Question
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 |
Compute simple and weighted Kappa Statistic(s) to compare both methods.
Answer :
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Skip in 10
We are asked to compute the simple (unweighted) and weighted Kappa statistics manually for a 5×5 table comparing two diagnostic methods. Let’s solve it step by step. --- ### Step 1: Organize the table The observed frequencies (O_{ij}) are: | Method-II \ Method-I | None | Mild | Moderate | Severe | Extreme | Row sum | | -------------------- | ---- | ---- | -------- | ------ | ------- | ------- | | None | 89 | 5 | 16 | 2 | 4 | 116 | | Mild | 36 | 3 | 15 | 6 | 2 | 62 | | Moderate | 20 | 4 | 22 | 6 | 1 | 53 | | Severe | 14 | 2 | 37 | 18 | 16 | 87 | | Extreme | 4 | 1 | 16 | 23 | 50 | 94 | | Column sum | 163 | 15 | 106 | 55 | 73 | 412 | Total observations (N) = 412 --- ### Step 2: Compute simple (unweighted) Kappa The formula for simple Kappa: [ \kappa = \frac{P_o - P_e}{1 - P_e} ] Where: * (P_o =) proportion of observed agreement * (P_e =) proportion of expected agreement by chance
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Related Questions
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 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 |
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 |
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.
Left and Right censoring