IGNOU PGDAST MSTE-004 2024 Assignment Cover

IGNOU MSTE-004 Solved Assignment 2024 | PGDAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

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Get the most comprehensive and accurate solution to the MSTE-004 assignment for the PGDAST program with our expert-written and verified MSTE-004 Solved Assignment 2024. This assignment covers all the questions with concepts of the MSTE-004 course and will help you score high grades in your examination. Our MSTE-004 Solved Assignment 2024 is a complete guide that includes step-by-step answers to all the questions and problems in the assignment, along with relevant examples and illustrations to make learning easier. This solution is written by experienced professionals who have a deep understanding of the subject and are well-versed in the latest course curriculum.

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IGNOU MSTE-004 Assignment Question Paper 2024

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1. 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 \(0.85\).

DiseaseTest resultTotal
+
Present17030200
Absent20280300

(b) For the following cohort study, the relative risk for the lung cancer among smokers is \(3.5\).

 Lung CancerNo Lung CancerTotal
Smokers10012201320
Non-smokers5022602310

(c) The logit link function is \(\log [-\log (1-\pi)]\).

(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.

2. Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.

 

3. A random sample of 250 patients was selected and their workout timing and diabetes status were recorded. The following table shows the workout timing and severity of diabetes:

Workout (in minutes)Severity of diabetes status
LowModerateHigh
0−15062719
15 to 30083617
30 to 45214533
245141806

Test at \(5 \%\) level of significance whether workout habit and diabetes are associated with to each other or not.

4.(a) Explain the assumptions underlying multiple linear regression model.

(b) Suppose a researcher wants to evaluate the effect of cholesterol on the blood pressure. The following data on serum cholesterol (in \(\mathrm{mg} / \mathrm{dL}\) ) and systolic blood pressure (in \(\mathrm{mm} / \mathrm{Hg}\) ) were obtained for 15 patients to explore the relationship between cholesterol and blood pressure:

S. No.Cholesterol (mg/dL)SBP (mm/Hg)
1300150
2410270
3380210
4530310
5570350
6490310
7340210
8320150
9280110
10550320
11340220
12350170
13410260
14390230
15450270

(i) Fit a linear regression model using the method of least squares.

(ii) Construct the normal probability plot for the data on serum cholesterol and systolic blood pressure.

(iii) Test the significance of the fitted regression model.

5. Write a short note on the following:

(i) Polytomous logistic models

(ii) Poisson regression

(iii) Kaplan and Meier method

6. The following data on diagnosis of coronary heart disease (where 0 indicating absence and 1 indicating presence), serum cholesterol (in \(\mathrm{mg} / \mathrm{dl}\) ), resting blood pressure (in \(\mathrm{mmHg}\) ) and weight (in \(\mathrm{kg}\) ) 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 CHDTotal Number of Patients
1420601020
2450681530
340054415
451074210
54806215

(i) Fit a multiple logistic model for the dependence of coronary heart disease on the average serum cholesterol and weight considering \(\hat{\beta}_{0}^{0}=4.279, \hat{\beta}_{1}^{0}=-0.035\) and \(\hat{\beta}_{2}^{0}=0.172\) as the initial values of the parameters (solve only for one Iteration).

(ii) Test the significance of the fitted model using Hosmer-Lemeshow test at \(5 \%\) level of significance.

 

7.(a) Describe censoring and differentiate between different types of censoring with the help of examples which are not considered in Block 4 of MSTE-004.

(b) 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 FactorParameter EstimateSE
Age0.1500.010
Gender0.4500.150
Systolic Blood Pressure0.0150.008
Smoking0.6500.170
Total Serum Cholesterol0.0020.004
Diabetes−0.3500.250

(i) Obtain hazard ratio and interpret the results.

(ii) Find the \(99 \%\) confidence interval for the hazard ratio.

(iii) Test whether the covariates are significant or not at \(1 \%\) level of significance.

\(2\:cos\:\theta \:cos\:\phi =cos\:\left(\theta +\phi \right)+cos\:\left(\theta -\phi \right)\)

MSTE-004 Sample Solution 2024

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