Question

Chi-square tests for association and proportions

18 Apr 2025
Answer :
Word Count : 126
AspectChi-square Test for AssociationChi-square Test for Proportions
PurposeTests whether there is a significant association between two categorical variablesTests whether the proportions of a categorical variable differ __________ ______ ___ _________ _________ ____ _________ ______.
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Chi-square tests for association and proportions

A study was conducted on 185 patients aged more than 45 years, which were 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). This study aims 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 -0.35 0.250

 

(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.

Describe censoring and differentiate between different types of censoring with the help of examples

To study the association between 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 a 5% level of significance using a suitable test

Relative risk and odds ratio

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