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
.
(a) True. Sensitivity is calculated as the proportion of true positives among all diseased cases. Here, sensitivity = 170 / 200 = 0.85. (b) False. Adjusted R² is calculated using the formula: [ \text{Adjusted } _______ _________ ________ _________ ________ __________ __________ ____ _________ _____.
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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 |
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
.
Probit model and Complementary log-log model.
Coefficient of determination and adjusted coefficient of determination.
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.
Chi-square test and McNemar’s test.
Explain the Kaplan and Meier method of estimation with an example.