Question 1

State whether the following statements are True or False. Give reason in support of your answer:

Accepted Answer

The following statements are evaluated for their truthfulness based on biostatistical principles commonly covered in courses like MSTE-004. Each statement is accompanied by a detailed reason, including calculations where necessary, to support the True or False assertion. The explanations aim for clarity and adherence to standard definitions.

Understanding these concepts is crucial for biostatistical analysis, from diagnostic test evaluation and regression modeling to survival analysis and clini

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-I Method-II None Mild Moderate Severe Extreme None 89 5 16 2 4

Accepted Answer

The Kappa statistic is a measure of inter-rater agreement for categorical items, correcting for agreement that occurs by chance. It is used to assess the reliability of agreement between two raters or, as in this case, two diagnostic methods. Both simple and weighted Kappa statistics provide insights into the level of agreement.

First, we compute the Simple Kappa (κ), which treats all disagreements equally, regardless of their magnitude. This is generally suitable for nominal scales, but serves

Question 3

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 46 52 39 65 54 49 76 71 Cholesterol 185 218 182 220 224 193 232 228 Group 2 Age 20 33 78 51 43 44 63 Cholesterol 180 238 275 244 242 268 260

Accepted Answer

To study the relationship between two quantitative variables like age and cholesterol level, Pearson's product-moment correlation coefficient (r) is the most appropriate statistical measure. This coefficient quantifies the strength and direction of the linear relationship between the variables. A value of 'r' ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.

From the MSTE-

Question 4

Fit the multiple regression model.

Accepted Answer

Multiple regression is an extension of simple linear regression, employed when a dependent variable (response variable) is influenced by two or more independent variables (predictor variables). In biostatistics, it helps to understand the combined effects of multiple factors on a biological or health outcome, while accounting for the individual contributions of each predictor.

The general form of a multiple regression model is expressed as:
`Y = β₀ + β₁X₁ + β₂X₂ + ... + βₖXₖ + ε`
Here, `Y` is

Question 5

Obtain the regression models for each group separately.

Accepted Answer

To obtain separate regression models for each group, we fit a simple linear regression equation for each group's data independently. The general form of a simple linear regression model is `Y = β₀ + β₁X + ε`, where Y is the dependent variable, X is the independent variable, β₀ is the intercept, β₁ is the slope, and ε is the error term.

For Group 1, using its specific observations (X₁, Y₁), the estimated model would be `Ŷ₁ = b₀₁ + b₁₁X₁`. The coefficients `b₀₁` and `b₁₁` are calculated using the

Question 6

Test the significance of the fitted model at 5% level of significance.

Accepted Answer

To test the significance of a fitted model, typically a regression model, at a 5% level of significance, we employ the F-test derived from the Analysis of Variance (ANOVA) table. This test assesses whether the independent variables, as a group, significantly explain the variation in the dependent variable.

First, we state the null (H₀) and alternative (H₁) hypotheses. The null hypothesis (H₀) posits that all regression coefficients (βᵢ) are zero, implying the model has no linear relationship an

Question 7

The amount of dose (xi), total number of patients who received medicine (nī) and number of cured patients (yi) are recorded in the following table: S. No. Xi yi ni 1 5 24 60 2 10 18 48 3 15 12 40 4 20 20 80 5 25 26 104

Accepted Answer

The provided data represents a typical dose-response experiment where the effect of different medicine doses on the proportion of cured patients is observed. This type of data, involving a binary outcome (cured/not cured) and a continuous independent variable (dose), is best analyzed using a Generalized Linear Model (GLM), specifically logistic regression. Logistic regression models the probability of an event occurring as a function of the independent variables.

The primary goal of analyzing

Question 8

Fit a logistic model considering initial values of β = -0.2 and β₁ = -0.04 up to only one iteration.

Accepted Answer

The logistic regression model, a key component in biostatistics, is used for predicting binary outcomes. Its parameters (β₀ and β₁) are typically estimated using the Maximum Likelihood Estimation (MLE) method.

Since the likelihood function for logistic regression is non-linear, direct analytical solutions for the MLEs are not possible. Instead, iterative numerical optimization algorithms, such as the Newton-Raphson method, are employed to find the parameter estimates. This process involves star

MSTE-004 Solved Assignment — January 2026 / July 2026

Biostatistics-II | IGNOU Post Graduate Diploma in Applied Statistics (PGDAST)

MSTE-004—January 2026 / July 2026

Biostatistics-II

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MSTE-004 Assignment Questions — January 2026

Q1. State whether the following statements are True or False. Give reason in support of your answer:

Q3. 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 46 52 39 65 54 49 76 71 Cholesterol 185 218 182 220 224 193 232 228 Group 2 Age 20 33 78 51 43 44 63 Cholesterol 180 238 275 244 242 268 260

Q3(i). Fit the multiple regression model.

Q3(ii). Obtain the regression models for each group separately.

Q3(iii). Test the significance of the fitted model at 5% level of significance.

Q4. The amount of dose (xi), total number of patients who received medicine (nī) and number of cured patients (yi) are recorded in the following table: S. No. Xi yi ni 1 5 24 60 2 10 18 48 3 15 12 40 4 20 20 80 5 25 26 104

Q4(i). Fit a logistic model considering initial values of β = -0.2 and β₁ = -0.04 up to only one iteration.

Q4(ii). Test the significance of the fitted model using the Hosmer-Lemeshow test at 5% level of significance.

Q5(a). Explain the Kaplan and Meier method of estimation with an example.

Q6. Differentiate the following with an example: