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 | ||||||||
| Low | Moderate | High | |||||||
| 0 −15 | 06 | 27 | 19 | ||||||
| 15 to 30 | 08 | 36 | 17 | ||||||
| 30 to 45 | 21 | 45 | 33 | ||||||
| ≥ 45 | 14 | 18 | 06 | ||||||
Test at 5% level of significance whether workout habit and diabetes are associated with to each other or not.
To test whether there is an association between workout timing and diabetes status, we can use the Chi-square test for association. The null hypothesis is that there is no association between the two variables, and the alternative hypothesis is that there is an association.
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Polytomous logistic models
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 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 | -0.350 | 0.250 | ||||
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 | ||||||||
| Low | Moderate | High | |||||||
| 0 −15 | 06 | 27 | 19 | ||||||
| 15 to 30 | 08 | 36 | 17 | ||||||
| 30 to 45 | 21 | 45 | 33 | ||||||
| ≥ 45 | 14 | 18 | 06 | ||||||
Explain the assumptions underlying multiple linear regression model.
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.
| Disease | Test result | Total | |||
| + | – | ||||
| Present | 170 | 30 | 200 | ||
| Absent | 20 | 280 | 300 | ||
| Lung Cancer | No Lung Cancer | Total | ||||||
| Smokers | 100 | 1220 | 1320 | |||||
| Non-smokers | 50 | 2260 | 2310 | |||||
(c) The logit link function is .
(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.
Kaplan and Meier method
Differentiate between Chi-square tests for association and homogeneity of proportions. Also mention the assumptions of these tests.