Polytomous logistic models
Polytomous logistic regression is a statistical method used to model the relationship between a set of independent variables and a categorical dependent variable with three or more levels. It is an extension of binary logistic regression, which is used to model the relationship between a set of independent variables and a binary dependent variable.
The main difference between binary logistic regression and polychotomous logistic regression is the number of categories of the dependent variable. In binary logistic regression, the dependent variable has only two categories, usually labeled as 0 __________ ________ _____ __________ _____ ____ ___ ___ _______ _____ _________.
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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 | ||||
Poisson regression
Polytomous logistic models
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 | ||||||
Suppose a researcher wants to evaluate the effect of cholesterol on the blood pressure. The following data on serum cholesterol (in mg/dL) and systolic blood pressure (in mm/Hg) were obtained for 15 patients to explore the relationship between cholesterol and blood pressure:
| S. No. | Cholesterol (mg/dL) | SBP (mm/Hg) | ||
| 1 | 300 | 150 | ||
| 2 | 410 | 270 | ||
| 3 | 380 | 210 | ||
| 4 | 530 | 310 | ||
| 5 | 570 | 350 | ||
| 6 | 490 | 310 | ||
| 7 | 340 | 210 | ||
| 8 | 320 | 150 | ||
| 9 | 280 | 110 | ||
| 10 | 550 | 320 | ||
| 11 | 340 | 220 | ||
| 12 | 350 | 170 | ||
| 13 | 410 | 260 | ||
| 14 | 390 | 230 | ||
| 15 | 450 | 270 | ||
Kaplan and Meier method
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.