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 | |||
(b) For the following cohort study, the relative risk for the lung cancer among smokers is 3.5.
| Lung Cancer | No Lung Cancer | Total | |||||||
| Smokers | 100 | 1220 | 1320 | ||||||
| Non-smokers | 50 | 2260 | 2310 | ||||||
(c) The logit link function is loglog .
(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.
Let's address each statement and evaluate whether it is true or false, providing explanations for each: ### (a) The value of sensitivity of the following results of a diagnostic test is 0.85. To calculate the sensitivity of the test, we use the formula: \[ \text{Sensitivity} = \frac{\text{True Positives}}{\text{True Positives} + \text{False Negatives}} \] From the table, the number of True Positives (TP) is 170 (disease present and test result positive), and the _________ __________ ________ ____ ______ ________.
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Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.
A study was conducted on 185 patients aged more than 45 years which are followed until the time of death or up to 10 years, whichever comes first. The patients have different covariates: age, gender (male/female), systolic blood pressure, smoking (yes/no), total serum cholesterol and diabetes (yes/no). The objective of this study is to determine which covariate influences the survival time. An analysis is conducted to investigate differences in all-cause mortality between men and women participating in the study. Suppose we obtain the following results after applying the Cox regression hazard model analyses:
| Risk Factor | Parameter Estimate | SE |
| Age | 0.150 | 0.010 |
| Gender | 0.450 | 0.150 |
| Systolic Blood Pressure | 0.015 | 0.008 |
| Smoking | 0.650 | 0.170 |
| Total Serum Cholesterol | 0.002 | 0.004 |
| Diabetes | -0.350 | 0.250 |
Polytomous logistic models
Kaplan and Meier method
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 | |||
as the initial values of the parameters (solve only for one Iteration).
Describe censoring and differentiate between different types of censoring with the help of examples which are not considered in Block 4 of MSTE-004.
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 | ||||