Question

A clinical study was conducted on individuals with advanced stage of Hepatocellular Carcinoma to test three lines of Treatments: T1, T2 and T3. Thirthy-six patients with stage III Hepatocellular Carcinoma who agreed to take part in the experiment were randomly allocated one of three line of Treatments T1, T2 and T3. The primary outcome was mortality, and patients were monitored for up to 60 months (5 years) after recruitment. The data (in months) so obtained are given as follows:  

Patient ID Survival time Outcome Treatment Patient ID Survival time Outcome Treatment
ID001 14 Died T3 ID019 50 Died T1
ID002 27 Unknown T1 ID020 54 Unknown T3
ID003 37 Unknown T3 ID021 57 Died T2
ID004 44 Died T1 ID022 60 Survived T3
ID005 27 Died T2 ID023 20 Died T1
ID006 29 Died T3 ID024 22 Unknown T2
ID007 50 Died T2 ID025 11 Unknown T2
ID008 31 Died T1 ID026 12 Unknown T1
ID009 54 Died T2 ID027 57 Unknown T3
ID010 32 Died T2 ID028 60 Survived T3
ID011 32 Unknown T2 ID029 44 Died T1
ID012 60 Unknown T1 ID030 47 Unknown T2
ID013 2 Unknown T2 ID031 32 Died T2
ID014 42 Died T3 ID032 34 Died T1
ID015 42 Unknown T2 ID033 17 Died T2
ID016 60 Died T3 ID034 6 Died T1
ID017 60 Survived T3 ID035 50 Unknown T3
ID018 47 Died T3 ID036 14 Unknown T2

 For this data,
(i) Construct Kaplan and Meier survival curves.
(ii) Test whether there is a significant difference between the survival distributions of the patients under all treatments at 5% level of significance. 

23 Mar 2023
Answer :
Word Count : 257

(i) To construct the Kaplan-Meier survival curves, we need to first calculate the survival probability for each treatment group at each distinct survival time point.

For Treatment T1:

Survival times: 2, 19, 34, 44

Number of patients at risk: 12, 11, 9, 7

Number of deaths: 3, 1, 1, 1

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__________ ____ ________ __________ _________ _______ ____ ______ _____ ________ __________ _______.
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_____ ______ _______ _____ __________.
___ __________ _________ ________ _____ ____ ___ _______ __________ _____ __________.
________ ______ ____ ________ ____ _____ _________ ___ _____ _____.
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__________ __________ __________ ________ _________ ________ _______ __________ ____ ______ __________ ____.
_____ __________ ____ __________ __________ __________ __________ _________ ________.
__________ _______ ___ _____ __________ _____ ___ ____ _____ ___.
_________ ________ __________ _________ _____ _________ _________ __________ _______ _____.
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Related Questions

A clinical study was conducted on individuals with advanced stage of Hepatocellular Carcinoma to test three lines of Treatments: T1, T2 and T3. Thirthy-six patients with stage III Hepatocellular Carcinoma who agreed to take part in the experiment were randomly allocated one of three line of Treatments T1, T2 and T3. The primary outcome was mortality, and patients were monitored for up to 60 months (5 years) after recruitment. The data (in months) so obtained are given as follows:  

Patient ID Survival time Outcome Treatment Patient ID Survival time Outcome Treatment
ID001 14 Died T3 ID019 50 Died T1
ID002 27 Unknown T1 ID020 54 Unknown T3
ID003 37 Unknown T3 ID021 57 Died T2
ID004 44 Died T1 ID022 60 Survived T3
ID005 27 Died T2 ID023 20 Died T1
ID006 29 Died T3 ID024 22 Unknown T2
ID007 50 Died T2 ID025 11 Unknown T2
ID008 31 Died T1 ID026 12 Unknown T1
ID009 54 Died T2 ID027 57 Unknown T3
ID010 32 Died T2 ID028 60 Survived T3
ID011 32 Unknown T2 ID029 44 Died T1
ID012 60 Unknown T1 ID030 47 Unknown T2
ID013 2 Unknown T2 ID031 32 Died T2
ID014 42 Died T3 ID032 34 Died T1
ID015 42 Unknown T2 ID033 17 Died T2
ID016 60 Died T3 ID034 6 Died T1
ID017 60 Survived T3 ID035 50 Unknown T3
ID018 47 Died T3 ID036 14 Unknown T2

 For this data,
(i) Construct Kaplan and Meier survival curves.
(ii) Test whether there is a significant difference between the survival distributions of the patients under all treatments at 5% level of significance. 

