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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Left and Right censoring
Explain the Kaplan and Meier method of estimation with an example.
A hypothetical study was conducted on ten participants who were followed up for the development of coronary heart disease (CHD) over a period of 10 years. The recorded data are given as follows:
| Participant ID | CHD Time |
|---|---|
| P1 | 5 |
| P2 | 8 |
| P3 | 2 |
| P4 | 6+ |
| P5 | 9 |
| P6 | 6 |
| P7 | 10+ |
| P8 | 4 |
| P9 | 8 |
| P10 | 4+ |
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.