Explain the Kaplan and Meier method of estimation with an example.
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Probit model and Complementary log-log model.
Explain the Kaplan and Meier method of estimation with an example.
2. A study was conducted to compare two diagnostic methods, say, Method-I and Method-II. The following table shows the classification of the presence of infection on a 5-point Likert Scale (none, mild, moderate, severe and extreme):
| Method-II | Method-I | ||||
| None | Mild | Moderate | Severe | Extreme | |
| None | 89 | 5 | 16 | 2 | 4 |
| Mild | 36 | 3 | 15 | 6 | 2 |
| Moderate | 20 | 4 | 22 | 6 | 1 |
| Severe | 14 | 2 | 37 | 18 | 16 |
| Extreme | 4 | 1 | 16 | 23 | 50 |
To study the relationship between age (in years) and cholesterol level (in mg/dL) of two groups of patients, the following data were recorded:
Group 1
| Age (years) | 46 | 52 | 39 | 65 | 54 | 49 | 76 | 71 |
|---|---|---|---|---|---|---|---|---|
| Cholesterol | 185 | 218 | 182 | 220 | 224 | 193 | 232 | 228 |
| Age (years) | 20 | 33 | 78 | 51 | 43 | 44 | 63 |
|---|---|---|---|---|---|---|---|
| Cholesterol | 180 | 238 | 275 | 244 | 242 | 268 | 260 |
Chi-square test and McNemar’s test.
State whether the following statements are True or False. Give reason in support of your answer:
(a) If there are 170 true positive cases out of 200 diseased cases, the sensitivity of the test will be 0.85.
(b) A multiple regression model with three regressor variables was fitted on 15 observations, and the following values were obtained:
Then, the adjusted R2 will be 0.9618.
(c) The method of least squares is used for fitting the logistic model.
(d) The survival function is the probability of an individual surviving less than a specified time t.
(e) If the relative risk for a clinical trial is , the relative risk reduction will be
.
4. The amount of dose (xi), total number of patients who received medicine (ni) and number of cured patients (yi) are recorded in the following table:
| S. No. |
|
|
|
| 1 | 5 | 24 | 60 |
| 2 | 10 | 18 | 48 |
| 3 | 15 | 12 | 40 |
| 4 | 20 | 20 | 80 |
| 5 | 25 | 26 | 104 |
(i) Fit a logistic model considering initial values of and
up to only one iteration.