
| 30 to 45 | 21 | 45 | 33 |
| ≥ 45 | 14 | 18 | 06 |
Kaplan and Meier method
Explain the assumptions underlying multiple linear regression model.
Poisson regression
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.
Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.
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 | Totel | |
| Smokers | 100 | 1220 | 1320 |
| Non-smokers | 50 | 2260 | 2310 |
(c) The logit link function is log
(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.