A researcher is interested to check the relationship between the serum creatinine (in mg/dL) with the weight (in kg) and gender (0 if female and 1 if male). The data were collected from the hospital records to examine the contribution of these variables to serum creatinine. A total of 40 patients were sampled and the data are shown in the following table: 

S. No. Serum Creatinine Weight Gender
1 0.7 46 1
2 1.3 65 1
3 1 59 1
4 1.5 84 0
5 1.7 91 1
6 1.5 78 1
7 1 53 0
8 0.7 49 1
9 0.5 42 0
10 1.6 87 0
11 1.1 53 1
12 0.8 54 0
13 1.3 65 1
14 1.1 61 1
15 1.3 71 0
16 1.3 71 0
17 1.2 68 0
18 1.3 65 1
19 1 55 1
20 1.2 66 0
21 1.1 55 1
22 0.9 55 0
23 0.9 62 0
24 1.1 65 0
25 0.8 54 0
26 0.5 45 0
27 0.6 45 0
28 1 62 0
29 0.5 40 0
30 0.9 58 0
31 1.3 65 1
32 1.1 58 1
33 1.4 67 1
34 0.8 42 1
35 1.6 81 1
36 1.8 92 1
37 1.5 80 0
38 1.7 91 1
39 0.8 55 0
40 0.5 33 0

(i) Prepare a scatter plot to get an idea about the relationship among the variables.
(ii) Fit a linear regression model and its related analysis at 1% level of significance.
(iii) Does the fitted regression model satisfy the linearity and normality assumptions?
(iv) Also, draw both fitted regression lines on the scatter plot. 

A random sample of 440 patients of cardiology department of a hospital was taken and their workout timing and severity of heart disease status were recorded. The following table shows the workout timing and severity of heart disease:  

Workout (in minutes) Severity of Heart Disease
Low Mild Moderate High Very High
No workout 5 13 26 21 23
0- 15 6 15 19 19 21
15 to 30 16 17 14 16 12
30 to 45 18 17 13 11 9
45 to 60 20 19 15 13 7
≥ 60 16 22 6 5 6

 Test at 5% level of significance whether workout habit and heart disease are associated with to each other or not.  

To study the association between the diabetic patients and their family history of diabetes, the following data were obtained on 70 subjects.  

Diabetes in Family Diabetes in Subject   Total
  Yes No  
Yes 14 3 17
No 3 50 53
Total 17 53 70

Which test is appropriate in this situation? Check whether the diabetes runs with generations in families or not at 5% level of significance using appropriate test.  

A hypothetical data of 40 patients on age (in years), weight (in kgs) and systolic blood pressure (in mm/hg) denoting 1 for high SBP and 0 for normal SBP are given in the following table:

S. No. Age Weight SBP
1 52 60 0
2 56 68 1
3 51 54 0
4 63 74 1
5 54 62 0
6 51 67 0
7 51 66 0
8 54 65 0
9 59 71 1
10 51 89 1
11 56 72 1
12 55 72 1
13 46 57 0
14 42 54 0
15 52 63 0
16 65 67 1
17 50 67 0
18 42 53 0
19 50 68 1
20 39 55 0
21 47 48 0
22 42 45 0
23 45 57 0
24 56 83 1
25 49 63 0
26 56 94 1
27 55 87 1
28 53 67 0
29 65 70 1
30 44 70 0
31 48 54 0
32 61 79 1
33 45 85 0
34 63 98 1
35 49 78 0
36 65 80 1
37 60 70 1
38 53 98 1
39 41 53 0
40 50 70 1

For this data:

(i) Fit a multiple logistic regression model.

(ii) Test the significance of the individual model coefficients β1 and β2 at 5% level of significance.

(iii) Obtain the 95% confidence intervals for β1 and β2 .

(iv) Determine the Nagelkerke pseudo R-squared

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